Practical type-safe XSLT 2.0 stylesheet authoring S0ren Kuula ...

! "$#&%'() *+-,./10-,234*576

8:9<;=>@?7AABDC

EFHGI =J=LKM=;ON)P<P E

Q

"!# %$&'!# ( )

* +-,/.10%23.546. 7

8:9;1<>=%?8A@B%;DC; E

) <>=%?8GFHJI(9K/L6MNCPORQ(LK/S%T;DUV@ 5

W XYKFZT[@\F]C^_L6;`@aIbL6McB%I(MNK6CP@ [d

*a* egfihj+k.52l,64/mbnom&p(qr.5s t/u

E <Yvw?j@B%9;DUxF_TF]CPOJHJF/OJ;`@ D

d <Yvw?jyCPz3KZ@a;DI )

| <\xHJ;DL5~(1F]C^R<YFDIb9%VFDIFRvK/^J;DT<Yvi )

& )E

3\<>=%?8-F]C^@IlFDI(McBFZCF]T~@aMN@ W5

*a*a* e0%h+ZmD46`n¡ /s¢qrs £(¤

¥\;DzMrCMNI(MNK6CP@¦FZC^RL6;`@aIbL6MNB%IbMNK6CP@ W[

g=I&~JT;`@a9;D;DI§@aMrUxQbTMrz5McB%FDI(MNK6C W5W

¨

3kT[K FZCPFZT~@aMc@ E5|

* nompZ, ]nrqN23 qrm(46s u&ut

)Y<>=%?8 F]TMr^6F IbMNK6C 53

W5F]THJF IbMNK6CK6z5FZTMN^/FDI(McK/C 3[E

3E K6^J; FJ@@aMN@IFZT[OK6L6MNI(9UV@ [)

m(462n6s¢qomb4 u7t

5dY=%K/Ux; L6;`@aHJTIb@ l)

3|Y\;DUVK/C@aI(LZF IK/L_F]Q(QbTMNB%FDI(McK/C l)

[ "!$#&

%&('*),+.-0/0132546-043),784:9;+.+.<=&07?>A@B1B4B<C'516D?9;1:9E1FG-0<=&07H<C@JIK25L=LAMG&?)IN&(13)O@:9QPR2578/ 9;43DS9;7T9;<=&?@3169ELU9;4B7V2'5LU9,@3@J);PW'*),+.+X),&S254B43),43@Y>$9;&?DZ@31:9;1B<C'Y9;L=L=F\[V254B<]P^F_<=&07O'*),+.-0<=LC2543@`9,Da[89;&?'*2b1Bc?2b1B<=+X2d);Pe9YIf9;4325&?2*@3@);Pg25[V25&h+X),432i254B43),43@jkmldnoD0)_'5/0+X25&T13@'Y9;&9;LC@:)qp2ePr),4B+s9;L=L=Fd1tF_-"2*Du>9;&?D432*'*25&G1BL=Fd<=1mc 9,@mp2*25&D025+X),&?@B1B4:9;132*DX1Bc 9;1v@:),/0&?DX9;L=1Bc?),/078c.&?),1v'*),+.-0LC25132$@B1:9;1B<C'f[,9;L=<CD?9;1B<C),&X);P kw_n_x1B4:9;&?@yPr),4B+X@z9;7T9;<=&?@31@B-2*'5<] 2*D`<=&0-0/01|9;&?Db),/01B-0/011tF_-"2WD02*@3'54B<=-01B<C),&?@e~rmxNm@K<C@gPR2Y9,@B<=p0LC28j

xgc?2s-0/04B-")8@32s);Pg1Bc0<C@WIK),4BM<C@13)b@Bc?)YI1Bc 9;1i@B1:9;1B<C'.[89;L=<CD?9;1B<C),&O);PNkw_nGx'Y9;&Ep"2Xp043),/078cT1i13)`1Bc?2@:9;+X2/01B<=L=<=1tF6<=&-04:9,'51B<C'Y9;Lkw_n_x9;/01Bc?),4B<=&07sIf),4BM`9,@1Bc 9;1$);Pv@31:9;1B<C'Y9;L=L=FJ[89;L=<CD?9;1B<=&07s'*),+.-0<=LC2543@m9;&?D'*)_D029,@3@B<C@B1B<=&07q<=&T1325784:9;132*DD025[V25LC),-0+X25&T125&G[G<=43),&0+X25&G13@m<=&9;-0-0L=<C'Y9;1B<C),&-043),784:9;+.+.<=&07?j$xgc?2WIK),4BM2a1325&?D0@f/0-"),&q-04325[G<C),/?@KIK),4BMs),&J@B1:9;1B<C'kw_n_xZ[89;L=<CD?9;1B<C),&>_432?&0<=&07e1Bc?2|+X251Bc?)GDs13)YIg9;43D0@g+X2*251B<=&071Bc?2`432*G/0<=4325+X25&T13@J<CD025&G1B<] 2*D\<=&9432Y9;Li~R9,@s),-0-)8@32*Do13)-0/04325L=FZ9,'Y9,D025+.<C'kw_n_xD025[V25LC),-0+X25&T1@B<=1B/ 9;1B<C),&$2Y9;L]1B<=+X2-254yPR),4B+s9;&?'*28>Q'*),&a D025&?'*2p0/0<=LCDa<=&079;& 9;L=F_1B<C'-0432*'5<C@B<C),&>,9;&?D),-"254:9;p0<=L=<=1FmIN<=1Bc1Bc?2@31:9;&?D?9;43D0@1Bc 9;1|9;432mp25L=<C25[V2*D`13).p2*'*),+X2D0),+.<=& 9;&T1|<=&`1Bc?2&?2Y9;4NPr/01B/04328VkAlnOw_'3c?25+s99;&?D`kw_n_x ¨ jaj

E2ePr/04B1Bc?254A<=&G[V2*@B1B<=7T9;132.@3),+X2@B<=+.-0LC254@B1:9;1B<C'.9;& 9;L=Fa@B<C@9;L=7V),4B<=1Bc0+X@APr),4Akw_n_x>9;&?D209;+.<=&?2ic?)I1Bc?25F'Y9;&op"2J/?@32*DOPR),4s9,Da[,9;&?'5<=&07h1Bc?261B<=+X2`);Pm254B43),4s9*Ig9;4325&?2*@3@X<=&-04:9,'51B<C'Y9;Lkw_nGx9;/01Bc?),4B<=&07?>c?25L=-0<=&07q13).@Bc?),4B1325&bD025[V25LC),-0+X25&T1A1B<=+X28j

<=& 9;L=L=FV>KIK2J-0432*@325&T1s9D025+X),&?@B1B4:9;13),4J9;-0-0L=<C'Y9;1B<C),&oP^4:9;+X25If),4BMPR),4.2_-254B<=+X25&T1:9;1B<C),&ZIN<=1Bc\@B1:9;1B<C'

9;& 9;L=Fa@B<C@m25&0c 9;&?'*2*Dkw_n_x 9;/01Bc?),4B<=&07J13)_),LC@Y>9;&?DIK2i25[,9;L=/ 9;132i1Bc?29;L=7V),4B<=1Bc0+X@m-0432*@325&T132*D/?@B<=&07`9@3251|);P432Y9;L@B1FGLC2*@3c?2*2513@Yj

P

• -043)_);P t);P^t'*),&?'*25-01$D025+X),&?@B1B4:9;1B<C),&1Bc 9;1Nkw_n_x ¨ j`~^kw_n_x ¨ f[89;L=<CD?9;1B<C),&b9;&?D`),&aL=<=&?2'*)_D029,@3@B<C@B1K13)G),LC@f'Y9;&qPr2Y9,@B<=p0L=F.p2<=&G1325784:9;132*D6<=&T13).9D025[V25LC),-0+X25&G125&T[_<=43),&0+X25&T1Y>0L=<=MV2|<=&J1Bc?2$If25L=L]MG&?)IN&b% @gPr),4@:25[V254:9;L),1Bc?254-043),784:9;+.+.<=&07sLU9;&078/ 9;7V2*@

• &2a1325&?@B<C),&b);Pv1Bc?2),&0L=F6MG&?)IN&-04:9,'51B<C'Y9;Lkw_nGx [,9;L=<CD?9;1B<C),&d9;L=7V),4B<=1Bc0+> 13)

E),4BMIN<=1BcSV kmlnw_'3c?25+s99,@`1Bc?2h<=&0-0/01;),/01B-0/01dD0)_'5/0+X25&T1d1tF_-"2D02?&0<=1B<C),&LU9;&078/ 9;7V28>0<=&?'5L=/?Da<=&07?

∗v_1325&?Da<=&07s1Bc?2mp 9,@B<C'9;L=7V),4B<=1Bc0+ Pr43),+ IK),4BM_<=&07XIN<=1BcLC)_'Y9;L]1tF_-"2m432578/0LU9;41B432*2LU9;&a78/ 9;7V2*@z13)@B<=&078LC21FG-2W~R9,@K),-0-")8@32*D13)W@B<=+.-0L=Fe/?@3<=&07e9mLC)_'Y9;L]1tF_-"2$9;-0-043)Y_<=+s9;1B<C),&

∗<=&?25L=FH+X)_D025L=<=&071Bc?2`kmldnw_'3c?25+s9ED?9;1:9h1tF_-"2*@Y>K-043)Y[_<CDa<=&07-0432*'5<C@:2`[,9;L=<CD?9;1B<C),&9;LC@3)iPR),4D?9;1:9

E),4BMqIN<=1Bcb1Bc?2&?),&T1B4B<=[_<U9;L&?25ISPR2Y9;1B/0432*@<=&`kw_nGx ¨ 254yPR),4B+ PR9,@B1e25&?),/078cEPR),4W),&aL=<=&?2s/?@:2.<=&H9;&H2*Da<=13),4v+W/?'3cOP9,@B13254W1Bc 9;&O1Bc?2X-04325[_<C),/?@9;L=7V),4B<=1Bc0+> D02*@B-0<=132e9;&`<=&?'5432Y9,@32<=&b)[V254:9;L=L'*),+.-0LC2_<=1F

43)Y[89;p0L=F643251:9;<=&d9;1LC2Y9,@B1N1Bc?2-0432*'5<C@B<C),&b);Pv1Bc?2MG&?)IN&d9;L=7V),4B<=1Bc0+

• @3),L=<CDu>u2_1325&?@3<=[V2J~R9;p),/01T;ML=<=&?2*@$T/ 9;L=<=1Fd@3);Pr1tIg9;432WPr4:9;+X25IK),4BMdPR),4|kw_nGx ¨ @B<=+.-0L=<] 'Y9Q1B<C),&> 9;& 9;L=Fa@B<C@$9;&?D6[89;L=<CD?9;1B<C),&

• 132*'3c0&0<CG/?2iPr),4m@B1:9;1B<C'Y9;L=L=F9;-0-043)Y_<=+s9;1B<=&07`1Bc?2i432*@B/0L=1m);P1325+.-0LU9;132i432*'5/043@B<C),&h),&[,9;4B<U9;p0LC2*@<=&`kw_n_x ¨

• @B<=&078LC2- 9,@:@Y>_PR9,@31Nkw_n_x ¨ @B1FGLC2*@3c?2*251@B<=+.-0L=<] 'Y9;1B<C),&b132*':c0&0<CT/?2

• D02Y9,D'*)_D029;&?D25+.-01FTt@325LC2*'51B<C),&D025132*'51B<C),&9;L=7V),4B<=1Bc0+Pr),4Nkw_nGx ¨

• &X9;L=7V),4B<=1Bc0+ PR),4vD025132*'51B<=&071325+.-0LU9;132*@z<=&.kw_n_x ¨ 1Bc 9;1v&?25[V254z),/01B-0/01zD?9;1:9a>8&?25<=1Bc?254zDa<=432*'51BL=F),4N[G<U9),1Bc?254$1325+.-0LU9;132*@

• &q9;L=7V),4B<=1Bc0+ D025132*'51B<=&07i/0&T/?@32*Dq<=&0-0/01K@3':c?25+s9WD02*'5LU9;4:9;1B<C),&?@>TPR),4K9W@BL=<=78cT1BL=F.432*@B1B4B<C'5132*Dq[89;4B<]9;&T1g);Pukw_n_x ¨ jzxgc0<C@f'Y9;&q@3254B[V2A9,@f9p 9,@B<C@PR),4f9?L=13254K7V25&?254:9;13),4Y>_c?25L=-0<=&07i432*Da/?'*2$<=&0-0/01f1B432*2@B<Y28j

!#"$%!&(')$!*+$!*+!,-*+./#*$+-0$1&2345&2-6678&"9:;<"6:>=$!$@?BAC$DE.9&$D&28FG$IH-9&JK-&$,-*L$M9/F0NPOBQR=!"9S,TU-$!*'):;85?KVW=XZY[? [[[K$5&\'G"6*]F^$,J$,_;F^SXH`'aFG#"9b=X>Y[[[cd$8F(,"6B"*H$!*eY[[[KFa-Z$Tf:]d6g-:]$,&-?J]"6*d&\&!=Z&P&334-&\&:]h!5HiNkjl8gmKg9&2-$!*c6-&&2$E:d*-fHn!8Fo$!4p5H,./#*$c9$!&#8^$!*_qWAr?V "6:]:;$g* $s')$,t-$!*`Hu$!* .$ wvx=TU=!&25* ./#*t6&2-y z2-t8|4|,^~44^3X8!g^f|8i

!5

kmldn(<C@i-043),p 9;p0L=F),&0L=F':c 9;L=LC25&07V2*DpTF"!AxNlnz> w0f%3%9;&?D &078L=<C@BcH<=&Hp"25<=&07$#&%('Jp2*@B1eMG&?)IN&LU9;&078/ 9;7V2.),&1Bc?2iE25p>9;&?Dh9,@A<=13@m@B-2*'5<] 'Y9;1B<C),&*) @ Q qFV2Y9;49;&0&0<=[V2543@:9;4BFb'5LC)8@:2*@|<=&>"PR25I '*),+.-0/0132549;-0-0L=<C'Y9;1B<C),&hD0),+s9;<=&?@A4325+s9;<=&dIN<=1Bc<]Pz&?),1|@:25[V254:9;L'*),+.-251B<=&07?>"1Bc?25&dLC2Y9,@B1A),&?2kmldnOLU9;&078/ 9;7V2i13)'*),&G1:9;<=&E1Bc?25<=4D?9;1:9`9;&?D2a':c 9;&07V2*@YAkAlnc 9,@m+s9,D02<=13@mIf9YFd<=&G13)`25[V254BFG1Bc0<=&076Pr43),+ LC257T9;L'*),/04B1?L=<=&07V@$13).c?),7PR9;4B+.<=&07?> 9;&?D`1Bc?25432@32*25+X@N13)Xp"2m&?),1Bc0<=&07s25&?D13).1Bc 9;11B4325&?Db9;&GFq1B<=+X2@:)G),&j

w_),+X2WkAlnO9;-0-0L=<C'Y9;1B<C),&?@|c 9*[V2e25[V),L=[V2*D<=&T13)q25&T1B<=1B<C2*@A);P1Bc?25<=4$)YIN&,+|25I@|9;7V25&?'5<C2*@$p043)V9,D0'Y9,@B1|<=&mw0w YL=<=p04:9;4B<U9;&?@v'Y9;13257V),4B<Y2<=&il A>*1tF_-2*@3251B132543@1FG-2*@3251<=&W-9;&?DIK25pi@3254B[_<C'*2*@1:9;L=MWw.- j /1032 'f9;&?Di954767%(' 20 D02?&0<=&07A9;&ekAlnq9;-0-0L=<C'Y9;1B<C),&*) @LU9;&078/ 9;7V28>89;&?DW@3),+X2K),4B7T9;&0<9;1B<C),&iD02*@3<=78&0<=&079;&?D6+s9;& 9;78<=&07X1Bc?25+ +s9;MV2A1Bc?25+ 1Bc?2mL=<=&078/ 9ePr4:9;&?'Y9);P1Bc?2mE25pj98g2*@B<CD02*@g1Bc?2*@32m@B1:9;&?D?9;43Da<9;1B<C),&9;-0-0L=<C'Y9;1B<C),&?@Y>vkmln\<C@W2Y9,@3F13)b/?@32PR),4i9;L=+X)8@B19;&TFhD?9;1:9b4325-0432*@325&T1:9;1B<C),&:-|-0-)8@B<=132qw.;mlnz><=13@-0432*D02*'*2*@3@:),4Y> 9;&kmldn9;-0-0L=<C'Y9;1B<C),&dD0)G2*@N&?),125[V25&b&?2*2*D`13)p"2m@B-2*'5<] 2*D`pGF69@3':c?25+s9a> 9;&?D`p25<=&074<'>= ?>@BAC'D4767E>FHG>F /JI >kmldn@:254B[V2*@b9,@`1Bc?2h@BF_&T1:9,'51B<C'E'*),&G1:9;<=&?254);P'*),/0&T1BLC2*@3@@B1B4B/?'51B/0432*DLU9;&078/ 9;7V2*@>4325-0LU9,'5<=&07@B+s9;L=LvLU9;&078/ 9;7V2*@);P1Bc?2),LCD@3':c?)G),Lv1Bc 9;12Y9,'3cc 9,D<=13@m)YIN&h@B1B4B/?'51B/0432K <]PKD02?&?2*DE9;19;L=LLK D0)YIN&13).1Bc?2mLC2a<C'Y9;LLC25[V25Lj

&b2?9;+.-0LC2W);P9;&kmldnOD0)G'5/0+X25&G1Y>?c?),LCDa<=&07q@31B4B/?'51B/0432*DbD?9;1:9X),&9.'*),+.- 9;&TFL) @|@9;LC2*@B-"2*),-0LC2i9;&?D'5/?@B13),+X2543@$<C@N<=&b<=78/0432 ¨ j

xgc?2ekAlnOLU9;&078/ 9;7V2W<C@|+X254325L=F@BF_&T1:9Q "9;&GFb@B1B4B/?'51B/0432?1B1B<=&07`9.1B432*2eIN<=1BcLU9;p"25LC2*Db&?)GD02*@A'Y9;&bp2D02*@3'54B<=p2*DE<=&OkAlnzj @:M ÖNQP -0/01<=1Y>*Rj=j=jq1Bc?2*@:2Xkmldn4325LU9;132*DO@B1:9;&?D?9;43D0@i@32*25+ G/0<=132.-)G),4Yixgc?2p 9,@B<C'LU9*FV254);P"1Bc?2N@B-"2*'5<] 'Y9;1B<C),&?@*S /?@31432578/0LU9;132*@1Bc?2N25&?'*)GDa<=&07e);Pu9;4Bp0<=1B4:9;4B<=L=FiPR),4B+X2*D1B432*2*@UT:jvxgc?25432+e/?@B1Kp2$@:),+X2$Ig9*Fs);P1325L=L=<=&07iINc 9;1K+s9;MV2*@f/0-69;&skmldnh9;-0-0L=<C'Y9;1B<C),&>09;&?Dsc?)I13)iD02*'5<CD02|INc?251Bc?2549mD0)_'5/0+X25&T1<C@);P 1Bc?2g4B<=78cG1MG<=&?D),4&?),1YjWVX6>%(' 2Y0 49;432g1Bc 9;1Y>G9,@PR),4B+s9;L?D02*@3'54B<=-01B<C),&?@1Bc 9;1z9;432gp),1BccG/0+s9;&ag9;&?D6+s9,'3c0<=&?2W432Y9,D?9;p0LC28>?@B-2*'5<]P^F_<=&07X9@B/0p?@3251);P1Bc?2kAlnt25&?'*)_D02*D61B432*2*@N1Bc 9;1p25LC),&07.13)9A- 9;4B1B<C'5/0LU9;4KkAlnb9;-0-0L=<C'Y9;1B<C),&j,VX6>%.' 20[Z\0 =]FÂ 0 #_F^` / <C@1Bc?2g-043)_'*2*@3@z);P"D02513254B+.<=&0<=&079;/013),+s9;1B<C'Y9;L=L=FINc?251Bc?2549;&JkAlndD0)_'5/0+X25&T1g<C@ Za0 =bF_AdceF_#&%:Ef'D4Hgh'i6j#W#H`9W@3'3c?25+s9 a<]Pu<=1f<C@<=&q1Bc?2$LU9;&078/ 9;7V2m@B-2*'5<] 2*DpGFJ1Bc?2W@3'3c?25+s9aj @3':c?25+s9iPr),4|),/04@:9;LC2*@N4325-),4B1$209;+.-0LC2e9;-0-0L=<C'Y9;1B<C),&9;-0-2Y9;43@<=&<=78/0432 ?j

wG1B4B/?'51B/0432*DXD?9;1:9m);Pr1325&&?2*2*D0@13)Ap"2g'*),&G[V254B132*D.13)m),1Bc?254z@B1B4B/?'51B/0432*DXD?9;1:9aek 0 # 0l7m '>EDnoF /CI <C@9|- 9;4B1);P1Bc 9;1Y> @:)X9;4321Bc?2+X2*':c 9;&0<C'*@$1Bc 9;1$25& 9;p0LC24j'pg 0 E 0 #_F_` / ì?A 0 # 0 Ef'pg1Ef'D4j' / # 0 #_F_` /"0o/ Aqg1Ef'D4j' / # 0 #_F_` /9;&?DS9hLU9;4B7V2d- 9;4B1J);PD?9;1:9<=&T132543':c 9;&07V2*@),&Z1Bc?2bE25pj (<=1Bc@B1B4B/?'51B/0432*D(D?9;1:9E4325-0432*@:25&T132*D(<=&kmldn>a<=1fp2*'*),+X2*@g<=+.+X2*Da<U9;13213)@BM_<=-61Bc?2ADa<C@31B<=&?'51B<C),&p"251IK2*25&`1Bc?247#_E m 6j# m Ei'iArA 0 # 0 -043),-254gIN<=1Bc[V2543@B/?@e<=13@ds5tuEf'pg1Ef'D4j' / # 0 #_F_` / >z9;&?DvSy/?@B143257T9;43DO1Bc?2X1:9,@3Mh9;&OkAln13)kmldn1B4:9;&?@yPR),4B+s9;1B<C),& LU9;&078/ 9;7V2iPr),41Bc0<C@m-0/04B-)8@328>ukw_n_x>uIf9,@D025[V25LC),-2*DhIN<=1BchE25pED?9;1:9J-0432*@325&G1:9;1B<C),&LU9YFV254B<=&07<=&+.<=&?Du>f9;&?DOc 9,@p2*25&o9bE),4BLCD(<CD02qE25pf),&?@3),4B1B<=/0+ ~^SVNe|2*'*),+.+X25&?D?9;1B<C),&\@B<=&?'*2 Q<w3w3w jx)GD?9YFV>G<=13@yxz2543@B<C),& Q <C@z1Bc?2$+X)8@B1-),-0/0LU9;4kmldnd13)kmldnd1B4:9;&?@yPR),4B+s9;1B<C),&qLU9;&078/ 9;7V28>a9;&?Dxz2543@3<C),&¨ ~^kw_n_x ¨ g<C@$9;1N1Bc?2eg9;&?Da<CD?9;132e$2*'*),+.+X25&?D?9;1B<C),&@B1:9;7V28>?@3)_),&`13)4325-0LU9,'*2zxz2543@B<C),& Q j

!#"$ %'& ()*$)*& +( $,+ -"$$(/..10 2 0 21'&+ &3*4++ &)+5&)+5+$! +6+!#"$ )+5&*&+"'7 $)(&8+(1"$" 7) +$ (& $7&9*:)$7+&+"'7 $)(&8+$; 5' "+"'7)$)(+& $7&*::)$7+&

*&()$& +( $,+ -"$$(0'2*..10 21'&+ &<+( &)+5&)+5+$!=8*6+!#"$ )+5&*&+"'7 $)(&8+(1"$" 7) +$ (& $7&>:)$7+&+"'7 $)(&8+$; 5' "+"'7)$)(+& $7&?:)$7+&

& ()*$&

( $)&

+"'7 $)()&" 7) +$ (@5 AB8+(1"$ & &CD<+(FE$4++ &$ +G&H=8(#"$ +$ *G&+"$+"'&)&<(,D<+(8+(15+ & 5& 5$IJ8+(6*8(#"$ )+5&

"$+"'+&+"'7)$)(+&" 7) +$ (@5 AB8+$; 5' "+'&+ )&K($8+$;;DL)G 5"+ )&$ +G&

HM.*(+$8$*;;=;$(N++$ *G&+"'7)$)(+&

" 7) +$ ()*&*&

>m Vk$<6:]\N OBQb*":]$,- V h!J' &-&X9&2$!&$!*_"6g&3:]9&? Vk:>c$!*PO^!d=X!/. :;*Z&5&E=g "!&3:]9&G$_h!yXd"6!&2:d-G') -"9B& !5"6-*-&Z:d$,-?IQ 69&'I!\"!&2:]-^&#*;d#&^$_SRUT 8|/V W :]$,$!&#*PXRBT /|/V Wg :]$,-H#*-$ hg-*E=,]ZY ?E$!:] V! #&>g&25*b$D3Fa *\[i$,]:d5$$,& -y $E=g-$!B!E"6:]c&5& X-H-WZ#&3G'-"9E&-&g-&$)] &^&5&?lXRBT /|/V W $!:] #&G#&2d!&-*E=gc')*$;*#&' "!&3:]W$!*E')G6')-$!>ZJ*-'): #&FG-?

_^ lVW$_N` GOBQL$!*-$]' &-&X-H&G*$!P=4;\9$g&3'): $< ! Y?

N

"'+ *) -BHH +9I$(G 22 0L+"'+ )1+(G "-BHH! "$ %*) M.$$*+ I#"$ K$(.7+-7+5 . 5A-(15'87*K$(+.7-B7*7+5.)5A &),)-*+ &"$+C4&* 71"& ),)*()$))'&"$ +C4& 7 "& ,+ )* ()*$-4+-.$$! ()*$-

-5'"" 7( 0 &*7+ "&

+"$ C4+& & ),)*" 7)$ ( +'&"$ +C4& 7 "& ,(+.-.$$! "'7 $)(-

-5'"" 7( '21 &*7+ "&

+"$ C4+& &, 7 "&

"$ C4&,)&

),)-" 7) +$ (- &"$+C4&& ),)*B+

4* (15'G'& ),)*B+$ *G1

4* 4'& ),)*"$" -

4*/.$$I()*$ '&&( 5'87+ + 5 A- 7 *

B(+ *715'(+A 4* (15'G'&

+"$ C4+& &+"$C4+D -()*$- &* *7+1"&),)-B+ )1 4+- ( 5 G &),)-')5 4*'4+'&

7 "&"$ +C4&

5/C4D+ )*C+E$$(- &(+ ( 5"' 5$,8*(15'G-'&7*)(15$+7-..10'210'2'&7*)(15$+7-*0 2*..0'2'&7*)(15$+7-*0 2 0'2..-'&

((15"'15$&5+C4+&

+"$C4+D - ( $ '&"$ +E$++&+ 5$,8*-.$$!( $-'&*7+ "&), -+'&+"$C4+&* *7+1"5 ""'7()-*0

)""'7( -B78$7AA-'&),)-" 7) +$ (-

4*(15'G-'&),)-')$7

4*5 +G(- & 7 "&

"$ +C4& )+&

* 71"&(15'87D)*B+"$$(-

7 *B(+ 7 5'(+A- 4+/.$$!JC++E$$(-'&)5$+&

+"$ E$&"$ +C4&"')&

g ! :]L&-&c-g2_&"9!:;H FG2$ $ N OBQ#""9!:;?$ -:d-$,&_$!:d5* V $g*RBT 8|/V W \*5"6#-*]3FG#"6\-"9@H4n!-"6$ZJ* [X--$,g&25&'@: $c$g&39$!"P*":]$,&-? I5:"9&G"6!*_g=;!/.\=X-$B*6h!$!-*c:]P-*=!H$!*_]6')$,@"6$g&3$,G$')"$!Z!8P"!&3:]JFGe!;,ZY 6&2& ')J-"9 4V! Fa#* !/.Z:]8.-*B;*5&2$IH@= J!&\=X-$:d2-*`?

%

)I 4 ( 5$-*0%M21*) =)* 9 $(G 0 C().$(* *) -BHH +9I$(G)0 *) -BHH+! "$ '&

(-0 A$+"'7 F)&)IJ+ +) "' H *+ &*)&+*A& 5 & +$( 5 &

*A&8+$A4&)*!+4'+

*+"''# ()*$))'&8$*A*4&,*)&

)*!= &

( + ()$ )1"'+&)IJ+ +) "' # +()*$ +'& "$(8$(A)*!+4/++*&

)*!= &

(9I E$$(,+8 5', "$$(&)IJ+ +) "''6 -"$$( '&)*! "'$$*&

(+A "$$(,+$$D7G4 " G 5'& I +, ..10 2 0'2 & ..10 0 I ++&

I$(*15&)*! +7$.

*+"'"$1" '&)*!$+(*5**&,)I#" $$&

)*!= &

(: 'A)515 A7F* +()*$ &)IJ+ +) "' # +()*$ '&)*!+4/++,+"'-'J+ '&8& I(15'87D)*B8G)"$$(- &)*!+4'+

*+"'/6* "$$(- &)*!( 5'87+& I4/+ *"' #)'&

+8+& IJ++&

(+>! ),$. * +()*$&)*!J+

" -'H ( $= & &

)*!7$. *+"'B+'& & !=+&

(+?! ( + &)*!J+ ) " HJ)1'&&

7 "$+"' 5 5. +58&)I#" $$&)*!J,- #"$" - & I4/+

" - #"$" - & I 7+$*. " HJ+ )1'&

I ++&)*!$+(15**&

$+(*5** 7 D+D$ +G& I(15'87D)*B(*.'&)*! +7$.

*+"' =$)+G '&)*!( 5'87+& I 7+$*. " U &

I$(*15&)*! "'$$*&

& !=+&

(I "$+"' 5&)*!J+ ) " H#"$+"' '& !( 5 87D)-B(.-'&)I +7+$. " -'H)5 &

)I(15'87& !=+&

(I ))&)*!J+ ) " H +'& !M.$(" *"' "'7 $)(-'&(&A&! "'7 +$ )() 5' * ))& I4/+ *"' U'&

A&)*!+4/++,+"'

/.$$15 G"*5 85 G )$7$# 0&% &(+&

)I=.$(+"'& !=+&w

( ) "'@" 7) +$ (@5' &)IJ+ +) "' #*#" 7)$ ( '&)*!(158D+ )*5 A *+"' B'&)*!+4/++,+"''#" 7)$ ( "'7)$)( #=6)5 A 5 A%J+ '&

)*!= &

(-0'2I (+A(,+, )$7F ($$( 5$ G*,+$(; (7 &)IJ+ +) "' $7- &A&( +5 G* .- 15A*+ '&)I +7+$. " U &A&

)*!= &)*!# 4+ +&

Y l:]\N "Q 9$g&3'): !*!"$!ZJW$_ !d'): JN OBQL$_ ! m?O&#"H-a$!*":]$, #&I!"65&&-*P=4 aN "Qx$!&3'):]-`h!9&3@hg$!*$ |*V/!g|*V :;89"9$!&^,

r1 ?lW:]#8P#& $ KFG K!k,a$*P& 9&! " $#dH,"-!&$!>$$TUN "Q--:d-$,&;=g "-*E;]-&GH$!*cN "Qo$!&3g"r$g&% JN "Qo:]-$9&G$!&2#*\:]#85& J=gG-./g85*`? Vk$4 4g'&)(/|*V/g,|*V $!&2!"r$;&2-5"r&l\&+*,-$!"6'X$*-& #8.^PW"$,4-:cH4$E:;8"9!-& 5"9 $!&2 - :]#8-&^$!* 5"69&25& Z!k$!k/[i$ =X-&2:]"9@H&G:dJFG<;&-"6-*E$* & "6$,64W-:c?#&P&3!"69 9/.-&`'ld$P>$!*<2$c' $*5&WE 5&2W->45&W$ $, &-"6-*c$*5&!/.\=X-$E"65&&-*`?

, ( 5$-*0%M21,& D))BHJ9 $(G 0 *)1 *) -BHH+! "$ '&*A&,15'+& +$(+15'+&,A&8$*A*4+& "$(8$(A & 3*4 &+8+D8G "$$( ..0'2 0 21 &

(&,A&D(*.- )+5$!=8(68+(H#"$ &C+<+(FE$+4+&A&A&( +5 G *.*- 5 A*-/9*:-'&*9*:A& (+&

(&,A&D(*.-BHH=.($8$;; "$ _=;$(N '&*K*($8$*;;DL+G 5"&A&A&( +5 G *.*- 5 A*-::-'&::A& (+& +8&

& <+( &+8+D8G "$$( 0'2..10 21 &

(&,A&D(*.- )+5$!=8(68+(H#"$ &C+<+(FE$+4+&A&A&( +5 G *.*- 5 A*-'>:-'&>:A& (+&

(&,A&D(*.-BHH=.($8$;; "$ _=;$(N '&*K*($8$*;;DL+G 5"&A&A&( +5 G *.*- 5 A*-'?:-'&?:A& (+& +8&

8+$A4&*)&

! NH`kGOBQ '`!W9$g&3'): $E ! YH$K$;!kN O QB$E mJ$g*;FG-&!"66T5* -*`?a&$g*-* ;^d$<Z=!8FW&5?

Q

wG/0-0-)8@32A@3),+X25p")_DaF.If9;&G13@N91B4:9;&?@BLU9;1B<C),&`);P1Bc?2$@9;LC2*@4325-),4B1K13)!|xNlnz>T+s9;MG<=&07i1Bc?2|@9;LC2*@4325-),4B1432Y9,D?9;p0LC2h<=& 9OE25pSp043)YI@3254Yj xgc?2h2?9;+.-0LC2dkw_n_x 1B4:9;&?@yPr),4B+ <=&<=78/0432 D0)G2*@J1Bc 9;1Yj xgc?21B4:9;&?@yPR),4B+<=1&?),1.9b- 9;4B1B<C'5/0LU9;4BL=FH-043251B1tFH-0<C2*'*2J);PA'*)GD02h~^p0/01-0LC2Y9,@3269,'*'*25-01Pr),4i1Bc?26@:9;MV26);P$1Bc?29;4B78/0+X25&G1|1Bc 9;1N<=1$25&?D02*D/0-`1Bc 9;1If9YF0 ?),&?2+s9*F6IK),&?D0254|<]P<=1If),4BM_@$9;1A9;L=L`(c?251Bc?254<=1$9;L=If9YF_@If),4BM_@ -|4NINc?251Bc?254|<=1N432Y9;L=L=FJ-043)_Da/?'*2*@7V)_)_Dr!|xNlnZ~R9,'51B/ 9;L=L=FV>?kmln !|xNln 0k5!AxNldnf'*)_D02

kw_nGx Q ><=13@:25L]PK9;&dkmldno9;-0-0L=<C'Y9;1B<C),&>c 9,@ALC),&07J-043)Y[V2*D<=13@AIK),4B1BcE9,@A9;&/0&0<=[V2543@:9;L2a-"254B1|13)G),L<=&kmldn1B4:9;&?@yPR),4B+s9;1B<C),&>0p0/01<=1c 9,@@:25[V254:9;LL=<=+.<=1:9;1B<C),&?@Y

•xgc?2WLU9;&078/ 9;7V2<C@A<=&0c?254325&T1BL=FDa<s'5/0L=1m13)J/0&?D02543@B1:9;&?DdPr),4m+X)8@B1A&?),&at2_-254B1D025[V25LC),-"2543@>9;L]1Bc?),/078cX<=1@32*25+X@z1Bc 9;1z<=13@z2a-0432*@3@B<=[V25&?2*@3@Ig9,@z1:9;4B7V25132*DR Sy/?@B14B<=78cG1UT G&?),14B<CDa<C'5/0LC),/?@3L=FX@B1B43),&07Pr),4$1Bc?2-0/04B-)8@32*@PR),4INc0<C':cd<=1|<C@/?@32*Du>"9;&?D/?@B/ 9;L=L=F@B1B43),&07J25&?),/078cb&?),1A13).p278<=[V25&b/0-d<=&'*),+.-0LC2'Y9,@32*@Yj

•xzF_-"2z@9QPr251FW9;&?D1tF_-"2K'3c?2*':MV2543@'Y9;&i@:9QPR2578/ 9;43De9;7T9;<=&?@B1v9gLU9;4B7V2'5LU9,@3@);P0-043),784:9;+.+.<=&07m254B43),43@xgc?)8@32)_'*'5/04B4B<=&07.INc?25&b9D?9;1:9i[,9;L=/?2);Pv@3),+X2mMG<=&?DJp2*'*),+X2*@N<=&0-0/01);Pv9'*),+.-0/01:9;1B<C),&b1Bc 9;1D0)G2*@A&?),1mIK),4BMdIN<=1Bc1Bc 9;1MG<=&?D);PfD?9;1:9ajdVX#_EU` /JI =]nr#_nDg.'iA = 0o/CIom.0<I 'D4./?@32#_nDg.'d4Dn\4>#p' 2 4X9;&?D4># 0 #_F^6 0o/X0 =]n\4>F 4$13)i+s9;MV2m9-043)_);P g1E>F^òE#HÈ mJ/ @B#_F 2 'A1Bc 9;1f1Bc0<C@g@B<=1B/ 9;1B<C),&6IN<=L=L"&?25[V254fc 9;-0-25& <]P1Bc?2W-043)G);P'Y9;&0&?),1$p2+s9,D028> 1Bc?2-043),784:9;+ IN<=L=Lp"2432BSB2*'5132*D`PR),4202*'5/01B<C),&> IN<=1Bcd9;&d254B43),4+X2*@3@:9;7V2m1325L=L=<=&07XINc?25432W<=&`1Bc?2-043),784:9;+ 9-043),p0LC25+If9,@NPR),/0&?Duj-|&e1Bc?2Kkmldn Qkw_n_xH@:'*25&?28>Qkmlnq<C@1Bc?2fD?9;1:9a>8@3'3c?25+s9,@D02?&?2K1tF_-"2*@9;&?Dekw_n_xH1B4:9;&?@yPR),4B+X@D02*@3'54B<=p26-043),784:9;+X@Y>p0/01.<=&o1Bc?26-0432*@:25&T1s@B<=1B/ 9;1B<C),&>g9;L=1Bc?),/078cZ@3':c?25+s9,@X+s9YFOp2`9;1.c 9;&?Du>kw_n_x D025[V25LC),-"2543@D0)d&?),1ec 9Y[V269-04:9,'51B<C'Y9;LN@B1:9;1B<C's1FG-2s':c?2*'3MV254.13)d78/ 9;4:9;&T132*2J1Bc 9;1i1Bc?25<=41B4:9;&?@yPR),4B+s9;1B<C),&b),/01B-0/01$IN<=L=L'*),&aPR),4B+13)X9i78<=[V25&b@:'3c?25+s9aj

•%t&G1325784:9;132*DdD025[V25LC),-0+X25&G1m25&G[G<=43),&0+X25&G13@m1Bc 9;1|@B/0-0-),4B1A9;&d25&0c 9;&?'*2*Db[_<C25I );Pz'*)_D02e9,@+X),4321Bc 9;&[Sy/?@B1f132_1f2_<C@31PR),4f@:25[V254:9;L -043),784:9;+.+.<=&07.LU9;&078/ 9;7V2*@Yjfw_25[V254:9;L"p)V9,@B1f),&aL=<=&?2A@3FG&G1:9,'51B<C'9;&?DW@325+s9;&G1B<C'[V254B<] 2543@1Bc 9;1c?25L=-W-043),784:9;+.+X2543@'*),4B432*'51v254B43),43@2Y9;4BL=<C254<=&W1Bc?2K-043)_'*2*@3@Yjkw_n_x'5/04B4325&T1BL=F6LU9;7V@p25c0<=&?D),&`1Bc?213)_),L=<=&07s@3'*25&?28

ld)8@31kmldn`2*Da<=13),43@zIN<=L=L?D0)|p 9,@3<C'Kkmln`@BFG&G1:9Qi':c?2*'3Ma@K9;&?Di+s9*F_p"2N@:'3c?25+s9A[89;L=<CD?9;1B<C),&>9;&?DE@3),+X2q);Pg1Bc?2s+X),432q9,Da[89;&?'*2*DD025[V25LC),-0+X25&G125&G[G<=43),&0+X25&G13@ePr),4kmln9;&?DEkw_n_x-043)Y[_<CD02.9;&9;p?@B1B4:9,'5132*D[_<C25I );Pz1Bc?2e1B4:9;&?@BPr),4B+>"IN<=1BcE9sD025p0/0787V254W9;&?D@3),+X29;& 9;L=F_@3<C@13)G),LC@|9,D0D02*Duj

!|)IK25[V254Y> 1Bc?2Pr/0L=L-)YIK254m);Pz),&aL=<=&?2e'*)_D02[89;L=<CDa<=1tF':c?2*'3M_<=&07`9;&?Db1tF_-"2W'3c?2*'3M_<=&07`9;L=7V);4B<=1Bc0+X@1Bc 9;1zc 9Y[V2-043)Y[V25&q2_1B4325+X25L=Fc?25L=-aPr/0L?13)m/?@32543@z);Pu%z@Pr),4z),1Bc?254z-043),784:9;+.+.<=&07LU9;&078/ 9;7V2*@Y>8@B/?':c9,@%t&G1B<=L=L=<?>,2*'5L=<=-?@32N9;&?Deld<C'543)8@3);Pr1 xA<C@B/ 9;L?wG1B/?Da<C)<C@'5/04B4325&T1BL=FeLU9,'3M_<=&07Pr),4Nkw_n_xj

[7 y

E2g?43@31z209;+.<=&?2NINc0<C':cX-043),p0LC25+X@@:2*25+ 13)mp"2g1Bc?2g+X)8@B1-04325[89;LC25&T1K<=&.-04:9,'51B<C'Y9;L?kw_nGxZ9;/01Bc?),4B<=&07?>9;&?DÌNc 9;1$c 9,@Np"2*25&dD0),&?213).@3),L=[V21Bc?25+j

! #"%$!&(')$+*-,/.0",21"%$+34*-,/.0576%8/*:9+;=<?>@"A34'CBD'="B/E-'F.A')9G&'=BD'=,7&'=,H9?"A,I1J'K6%9+L$+'=;GE-*-MN'O6L9+"A3P6Q9+*SRC5(*-.A5/E-*-.A5H9+*-,/.0"%1T')$U$+"$+;RK6L(;U'K&V8HWX'K&(*:9+;F'=E-;U')YF5(')$+'AZ

Q Q

7Nu "!$#%'&(*)

xgc?2f@B1:9;1B<C'Kkw_n_x[89;L=<CDa<=1tFW-043),p0LC25+<C@;A<=[V25&i9;&ikw_nGxO1B4:9;&?@yPR),4B+s9;1B<C),&T9;&?DW1Bc?2kAlnJ@3'3c?25+s9,@

Din, Dout

>D0)G2*@<=1c?),LCD1Bc 9;11Bc?21B4:9;&?@yPR),4B+s9;1B<C),&>INc?25&h4B/0&),& 03/ ndD0)_'5/0+X25&T1INc0<C':cE<C@[89;L=<CDIN<=1Bc432*@3-"2*'5113)

Din

>0IN<=L=L-043)_Da/?'*2W9i432*@B/0L=11Bc 9;1N<C@N[89;L=<CD`IN<=1Bc432*@3-"2*'51N13)Dout

,+

xgc?2@:),L=/01B<C),&b);P1Bc0<C@$-043),p0LC25+<C@N<=&G1325432*@B1B<=&07XPR),4@325[V254:9;L432Y9,@3),&?@

`.-0/ 213 l9;&TFX-043),784:9;+X@9;&?DJ@3254B[_<C'*2*@f9,'*'*25-01B<=&07<=&0-0/01f<=&q1Bc?2$Pr),4B+ );PkAlnD0)G'5/0+X25&G13@fc 9*[V29IK25L=L]tD02?&?2*DJp25c 9*[_<C),4PR),4fD0)_'5/0+X25&T13@f1Bc 9;1N9;432$[89;L=<CDXIN<=1BcJ432*@B-2*'5113)9- 9;4B1B<C'5/0LU9;4N@3':c?25+s9a>p0/01m&?),1|PR),4mD0)G'5/0+X25&G13@1Bc 9;19;432e&?),1YjW%P/?@3<=&07qkw_nGx 13)J7V25&?254:9;132.@B/?':chD0)G'5/0+X25&G13@Y>u<=1A<C@D02*@B<=4:9;p0LC213)M_&?)YI INc?251Bc?254 0 =&=);Pv1Bc?2D0)G'5/0+X25&G13@|9;432@:'3c?25+s9Q[89;L=<CDuj

4 / 5-r56>[(7/3 %P9i@B1:9;1B<C'm[89;L=<CDa<=1tFq78/ 9;4:9;&T132*22a<C@B13@Y>_1Bc?25&9;&TF6@3':c?25+s9i[,9;L=<CD?9;1B<C),&6PR),4f25&?@3/04B<=&07kw_n_xS),/01B-0/01K[89;L=<CDa<=1tFJ'Y9;&qp2|4325+X)Y[V2*Du>?9;&?DqIN<=1Bcq1Bc 9;1g1Bc?2|&?2*2*Dq13)i'*),&?@B<CD0254fINc 9;1N@Bc?),/0LCDp"2qD0),&?2s<]P@3':c?25+s9d[,9;L=<CD?9;1B<C),&OPR9;<=LC@j 43),784:9;+X@1Bc 9;1W/?@:2q),/01B-0/01);P1Bc?2Xkw_nGx &?2*2*DO&?),1<=+.-0LC25+X25&T1|<=&0-0/01[,9;L=<CD?9;1B<C),&> ),4Nc 9*[V2i9;&TF6254B43),4c 9;&?DaL=<=&07XPR),4@3'3c?25+s9Q<=&G[,9;L=<CDd<=&0-0/01Yj

xgc?2X@31:9;1B<C'kw_n_x [89;L=<CD?9;1B<C),&-043),p0LC25+ c 9,@p2*25&h1Bc?2.@B/0p(SB2*'51W);Pg9J78432Y9;1eD02Y9;L);Pf432*@:2Y9;43'3c%1m<C@&?)INc?25432&?2Y9;4$2Y9,@BFVjxgc?2APr/0L=Lukw_nGxLU9;&078/ 9;7V2W<C@Nx/04B<=&07J'*),+.-0LC2513298V>a+X2Y9;&0<=&07d~r<C'*23) @$xgc?2*),4325+q1Bc 9;1<=1<C@<=+.-)8@3@B<=p0LC213)$@3),/0&?DaL=FW9;&?D'*),+.-0LC251325L=F-043)Y[V2g9;&TFm<=&G1325432*@B1B<=&07|-043),-254B1tFV>,@B/?':ci9,@[,9;L=<CDa<=1FV>9;p),/01kw_nGx @31tF_LC2*@Bc?2*2513@Yj

|2*@32Y9;43'3c?2543@c 9Y[V2i1:9;MV25&h1tIK)`Da<;:u254325&T1W9;-0-043)V9,':c?2*@W9;43),/0&?D1Bc0<C@A-043),p0LC25+ z<=1Bc?254432*@B1B4B<C'51B<=&07`13)&?),&atx/04B<=&07,t'*),+.-0LC25132@B/0p0LU9;&078/ 9;7V2*@K);Pkw_nGx>_9;&?DX-043)Y[_<=&07eD02*'5<CD?9;p0<=L=<=1FPr),41Bc?)8@328>T),4@9,'54B<] '5<=&07D02*'5<CD?9;p0<=L=<=1Fd9;&?D6+s9;MV2D0).IN<=1Bcb2*@31B<=+s9;132*@Yj

=<ZF/B%I @K/THJI(McK/CP@\zK/L IKb~R@aHJS%TFZCPOJHJF/OJ;`@

ld<=LC)b2519;Lj M Q<w\P If25432J9;+X),&071Bc?2.?43@B1e13)PR),4B+W/0LU9;132J2?9,'51W[89;L=<CD?9;1B<C),&>vINc0<C'3cH1Bc?25FE'Y9;L=LC2*D1FG-2':c?2*'3M_<=&07?>PR),4W9qP^4:9;78+X25&G1W);Pgkw_n_xjxgc?25<=4e9;& 9;L=Fa@B<C@m<C@p 9,@32*D/0-),&h+X)_D025L=<=&071Bc?21B4:9;&?@yPR),4B+ 9,@9>a@ g.'<GQG>= 'r#_E 0o/ 47A m 6 '>E5>9;&?D1Bc?2.<=&0-0/01e9;&?DE),/01B-0/01i@3'3c?25+s99,@1Bc?2.432578/0LU9;41B432*2.LU9;&078/ 9;7V2*@W1Bc 9;1If2WIN<=L=Lv9;LC@3)./?@328jgxgc?25F`1Bc?25&9;4B78/?2W1Bc 9;1$1Bc?2e@B1B4:9;<=78cT1yPR),4BIf9;43D@3),L=/01B<C),&> & 9;+X25L=F6?&?Da<=&07q1Bc?2W<=+9;7V2q);Pf1Bc?2.1B4:9;&?@BPr),4B+ 4325-0432*@:25&T132*DOpTF1Bc?2.1B4:9;&?@yPR),4B+X254W<C@&?),1W-")8@3@3<=p0LC28>p2*'Y9;/[email protected]&?254:9;L=L=FV>1Bc?21B4:9;&?@yPR),4B+ <=+s9;7V2<C@|&?),1A9.432578/0LU9;4A1B432*2LU9;&078/ 9;7V2.9;&?Dd'Y9;&b1BcT/?@A&?),1|p"2':c?2*'3MV2*DdPR),4$<=&?'5L=/?@B<C),&<=&1Bc?2`),/01B-0/01432578/0LU9;4.1B432*2JLU9;&078/ 9;7V28j%&?@B132Y9,Du>1Bc?25FO<=&T[V254B1.1Bc?2J1B4:9;&?@yPR),4B+ 9;&?DO+s9;-1Bc?2` m #]g m #LU9;&078/ 9;7V2s13)9J432578/0LU9;41B432*2.LU9;&078/ 9;7V28jX%tPK1Bc 9;1LU9;&078/ 9;7V2X<C@1Bc?25&O96@B/0-254BLU9;&078/ 9;7V2X);Pg1Bc?2<=&0-0/01@3':c?25+s9() @LU9;&078/ 9;7V2K <=&?'5L=/?@B<C),&Pr),4m432578/0LU9;41B432*2iLU9;&078/ 9;7V2*@m<C@D02*'5<CD?9;p0LC2K 1Bc?25&1Bc?2e<=+s9;7V2);P1Bc?2<=&0-0/01$LU9;&078/ 9;7V2<C@@B/0432m13)Xp"2'*),&G1:9;<=&?2*D<=&`1Bc?2),/01B-0/01LU9;&078/ 9;7V28j

?|&aPr),4B1B/0& 9;1325L=FV>G1Bc?25<=4K9;-0-043)V9,':cq<C@&?),1[V254BFi-04:9,'51B<C'Y9;L>a9;-0-0L=F_<=&07W),&0L=F13)9@B/0p?@3251);Pkw_nGxo1Bc 9;1<C@@3)@3+s9;L=L?1Bc 9;19;&TF.@B/?':cs@B1tF_LC2*@Bc?2*251+.<=78cG1f9,@vIK25L=L p"2f<=&?@B-2*'5132*D.pGFec 9;&?Dujxgc?2g1B<=+X2'*),+.-0LC2a<=1tF.);P

@BA 5/*-;F'DC@9+'=,/&(;BE@YF*:9+5/"AL9 6,HWXR 5/6E-E-'=,/.'FE/9+"I3 L/E:9+*-B/E-' *-,(B/L(9O6%,7&X"AL(9+B(L(9F;UR!5/'=3P6%;BGHFIKJLNMOG A 5/')$+' 'BPN'), 'DC*-; 9+; 6 L(,/*KPN')$+;+6%E A L$+*-,/. 3P6%R 5(*S,(' *-34B/E-'=34'=,H9+'K& *-, Q0>,R A E 6%9

SUTVTNWXZYVY2[V[F[\O]V^5_a`9bFcd\feNgBhiYNTN]9j,_^Uk,Ya]9Tahl\mSUTah

Q¨

1Bc?29;L=7V),4B<=1Bc0+ <C@|cTF_-25432_-),&?25&T1B<U9;L>"+s9;M_<=&07q[89;L=<CDa<=1tF),&0L=F`1Bc?2*),43251B<C'Y9;L=L=FD02*'5<CD?9;p0LC28j$x) 9YIf9(M ÖP<=+.-043)[V2*D1Bc?21B<=+X2E'*),+.-0LC2a<=1tF);P1Bc0<C@13)o2a-"),&?25&G1B<U9;L>mp0/011Bc?2E),p(SB2*'51`kw_n_x @3/0p0LU9;&078/ 9;7V24325+s9;<=&?2*Dd@B+s9;L=Lj

Q(QbL%K <]MrUxFDI(; @K6TH]IbMNK6CP@

M Q Q7P -043)Y[_<CD0261Bc?2J7843),/0&?DHIK),4BMEPR),4.@3),+X2J2Y9;4BL=FO@B1:9;1B<C'`9;& 9;L=Fa@B<C@),&Hkw_n_x +A),1[,9;L=<CD?9;1B<C),&>p0/019;& 9;L=Fa@B<C@$);Pz),1Bc?254A<=&T1325432*@B1B<=&07J-043),-254B1B<C2*@|);Pkw_nGx @B1tF_LC2*@Bc?2*2513@/0&?D02549;&d9,@3@3/0+.-01B<C),&b1Bc 9;1$kmln<=&0-0/01<C@g[89;L=<CDJIN4B1Yj9e78<=[V25&@3'3c?25+s9ajxgc?25Fq/?@32*D`9;&b9;-0-043)V9,':cb);P+X)_D025L=<=&07.kw_n_x @B1FGLC2*@3c?2*2513@9,@784:9;-0c?@Y>v9;&?DE25[89;L=/ 9;1B<=&07b2a-0432*@3@B<C),&?@1Bc 9;1i9 :2*'51W'*),&G1B43),L )I 0 GD47#_E 0 6<#_=]n8>&?),1W)Y[V254ekAlno&?)_D02*@p0/01m)Y[V254A1Bc?25<=4A@:'3c?25+s9JD02*'5LU9;4:9;1B<C),&?@Yj @A9X432*@B/0L=1Y> 1Bc?25FÌK25432.9;p0LC2W13)qD02513254B+.<=&?2i43),/078c0L=FINc0<C':c- 9;4B13@q);Pm9@B1FGLC2*@Bc?2*251q'Y9;&o- 9,@3@X'*),&T1B43),L|13)INc0<C'3c\- 9;4B13@>f9;&?Du>K- 9;4B1B<C'5/0LU9;4BL=F<=&T1325432*@B1B<=&07?>gINc0<C':c'*),&G1B43),L )YI@.@32*25+13)2_<C@B1ipTF9LC)_),MO9;1i1Bc?26@B1tF_LC2*@Bc?2*251X9;LC),&?28>p0/01X9;432`9;L=If9*Fa@ 0 GD4<' / #WINc?25&-043)_'*2*@3@B<=&07XkmlnED0)G'5/0+X25&G13@$1Bc 9;1$9;432[,9;L=<CDÌN<=1Bc`432*@3-"2*'5113)X9.- 9;4B1B<C'5/0LU9;4|@3':c?25+s9aj

x)W9ALU9;4B7V22a1325&T1Y>a9;&s9;-0-043)*a<=+s9;1B<=[V2$@3),L=/01B<C),&.PR),41Bc?2@B1:9;1B<C'gkw_n_xo[,9;L=<CD?9;1B<C),&q-043),p0LC25+c 9,@p2*25&PR),/0&?Du>0pTFM ¨ P 9;&?D M ¨ P );P1Bc?2 ?|&0<=[V2543@B<=1F6);P 9;4BcT/?@Yj

xgc?25<=49;-0-043)V9,'3c4325L=<C2*@),&i9 'iA,g.òF / # òc 0o/X0 =]n\4>F 4K),&e1Bc?2zkw_nGxH'*)_D028>Q78<=[V25&9;&e<=&0-0/01@3'3c?25+s9() @'*),&?@B1B4:9;<=&G13@Y>aPR),L=LC)YIf2*D`pTFq1Bc?2A'*),&?@31B4B/?'51B<C),&);Pv9:4 mJ2d2Y0 EDn I E 0 g %G>?7V25&?254:9;1B<=&07s9e@3/0-"254BLU9;&078/ 9;7V2);P1Bc?2NLU9;&078/ 9;7V2$1Bc 9;1z1Bc?2N1B4:9;&?@yPR),4B++s9YF),/01B-0/01Yjvxgc?2@3/0+.+s9;4BFi784:9;-0cs<C@v?& 9;L=L=F[,9;L=<CD?9;132*Ds9;7T9;<=&?@319;&),/01B-0/01A@3':c?25+s9X/?@3<=&07J9;&9;L=7V),4B<=1Bc0+ Pr43),+ 9sDa<;:254325&G1|-043)\SB2*'51Y> 432*@3/0L=1B<=&07s<=&d25<=1Bc?2549.+X2*@:@:9;7V21Bc 9;1A1Bc?2e),/01B-0/01m<C@m9;L=If9YF_@m'*),&T1:9;<=&?2*D<=&d1Bc?2WLU9;&078/ 9;7V2);Pz1Bc?2i),/01B-0/01@3'3c?25+s9a>),4A9sL=<C@B1A);P254B43),4+X2*@3@9;7V2*@Yjvxgc?2g9;& 9;L=Fa@B<C@<C@,F / 6f` 2 g1= '7#p'5>8+X2Y9;&0<=&071Bc 9;11Bc?2f432*@B/0L=1v<C@9;&.2*@B1B<=+s9;132N9;&?De<C@v@3),+X251B<=+X2*@IN43),&07?>_p0/01K9;LC@3)47` mJ/ A8>T+X2Y9;&0<=&07e1Bc 9;1K1Bc?2$9;-0-043)*a<=+s9;1B<C),&6<C@K9;L=Ig9*Fa@13)W1Bc?2@B<CD02$);Pu4325-),4B1B<=&07W13)_)+s9;&GFq254B43),43@Y @B1FGLC2*@Bc?2*251f1Bc 9;1f+s9*Fs@3),+X251B<=+X2*@f-043)_Da/?'*2A<=&T[89;L=<CDq),/01B-0/01g<C@K&?25[V254K- 9,@3@:2*Dq9,@g),&?21Bc 9;1IN<=L=L&?),1Y>0p0/011Bc?2'*),&T[V2543@:28> 4Hg m E>F_` m 4'>E>EiòE 45>?@3),+X251B<=+X2*@$c 9;-0-"25&?@Yj

xgc?2J9;L=7V),4B<=1Bc0+ <C@W1:9;4B7V25132*DH9;1e-04:9,'51B<C'Y9;Lkw_nGx>v9;&?DE<=1Ig9,@eD025+X),&?@31B4:9;132*D13)bIK),4BMhIN<=1BcH9@3251);P432Y9;L]If),4BLCDOkw_n_x @31tF_LC2*@Bc?2*2513@i9;&?DH@3':c?25+s9,@Y>IN<=1Bc9432Y9,@3),& 9;p0LC2J&T/0+Wp254);P$@B-0/04B<C),/?@254B43),43@Yj!A)YIf25[V254Y>?<=1<C@NL=<=+.<=132*D13)IK),4BM_<=&07q),&0L=FJIN<=1Bcvxz2543@B<C),& Q );Pkw_n_x> 9;&?D`),&0L=F6IN<=1Bc`kmldn9) @4:9;1Bc?254-04B<=+.<=1B<=[V2hp0/0<=L=1y<=& @3'3c?25+s9HLU9;&078/ 9;7V28>mmxNjN%t19;LC@3)H+s9;MV2*@`4:9;1Bc?254`43),/078c 9;-0-043)Y_<=+s9;1B<C),&?@9;1-0LU9,'*2*@Yj

E2qIN<=L=L/?@32s1Bc0<C@i9;L=7V),4B<=1Bc0+<C@W1Bc?2sp 9,@B<C@e);P$),/04eIf),4BM">v2a1325&?Da<=&079;&?DO<=+.-043)Y[_<=&07<=1W<=&@325[V254:9;L9,@B-2*'513@13)6If),4BMd<=&9;&E),&aL=<=&?2.2*Da<=1B<=&07?>&?2_1y7V25&?254:9;1B<C),&Okw_n_x'*),&T132a1Y>9;&?DE9,D0Da<=&07b&?25I@B/0pa9;L=7V),4B<=1Bc0+X@m9;&?DD?9;1:9.2a1B4:9,'513),43@N13).<=1Yj

7#t ('B "! #"% & (' *)

xIK)+.<=&0<]t@B/04B[V25Fa@If25432'*),&?Da/?'5132*Du>V13)m7V2519;&.<CD02Y9m);P"INc0<C'3cq9,@B-2*'513@v<=&INc0<C'3cX1Bc?2g+X)8@31-04:9,'51B<C'Y9;L-043),p0LC25+X@|IN<=1Bckw_nED025[V25LC),-0+X25&T19;43225&?'*),/0&T1325432*D9;&?D`c?)YI1Bc?2*@32-043),p0LC25+X@$'Y9;&bp"2m+X251Yj

Q

analysis deploymentimpl.design

4 P&2>-3>'I&2' 3F^W*-.-:]$,- -Qk-.-:]$, '@$,d$$.4g&' 3F&^\*8FG$E FG$!*;$!*K=:]4d*`? " !8$!&ak=g-.-*]>=X $g*9&344*@H,*5&2$K*-"6#&$!& W:;*H$!*L"6*]& :]:]$,-*`?k' $@H&2=!"9S& "-"65 "4!$!&Jd')!$!*e_=gE*\[i$,\g$b8Jh!9&2,-Hl$!*b$&>$5*L =gET $!4p-*x$g*b5*-&$5*`? "4' 3F;&Z9 "6:d!-*DFG &6=!"9S&-H=G! &2:;G$!*EJ---H,J5&&g-$!&2.?

\;"J; T[K6Q(;DL_yCPI(;DLa]MN;" @

LC)_'Y9;L'*),+.- 9;&TFV>v/?@B<=&07bkw_n_x 2a1325&?@B<=[V25L=F<=&E<=13@-043)_Da/?'51B<C),&>9;78432*2*DE13)`- 9;4B1B<C'5<=- 9;132q<=&E<=&G13254y[_<C25I@Yjzxgc?2'*),+.- 9;&GFV>"wG1B<=p)0>a<C@N<=&`1Bc?2m-0/0p0L=<C@Bc0<=&07Xp0/?@B<=&?2*@:@Y>?9;&?D6432*'*25<=[V2[V254BFJLU9;4B7V2kAlnED0)_'5/a+X25&G13@AP^43),+ '5/?@B13),+X2543@u),&?2iD025[V25LC),-254A1:9,@3M<C@A13)sIN4B<=132i1B4:9;&?@yPR),4B+X@A1Bc 9;1m'*),&G[V254B1m1Bc?2*@32i<=&T13)`9;&<=&ac?),/?@32ikmldnOLU9;&078/ 9;7V28jAxgc?2W<=&ac?),/?@32ikmldn>?/?@B/ 9;L=L=F4325-0432*@:25&T1B<=&076-043)GDa/?'51m'Y9;1:9;LC),7V@Y>"<C@|1Bc?25&-043)_'*2*@3@32*DZ~^<=&?D02a<=&07?>- 9;78<=& 9;1B<C),&O2513'8j \9;&?DE1B4:9;&?@yPr),4B+X2*DE13)b9J1Bc0<=43DEkmldnoPr),4B+s9;1PR),4D025L=<=[V254BFp 9,':MJ13)X1Bc?2'5/?@B13),+X254Yj

m25[V25LC),-2543@ec 9,DL=<=1B1BLC2s'*),&?'*254B&OPr),4e@3'3c?25+s9b[,9;L=<CDa<=1FE);PN1Bc?2s432*@B/0L=1e);P1Bc?25<=4W1B4:9;&?@yPR),4B+X@Y>9,@1Bc?25FIf25432|[V254BFsIK25L=L9,'*T/ 9;<=&G132*D6IN<=1Bcq1Bc?2|<=&ac?),/?@32m@3':c?25+s9a>?9;&?DJ9;L=+X)8@B1N9;L=If9YF_@g7V),1g'*),4B432*'51B&?2*@3@g4B<=78cG1pGFZ'Y9;432P^/0Lm'*),&?@B<CD0254:9;1B<C),&SINc?25&(1Bc?2b1B4:9;&?@yPR),4B+ If9,@JIN4B<=1B1325&>),4JpTF\@B<=+.-0L=FZ@9*F_<=&071Bc 9;1J1Bc?25<=4),/01B-0/01iIf9,@W4B<=78cT1Y>9,D?9;-01B<=&07d1Bc?25<=4W<=&ac?),/?@32X13)_),LC@WD0)IN&O1Bc?2.-0<=-25L=<=&?2X13)d9,'*'*25-01W<=1Yj6xgc?25F/?@32*D@B-2*'5<U9;L=<Y2*Dkmldn2*Da<=1B<=&0713)_),LC@vL=<=MV2gkmldnbwG-GFe13),7V251Bc?254zIN<=1BcX'*),+.+X),&.132a12*Da<=13),43@vPR),49;/01Bc?),4B<=&071B4:9;&?@yPR),4B+X@g<=&Jkw_n_x Q >?9;&?DJkm9;LU9;&a SK),&6D02*Da<C'Y9;132*D ;58Z@3254B[V2543@KPR),4f202*'5/01B<=&071Bc?25+j(<=1Bcq[V254BFLU9;4B7V2D0)_'5/0+X25&T13@> 9i4B/0&b'*),/0LCD`1:9;MV2+X),4321Bc 9;&d9D?9*F613)X'*),+.-0LC251328j

xgc0<C@e-043)G'*2*@:@e);P$9,D_c?)_'X432*'*)_Da<=&079;&?DL=<=1B1BLC2s),4W&?)b/?@32s);P@3':c?25+s9,@@32*25+X@[V254BFh1FG-0<C'Y9;LKPr),4e1Bc?2/?@32e);PkAlnEPR),4B+s9;13@m9;&?Dkw_nGx<=&d)5:"1Bc?2E25p@3251B1B<=&07V@jNA25L=<=[V254BFb9;&?Db43251B/04B&@:'3c?25+s9,@Y> INc?25&9Y[,9;<=LU9;p0LC28>?9;L=Ig9*Fa@gIK25432A78<=[V25&9,@9Rtc 9;&?D_tD0)IN&?@UT:>?Da<=432*'51BL=F.Pr43),+ 9W'5/?@B13),+X254gIN<=1Bc6&?)e-")8@3@3<=p0<=L=<=1tFs);P9;L=13254:9;1B<C),&?@Yj

(<=1Bc432*'5/04B4B<=&07\2_-254B<C25&?'*2*@);PW1B4:9;&?@BPr),4B+X@);Pe[V254BFLU9;4B7V2D0)_'5/0+X25&T13@P9;<=L=<=&07Z9QP^132546c?),/043@`);P202*'5/01B<C),&>a25<=1Bc?254Kp2*'Y9;/?@32|+X25+X),4BFXc 9,DX4B/0&6),/01Y>G),4fp2*'Y9;/?@32|9;&q<=&T[89;L=<CDs-0<C2*'*2A);P1B4:9;&?@yPR),4B+ '*)_D02Ig9,@?& 9;L=L=FO1B4B<=787V25432*Du>NwG1B<=p)IK254326[V254BFH<=&T1325432*@B132*D<=&Z9;&GFO13)_),Lg1Bc 9;1X'*),/0LCDo25&0c 9;&?'*2`1B<=+X29;&?D+X25+X),4BFq-"254yPR),4B+s9;&?'*2m);Pkw_n_x>ac?25L=-0<=&0713)W4325L=<C25[V2m),/01yt);P^+X25+X),4BFsP9;<=L=/0432*@Y>09;&?DJ@Bc?),4B1325&0<=&07.1Bc?21B<=+X2$p"2PR),432N),1Bc?254zP9;<=L=/0432*@z25[V25&T1B/ 9;L=L=Fsc 9;-0-"25&jvxgc?2D025[V25LC),-2543@If254322*@B-2*'5<U9;L=L=F<=&T1B4B<=78/?2*DqpTF1Bc?2<CD02Y9W);P913)G),L?1Bc 9;1Y>_),&s1Bc?2p 9,@B<C@);P9;&X<=&0-0/01f@3'3c?25+s9i9;&?Ds9;&skw_n_xZ@B1FGLC2*@Bc?2*251Y>_'*),/0LCDX7V25&?254:9;132A9-04321B4:9;&?@yPR),4B+ <=&q@3),+X2PR9,@B132541B4:9;&?@yPr),4B+LU9;&078/ 9;7V28>_4325+X)Y[_<=&07e/0&G/?@32*Ds@B/0p01B432*2*@Pr43),+ <=&0-0/01kmln1B432*2*@Yj >@9+*-8D" ;F&'BPN'=E-"BD')$+; Y ')$+'0,("9O6=YC6Q$+'0"1 > A Q "%$F"9+5(')$F5/*-.A5 BD')$U1"%$+3P6,/R)' ; 9U$+'K634*-,(. 9U$!6,(; 1"%$+34')$C9+'=R!5/,/"E-"A.A*-'=;

Y "L/ES&6B/B(E:W 9+"9+5('=*:$Y#"$+M G9;U'='=34;49+5/6%9X9+5/')WYF*-ESE .A'=,(')$!6E-E:W ,/"%9E 6;XMN')W; 6 1J'K6%9+L$+'*S,(R="A34B/6%9+*-8/E-' YF*:9+5; 9U$+'K634*-,(.#YC6%; "%1J9+'=, L(;U'K& G

Q

analysis deploymentimpl.design

! PV FG$c!e"-$x!/.Z=g-$e')8F^-*@H@$!*e& $!*e:]#&&$!&P"$ !/.>')8Fa5* $B*.-:]$,>"65&& F^/ '): =!&2#";$g4&#& $!*b*-&$@yl$Z6$ /F]'!Z$,' P*!84:]$,W#&W=!* *,!3 :;$!:]$,-? ",98#"J$g4&#&H$,-985*c$,K&2$!**_*-.!:d-$,,$gH"-$R:]#"M*-"6E:;$4 $!&]&2!$!&; *-&$R$!* :]-:]$,$@H-!$;$!"5&*,!3 $g*c&/.4$!Z#&22T :]$4Pg&-?

y'CI(;DL6CP; I§z3K6L%H]UV@

&?),1Bc?254i@3/04B[V25FIg9,@W+s9,D02s<=&1Bc?2 "$ ==) &?25I@B7843),/0-),& ?A@325&?251Yixgc?2X&?25I@B7843),/0-O<C@9sPR),4B/0+PR),4|7V25&?254:9;LkmlnHG/?2*@B1B<C),&?@9;&?D9;&?@BIK2543@Yj|/?2*@31B<C),&?@m4325LU9;132*Dd13)Jkw_nGxIf25432e<C@:),LU9;132*Du>9;&?DDa<=[_<CD02*D`<=&G13).43),/078cd'Y9;13257V),4B<C2*@Yjxgc?2432*@B/0L=1<C@g<=&bx9;p0LC2 Q j

S@B%HJL6MrI(~wK6z BK/CIbLK/Tz5T[K

?),4K1Bc?2/0&0<=&0<=1B<U9;132*Du>09;&?Ds25[V25&sPr),4K1Bc?2$9,Da[89;&?'*2*Dskw_nbD025[V25LC),-254Y>_-043),p 9;p0L=F.1Bc?2c 9;43D02*@B1K-043),p0LC25+<=&Z9;& 9;L=F *<=&079;&o2_<C@B1B<=&07hkw_nS1B4:9;&?@yPR),4B+ <C@i13)h'*),+.-04325c?25&?Do1Bc?2J-")8@3@3<=p0LC2J'*),&G1B43),L )YI);PA1Bc?21B4:9;&?@yPR),4B+(c0<C'3cd1325+.-0LU9;132*@+s9*F6- 9,@3@$'*),&T1B43),L13)INc0<C':c> 9;&?D`<=&`INc0<C':cd'*),&G132_1

f),+.+X),&kw_n_xD025p0/0787V2543@|'Y9;&b[_<C@B/ 9;L=<Y21Bc?2'*),&G1B43),L )I PR),4$91B4:9;&?@yPR),4B+ );Pz9.@B<=&078LC2<=&?@31:9;&?'*2D0)_'5/0+X25&T1Y> 9;&?D6@3)'Y9;&`'Y9;&61Bc?2AIK25L=L]M_&?)YIN&rRtc 9,':M Tm);P9,D0Da<=&07X@3),+X2A132a1f<=&61325+.-0LU9;132*@gPR),4f1B4:9,'*29;p0<=L=<=1FVj$xgc?2*@329;-0-043)V9,'3c?2*@Y>"c?)IK25[V254Y>432*G/0<=432W1Bc 9;1m9;&b<=&0-0/01A<=&?@B1:9;&?'*2W<=&0-0/01A<C@|9Y[,9;<=LU9;p0LC2i13)s132*@B1IN<=1Bc>09;&?Dq<=1K'Y9;&Jp"2A91B<=+X2t'*),&?@B/0+.<=&07X9 :9;<=4K13)e'*),+X2A/0-sIN<=1Bc6),&?2$1Bc 9;1fIN<=L=L 1B4B<=787V254g2?9,'51BL=FX1Bc?2 ,HWH",/'#&(*-;+6.%$+'='=*-,/.0*-;?'=,/R)"AL($!6%.A'K& 9+"0&("KYF,/E-"A6A& ;?ES6%9+'); 9 lQ R >R!5/')3P6 6%,7& 9+" Q A RQ0> R A

; 9 WE-'=;U5/')')9 "%$ B/*-R M 9+5(' 7E-'=;01J$+"3 9+5('4B($+""! '=R 92B$+"A.$!6%34;BE 6Q9$#%&#('*)+%,.-*)+/('"#/)102* ('3 4 E 6,/& 9U$UW9+"7.L($+'5/"KY *:9OY#"$+M@;BG

- @N-043),p0LC25+ f),/0&G1m2*@3'54B<=p0<=&07q9D02*@B<=432*D1B4:9;&?@yPr),4B+s9;1B<C),&> 432*T/?2*@31B<=&07s'*),+.-0LC25132W@3),L=/01B<C),& Q¨$25LU9;132*D13)kw_n_xINc0<=132*@B- 9,'*2Wc 9;&?DaL=<=&07 $25LU9;132*D13)kAlnh& 9;+X2*@B- 9,'*2*@$<=&kw_n_x9;&?D`k 9;1Bc ¨!A)YI 13).@325LC2*'51M &?)GD02*@NIN<=1Bcd@3),+X2m-043),-"254B1F P <=&`k 9;1Bc Q<w!A)YI 13).'*),L=LC2*'51|9;L=LyM &?)GD02*@NIN<=1Bcd@3),+X2-043),-254B1tF P <=&b97843),/0- l2Y9;&0<=&07q9;&?D'*),&T132a1$D025-25&?D025&?'5F`);P $5'15$ 9;&?D #

n% ¨

$25LU9;132*D13).),1Bc?254k 9;1BcPr/0&?'51B<C),&?@ -|1Bc?254kw_nGx -043),p0LC25+X@ Q kw_nGx4325LU9;132*Du> &?),1N-043),p0LC25+X@ Q

=c WZ:d$,!&P' N "Q^T --*<-*&k$<!SR /!^,aC` qk&$P$-FW&2@Hi*.,#*5*$,;E"--&-?

Q

@B<=1B/ 9;1B<C),&d13)Xp2'3c?2*':MV2*DPR),4Y>?IN4B<=132<=1Y> 9;&?Db@31325-1Bc043),/078cb1Bc?2eD025p0/0787V254|13).1Bc?2W@B1:9;7V2W);P<=&T1325432*@31Yjm25p0/0787V2543@g78<=[V2A&?)e'5L=/?2AINc 9;1g1Bc?2|1325+.-0LU9;132'*),&T1B43),L )YIS+s9*Fqp"2$PR),4f),1Bc?254ND0)_'5/0+X25&T13@g1Bc 9;&61Bc?2@B-2*'5<] 'X),&?2./?@:2*D<=&E1Bc?2.D025p0/07878<=&07d@32*@:@B<C),&>9;&?Dh'*),+.-0LC2D025p0/07878<=&07b@:2*@3@B<C),&?@'Y9;&Ep2.2Y9,@BF13)LC)8@32J)Y[V254B[_<C25I);PBjf)_D02s4325- 9;<=4+s9,D02`9QP^13254D025p0/07878<=&07E9;LC@3)d1325&?D0@e13)p2Xp 9,Du>z);Pr1325&H<=&T1B43)_Da/?'<=&07R@3-"2*'5<U9;Lz'Y9,@32*@iT.9;&?Dh'*),+.-0L=<C'Y9;1B<=&071Bc?2.@B1B4B/?'51B/0432X);Pg1Bc?2X'*)_D02iP^/04B1Bc?254Yj:-|&E1Bc?2.),1Bc?254Wc 9;&?Du>D025p0/0787V2543@m9;432m[,9;L=/ 9;p0LC2Pr),4N<=&?@3-"2*'51B<C),&b);Pv[89;L=/?2'*),+.-0/01:9;1B<C),&?@Yj

wG1:9;1B<C'g9;& 9;L=F_@3<C@);P?kw_nz>YINc?254321Bc?2z<=&0-0/01@:'3c?25+s9$<C@1:9;MV25&i<=&T13)|9,'*'*),/0&G1~R9;&?DW25[V25&WINc?25432K<=1<C@&?),1<C@f- 9;4B1B<C'5/0LU9;4BL=Fq@3/0<=132*DJ9,@g9p 9,@3<C@zPR),4f9W13)G),L'*),+.-0/01B<=&07X9;&?Ds[_<C@B/ 9;L=<*<=&07i1Bc?2$-)8@3@B<=p0LC2A'*),&T1B43),L )Ip251tIf2*25&1325+.-0LU9;132*@j ?$L=1B<=+s9;1325L=FV>9X@B1:9;1B<C'i9;& 9;L=F_@3<C@p 9,@32*Db13)G),L'*),/0LCD78<=[V21Bc?2e@B1tF_LC2*@Bc?2*251m9;/01Bc?),41Bc?2JD025p0/07878<=&07d<=&?@3<=78cT1.);P,R 9;L=LK<=&?@B1:9;&?'*2*@9;1W1Bc?2J@:9;+X2s1B<=+X2>T:>v<=1e'*),/0LCDH@:9*[V2sc0<=+ 1Bc?2s1B43),/0p0LC2q);PIN4B<=1B<=&07JD025p0/07878<=&07X<=&?@B1:9;&?'*2*@Yj 43),p 9;p0L=F`1Bc?2m+X)8@B1N<=+.-"),4B1:9;&G1$p25&?2?1<C@Y%1'Y9;&`c?25L=-d9,Da[89;&?'5<=&07+e/?'3ch);P1Bc?2i9YIf9;4325&?2*@3@m);P1Bc?2W432Y9;Lg~R9,@$),-0-)8@32*D13)sINc 9;1|1Bc?2eD025[V25LC),-"254Ac 9,D<=+s9;78<=&?2*D $'*),&T1B43),L )I\<=&s9m@B1tF_LC2*@Bc?2*251Pr43),+ #p'D47#1B<=+X2g13):'fAoF&#1B<=+X28>_9;&?DX9*If9;4325&?2*@:@K);P254B43),43@vP^43),+ A 'pg1= `on 2 ' / #1B<=+X213).132*@31N1B<=+X28>0INc0<C'3c>?Pr),4$9@B/ s'5<C25&G1BL=F6PR9,@31$9;& 9;L=F_@B<C@>0'*),/0LCD`p"2m1Bc?2W@:9;+X29,@2*Da<=11B<=+X28j

%&.D02*@B<=78&.4:9;1Bc?2541Bc 9;&s9;& 9;L=F_@3<C@vIK),4BM>8IK2N'*),&G1325&?D.1Bc 9;19A@B1:9;1B<C'8>V),&aL=<=&?2 )YIo[_<C@B/ 9;L=<Y254p0/0<=L=1<=&G13)9;&J2*Da<=13),4f'Y9;&J@B<=78&0<] 'Y9;&T1BL=Fs@3c?),4B1325&q1Bc?2|'5F_'5LC2$1B<=+X2$);Pu1B4B<U9;L9;&?Dq254B43),4KD025[V25LC),-0+X25&G1Y>apTF./0-D?9;1B<=&07Da<C@B-0LU9YFV2*DJPr2*2*Dap 9,':Ms<=+.+X2*Da<U9;1325L=FV>0<=&?@3132Y9,DJ);P1Bc?2$/?@B/ 9;L1R2*Da<=1yt@:9Y[V21B4BF Tm'5F_'5LC28jxgc?2|?43@B1g'Y9;13257V),4BF);P),/04 "$ ==) @3/04B[V25FW<=&?Da<C'Y9;132*@1Bc 9;1kw_nGxoD02*@3<=78&.<C@ AoF 6 m = #R>V9;1vLC2Y9,@B1vPr),4v1Bc?2fp2578<=&0&?254Y>),4K+s9*F_p"2$1Bc 9;1zkw_n_xS9;/01Bc?),43@7V25&?254:9;L=L=Fs9;432$LU9 *FVjxgc?2$LU9;1B13254If),/0LCDq'*),&G1B4:9,@B1IN<=1BcJ),1Bc?254?A@325&?251'*),+.-0/013254|-043),784:9;+.+.<=&07q7843),/0-?@Y>aINc?25432W-"2*),-0LC2m4:9;4325L=F9,@BMqPR),4'*),+.-0LC25132W@3),L=/01B<C),&?@Yj

S@B%HJL6MrI(~wK6z <\FDI(9

-|&?2i432*)_'*'5/04B4B<=&07J-043),p0LC25+>- 9;4B1B<U9;L=L=FbL=<=&0MV2*DdIN<=1Bc1Bc?2'*),&T1B43),L )YI -043),p0LC25+><C@|1Bc?2e'*),+.-04325c?25&a@B<C),&S);Pkw_nGxz) @62a-0432*@3@B<C),&ZLU9;&078/ 9;7V28>$k 9;1Bc>IN<=1Bc9;&25[89;L=/ 9;1B<C),&(+X)GD025LA1Bc 9;1q<C@qL=<=1B1BLC2d/?@32*D25LC@325INc?254328j"M ¨3\P c 9,@eIN4B<=1B1325&96INc?),LC2q432*@32Y9;43':cO- 9;-254W1B4BF_<=&07b13)b+s9;MV2q9@:25&?@B<=p0LC2X+X2Y9;&0<=&07),/01);Pg1Bc?2.If9YFk 9;1Bc g 0 #^#p'7E / 4d~R9`432*@B1B4B<C'5132*DhM_<=&?Dh);Pg2a-0432*@3@B<C),&?@|If25432sD02?&?2*Dh<=&96Da4:9QPr1W);Pg1Bc?2kw_nGx$2*'*),+.+X25&?D?9;1B<C),&> 9;&?D`Da<CD6&?),1N&?2578LC2*'51$13)+X)G':MJ),1Bc?254@325+s9;&G1B<C'5<C@B13@NPR),4g-0/0p0L=<C@Bc0<=&07s'*)_D02L=<=p04:9;4B<C2*@$Pr),4N1Bc?2@9;+X2-0/04B-")8@:2),&d9i+.<C@B/0&?D02543@B13)_)GD`Pr),/0&?D?9;1B<C),&Vj

+X),4326-04:9,'51B<C'Y9;Lg-043),p0LC25+ IN<=1Bck 9;1Bco<C@i1Bc?2q4:9;1Bc?254X'*),&aP^/?@B<=&07Ig9*F1Bc 9;1kmldn(& 9;+X2*@B- 9,'*2*@9;432i432PR254B432*Dd13)qPr43),+ IN<=1Bc0<=&h2a-0432*@3@B<C),&?@Y !|254328>9;&),&aL=<=&?2i13)G),LDa<C@B-0LU9YFG<=&07643),/078c0L=FbINc 9;12Y9,':c2a-0432*@3@B<C),&+s9YF`@325LC2*'51NIK),/0LCDbp"2m432Y9;L=L=F6/?@32Pr/0Lj

k 9;1BcJ7V25&?254:9;1B<C),&613)G),LC@K2_<C@31&?)YI(<=&q@:25[V254:9;L kmldn%z@>T25& 9;p0L=<=&07i-"),<=&G1y9;&?D_t'5L=<C'3MJ9,@:@325+Wp0L=FX);Pp 9,@B<C'k 9;1Bcb2a-0432*@3@B<C),&?@Y>0p0/01N1Bc?25<=4|2_-0432*@3@3<=[V25&?2*@3@N<C@N4:9;1Bc?254|L=<=+.<=132*Duj

xgc?2 ?A@325&?251@B/04B[V25FO@B-2Y9;Ma@PR),4c 9;43Da&?2*@3@.);P$k 9;1Bc>13)G)0 |/?2*@B1B<C),&?@s9;p),/01ic?)I 13)'*),&?@31B4B/?'51k 9;1Bc2_-0432*@:@B<C),&?@NIK254321Bc?2+X)8@B1|9,@BMV2*D`);Pz9;L=Lkw_nGxT/?2*@B1B<C),&?@j

>')''I NLNMOE7B G JUE/", I 6E-ES6R)' 6%,7& L(,/34*-RK6,,MOG

Q<

C^J;DLZ@IlF]C^JMrCPORz5HJCPB%IbMNK6CFZT Q(LK6OJLZFZUxUxMrCO

kw_nGx<C@mD02*@B<=78&?2*D)Y[V2549XP^/0&?'51B<C),& 9;Lv- 9;4:9,Da<=78+>IN<=1Bc@B1B4B/?'51B/04:9;Lv1325+.-0LU9;132e432*'5/043@3<C),&>9;&?Db[89;4B<]9;p0LC2*@1Bc 9;19;432$9,@3@B<=78& 9;p0LC2N),&0L=F.9;1z1Bc?2gp2578<=&0&0<=&07W);P@31tF_LC2*@Bc?2*251z),4z1325+.-0LU9;132N<=&G[V)G'Y9;1B<C),&jn2Y9;4B&0<=&0713)+s9,@3132541Bc?2g1B4B<C'3Ma@);P 1Bc?2NP^/0&?'51B<C),& 9;L?-043),784:9;+.+.<=&07e1B4:9,D02gc 9,@13)mp2N)Y[V2543'*),+X2pGFe1Bc?2-043),784:9;++X254Y>T&?)+s9;1B13254zINc 9;1Yj &TF_If9*FV>GIN<=1BcX1Bc?2gLC)_)8@328>T@31B4B/?'51B/04:9;L?+s9;13'3c0<=&07i);P"- 9;1B13254B&?@Y>_9 )YIN784:9;-0c?25413)_),L);P'*),/043@32m<C@$9c?25L=-j

7#¤ $ '& & l

L=13)Y[89() @kmldnwG-GFe<C@m-043),p 9;p0L=F1Bc?2p"2*@31AM_&?)YIN&hkmlnt@B-2*'5<U9;L=<Y2*DE2*Da<=13),413)GD?9YFVj%t1APR2Y9;1B/0432*@kw_nGx 2*Da<=1B<=&07s/0&?D0254A),&aL=<=&?213)_),L1B<=-78/0<CD?9;&?'*28>9;&?DDa<;:254325&G1m9;p?@31B4:9,'5132*D[_<C25I@$),&b@B1FGLC2*@3c?2*2513@Yjw_':c?25+s9Q9*If9;432ikw_nGx ¨ js2*Da<=1B<=&07?>?D025p0/07878<=&07J9;&?D1B4:9;&?@yPr),4B+s9;1B<C),&b<C@N&?)YI@3/0-0-"),4B132*Du>0p0/01$1B4:9;&?@yPR),4B+s9;1B<C),&?@N9;-0- 9;4325&T1BL=Fs),&0L=F.If),4BM.P^43),+ IN<=1Bc0<=&q1Bc?2|%jG%t1g9;LC@3)p)V9,@B13@1Bc?2 Rt/?@B/ 9;L TNk 9;1Bc Q 9;&?Dk 9;1Bc ¨ -"),<=&G1y9;&?D_t'5L=<C'3M-043),13),1tF_-0<C'Y9;L2a-0432*@3@B<C),&7V25&?254:9;13),43@W9;&?DE9;&k 9;1BcE25[89;L=/ 9;13),4Y>up0/01&?)@B1:9;1B<C'e9;& 9;L=F_@B<C@NPr2Y9;1B/0432*@Yj

wG1FGLC2px|<C@B<C),&>_9;LC@3)|P^43),+ L=13)Y[89a>,PR2Y9;1B/0432*@v7V25&?254:9;1B<C),&X);P kw_nGxo'*)_D02KPr),4z9$0a2*D@325LC2*'51B<C),&.);P),/01B-0/01LU9;&078/ 9;7V2*@Y>"9;&?D`4:9;&?D0),+kmldnE<=&0-0/01Yj

wG1FGL=/?@wG1B/?Da<C)c 9,@9;p),/011Bc?2z@9;+X2vPr2Y9;1B/0432*@9,@ukmldn6wG-TFV>;IN<=1Bce9N'*),/0-0LC2K);P_<=&G1325432*@B1B<=&07m9,D0Da<=1B<C),&?@ &kw_n_x-043);?LC254Y>T9;&?D.9AD?9;1:9Qt),4B<C25&T132*DXD025p0/0787V254z1Bc 9;1vIN<=L=Lap 9,'3MG+s9;->G9;1z9$+X),/?@32N'5L=<C'3Mi),&.@3),+X2kw_nGx ),/01B-0/01Y>v13)b1Bc?2skw_nGx<=&?@B1B4B/?'51B<C),&H1Bc 9;1i'5432Y9;132*DO<=1Yjnu<=MV2qkmldnwG-TFV>wG1FGL=/?@XwG1B/?Da<C)dc 9,@@3':c?25+s9Qt@B/0-0-),4B132*D.'*)GD02K[G<C25I@v9;&?Di'*),+.-0LC251B<C),&.9;&?D9|DaFG& 9;+.<C'fD025p0/0787V254Y>8p0/01&?)$@B1:9;1B<C'g9;& 9;L=F_@3<C@Y>+e/?'3cbLC2*@:@N[,9;L=<CD?9;1B<C),&j

qC Q Y

E2p 9,@:2),/04-043),-")8@9;LuPr),4$9i13)_),L<=+.-043)[G<=&07X1Bc?2kw_n_x9;/01Bc?),4B<=&07q@:'*25&?2@B<=+.-0L=F6),&

•c 9;1NIf2p"25L=<C25[V2IN<=L=Lp"2m/?@:2P^/0Lu<=&d9i-04:9,'51B<C'Y9;L1tF_-"2t@9QPr2mkw_nGx ¨ jX9;/01Bc?),4B<=&07q'*),&G132_1

•c 9;1NIf2mPr),/0&?D13)p"2m-)8@3@B<=p0LC28>0p 9,@:2*D`),&b2_1325&?Da<=&07s1Bc?2M ¨ P 9;L=7V),4B<=1Bc0+

9;&?DDa<C@B43257T9;43DH'*),&?@B<CD0254:9;1B<C),&?@s9;p),/01e7V25&?254:9;LfPR2Y9;1B/0432*@i1Bc 9;19;432q&?),1e4325LU9;132*DH13)d1Bc?2J9;L=7V),4B<=1Bc0+>9;&?DZ9;p),/01.7V25&?254:9;L$/?@9;p0<=L=<=1tF L=1Bc?),/078c9;L=L$1Bc0<C@X'*254B1:9;<=&0L=F<C@.<=+.-"),4B1:9;&G1.PR),4.1Bc?2@B/?'*'*2*@3@.);P9'*),+.-0/013254|13)G),L>0<=1N<C@&?),1|9'*25&T1B4:9;L@B/0p(Sy2*'51);Pv1Bc0<C@If),4BM"j

SUTVT2W XZYVY2[F[V[\2TUg.\ZeFgBhiYaW9jUgN`N]5eaT9_N`9b \OSUT2hVY SUTVT2W XZYVY2[F[V[\2Ta] !aTN]U`,_Fg\feFgBhiY

QQN

£*Nu % & #"& & U!l D'&%

xgc?29;L=7V),4B<=1Bc0+ pTF M ¨ P JM ¨ P IN<=L=LD0)ep 9,@B<C'A[89;L=<CD?9;1B<C),&6);P-04:9,'51B<C'Y9;Lukw_n_x>09;&?DJ@:),+X2AD?9;1:9e2a1B4:9,'1B<C),&b'Y9;&d2Y9,@B<=L=Fqp29,D0D02*Duj

wG/0+.+s9;4B<*<=&07e1Bc?2g-043),p0LC25+X@<=&-04:9,'51B<C'Y9;L D025[V25LC),-0+X25&T1f);P 4325L=<U9;p0LC2gkw_nGx1Bc 9;1If2gIN<=L=L01B4BFe'*),/0&T13254pGFJp0/0<=LCDa<=&07q13)G),LC@NPr),4N1Bc?25+

•<=&?D`~r),&aL=<=&?28>GDa/04B<=&072*Da<=1254B43),43@v1Bc 9;1+s9;MV2N@3),+X2f1B4:9;&?@yPr),4B+s9;1B<C),&s432*@B/0L=13@vp"2*'*),+X2g<=&G[,9;L=<CDIN4B1Yj13)1Bc?2),/01B-0/01$@:'3c?25+s9aj

•%tL=L=/?@B1B4:9;132 )I@$);P'*),&T1B43),Lv9;&?D`&?)GD02*@p"251IK2*25&b1325+.-0LU9;132*@~r),&aL=<=&?28>?Da/04B<=&07s2*Da<=1j

•%tL=L=/?@B1B4:9;132d9;-0- 9;4325&T1BL=F\-0LU9;/?@B<=p0LC28>fp0/01q&?),&?2_<C@B1325&G1 )I@~r),&aL=<=&?28>gDa/04B<=&07O2*Da<=1j(xgc0<C@X<C@'*),+.-0LC25+X25&T1:9;4BF`IN<=1Bc1Bc?2e9;p")[V28j

•A25132*'51$k 9;1Bc&?)_D02@325LC2*'51B<C),&b2a-0432*@3@B<C),&?@N1Bc 9;1$&?25[V254$@325LC2*'51),4+s9;13':c9;&TF_1Bc0<=&07?j

•A25132*'51D02Y9,Dh'*)_D028>9;&?DhD025132*'51'*),&T1B43),L )YI@1Bc 9;1&?25[V254432Y9,':c9;&TF_1Bc0<=&07b'*),&T1B4B<=p0/01B<=&07d13)),/01B-0/01Yj

•8f)_)8@B1|-"254yPR),4B+s9;&?'*28 ;m25&?254:9;132i-04321B4:9;&?@yPR),4B+X@A<=&9q@B1B432Y9;+.<=&07J1B4:9;&?@yPr),4B+s9;1B<C),&hLU9;&078/ 9;7V28>'5/01B1B<=&07q9*Ig9*FD?9;1:91Bc 9;1$<C@N&?25[V254/?@32*D6pGFJ1Bc?2+s9;<=&`1B4:9;&?@yPr),4B+j

xgc?2mL=<C@B1);Pv),1Bc?254N&0<C'*251B<C2*@N13)<=&?'5L=/?D02<=&61Bc?2m/0L=1B<=+s9;132kw_nGxS13)_),Luc 9,@g&?).25&?Duvkw_nGx7V25&?254:9;13),43@7V25&?254:9;1B<=&07hkw_nGx@PR),4i9@3251);P-043),13),1tF_-"26<=&0-0/01X9;&?DH),/01B-0/01D0)_'5/0+X25&T13@d~^1Bc?2543269;432q<=&a?&0<=1325L=F+s9;&GF@3),L=/01B<C),&?@PR),4$2Y9,':c'Y9,@32>?kw_n_x '*),+.-0<=LC2543@|1Bc 9;1|'*),+.-0<=LC2PR9,@313254kw_n_x -043)G'*2*@3@:),43@NPR),4$),&?2<=&0-0/01LU9;&078/ 9;7V2s9;&?Dh),&?2i1B4:9;&?@yPR),4B+ K ),49J'*),+.-0<=LC254W'*),+.-0<=LC254Y>7V25&?254:9;1B<=&07-043)_'*2*@3@3),43@APR),4),&?2<=&0-0/016LU9;&078/ 9;7V28>m9;&TF\1B4:9;&?@yPR),4B+j -|/01B-0/01`@3'3c?25+s9O<=&aPR254325&?'*225&078<=&?2*@qPR),4q<=&0-0/01`@3':c?25+s9,@9;&?D1B4:9;&?@yPR),4B+X@Y>?),4$1Bc?2),1Bc?254If9YFb9;43),/0&?Du> 9;LC@3).If),/0LCD`p"2m&0<C'*213).c 9*[V2 ?@:)IK),/0LCDd9.1B4:9;&?@yPr),4B+'5LU9,@:@9;& 9;L=F Y254Y>V1Bc 9;1'*),/0LCD1B4:9;&?@BLU9;132g- 9;4B1z);Pu9;L=La);Pu9|1B4:9;&?@yPr),4B+ 13)9A@B<=+.-0LC2549;&?DiP9,@B13254v1B4:9;&?@yPR),4B+s9;1B<C),&LU9;&078/ 9;7V28j L=Lu1Bc0<C@PR9;L=LC@Np25FV),&?D61Bc?2<=&G1325&?D02*Db@3'*),-2);P1Bc0<C@$-043)\Sy2*'51Yj

;6HJMrL6;DUx;DCIb@gz3K6L_F_QbL6F/B%I(McB%FZTIbKZK/T

xgc?25432i9;432@3),+X2p 9,@B<C'm432*G/0<=4325+X25&T13@$Pr),4$9.13)G),Lu13)p29;-0-0432*'5<U9;132*D9;&?D6/?@:2*Db9;1$9;L=L

Q j%t1e+W/?@B1p2J9;-0-0L=<C'Y9;p0LC2qPR),4e432Y9;L]If),4BLCD1:9,@BMa@Yjb?),4.),/04ikw_n_x 13)G),L>v1Bc 9;1+X2Y9;&?@i1Bc 9;11Bc?213)G),L

•lb/?@B1NIf),4BM6IN<=1Bc1Bc?2mkw_n_x xz2543@3<C),& ¨ jLU9;&078/ 9;7V2

•lb/?@B1NIf),4BM6IN<=1Bc1Bc?2m+X)8@B1IN<CD025L=FJ/?@32*D@3':c?25+s9LU9;&078/ 9;7V2*@

¨ j%t1N+e/?@B1|9;-0-2Y9;4N13).p2);P+X),432c?25L=-b1Bc 9;&1B43),/0p0LC28

•%t1+e/?@B1p2K9;p0LC213)|9,'51B/ 9;L=L=F+.<=1B<=7T9;132g9;1LC2Y9,@B1@3),+X2);P01Bc?2z/?@:254<) @D0),/0p013@v9;&?DW'*),&?'*254B&?@Yj

Q %

•%t1N+e/?@B1-254yPr),4B+ If25L=L>?IN<=1Bc?),/01|9;&0&?)FG<=&07J@BL=/07878<C@Bc0&?2*@3@Yj

•%t1N+e/?@B1$D025L=<=[V254$2Y9,@B<=L=FJ/0&?D02543@B1:9;&?D?9;p0LC2W432*@B/0L=13@Yj

•%t1N+e/?@B1&?),1gPR),43'*21Bc?2m/?@325413)1Bc0<=&0M`);P25[V254BFG1Bc0<=&07X<=&9i&?25I 9;&?DDa<;:u254325&T1Ig9*FVj

aj%t1N+e/?@B1p29;p0LC2m13)X'*),+.-25132IN<=1Bc<=13@$9;L=13254B& 9;1B<=[V2*@YjK?),41Bc?2kw_n_x @3251B1B<=&07?>01Bc?25F`9;4328

•A25p0/0787V2543@

•l9;&G/ 9;L1B4B<U9;L4B/0&?@

xgc?2.)[V254:9;L=L-043),p0LC25+ );Pf1Bc0<C@AIK),4BM<C@|13)6@Bc?)I 1Bc 9;1A<=1m<C@|PR2Y9,@B<=p0LC2i13)J'*),&?@31B4B/?'519q-04:9,'51B<C'Y9;L13)_),L><=&G1325784:9;132*Db<=&G13)s9;&b2*Da<=13),4Y>01Bc 9;1NPr/0L]?L=LC@$9;L=L1Bc0<C@j

L=1Bc?),/078cZkmldn mxNM oP <C@X@B/04B-04B<C@B<=&078L=F\'Y9;- 9;p0LC2d);PmD02*@:'54B<=p0<=&07+X)8@B1s);P1Bc?2@:'3c?25+s9,@q/?@32*D ><C@6'Y9;&(p"2b-0432*Da<C'5132*D13)Op2*'*),+X2b784:9,Da/ 9;L=L=F\-0c 9,@:2*D),/01NKQj LU9;4B7V2b&G/0+Wp254`);PW-043),-")8@9;LC@XPR),4@B1B43),&07V254Akmldn@3':c?25+s9XLU9;&078/ 9;7V2*@Ac 9*[V2i25+X254B7V2*Dujz-$Pz1Bc?2*@328> V) @|kAlnw_':c?25+s9JA2*@:'54B<=-01B<C),&~^kw_ M Q7P M ¨aP 9;&?D M P z9;&?D- w_%ywX)G$25LU9Q+z;dM P c 9Y[V2$p2*'*),+X21Bc?2$+X)8@B1IN<CD025L=F./?@32*Du>GIN<=1Bcskmlnw_':c?25+s9s9,@N1Bc?2)/s'5<U9;L=L=F`25&?D0),43@32*DSVS|2*'*),+.+X25&?D?9;1B<C),&j

8g2*'Y9;/?@32N1Bc?2kw_n_xoLU9;&078/ 9;7V2<C@z&?)YIoP9,'5<=&07e9A1B4:9;&?@B<=1B<C),&sP^43),+xz2543@B<C),& Q 13)zxz2543@B<C),& ¨ >8If2p25L=<C25[V21Bc 9;11Bc?26'5LU9;<=+IN<=L=Lg),&0L=Fc?),LCDO<]P|kw_n_x ¨ <C@@B/0-0-"),4B132*Duj LC@3)0>@B<=&?'*2q1Bc?2J+X)8@B1iIN<CD025L=FO@3':c?25+s9LU9;&078/ 9;7V2J<=&1Bc?2XPr),432*@:2*2Y9;p0LC2XPr/01B/0432q@:2*25+X@13)dp"2.1Bc?2qE),4BLCDO<CD02sE25pf),&?@3),4B1B<=/0+v) @~^VNkmldnw_'3c?25+s9 + >9;&?DO@B<=&?'*2Xkw_n_x ¨ <=13@325L]P13)d@3),+X2s2a1325&T1D025-25&?D0@e),&OkAlnSw_':c?25+s9a>vIK2qIN<=L=L2a1325&?D`1Bc?2M ¨ P @31:9;1B<C'mkw_n_x [89;L=<CD?9;1B<C),&d9;L=7V),4B<=1Bc0+13)If),4BM6IN<=1Bc1Bc 9;1$@3':c?25+s9LU9;&078/ 9;7V28j

£*#t &"l

xgc?2'*),432W'5LU9;<=+<C@N1Bc 9;11Bc?2M ¨ P @31:9;1B<C'[,9;L=<CD?9;1B<C),&9;L=7V),4B<=1Bc0+ 'Y9;&p22_1325&?D02*D13)0

•E),4BMqIN<=1Bckw_n_x ¨ j

•E),4BMJIN<=1BcbkAlnOw_'3c?25+s9a> IN<=1Bc?),/01A9;-0-043)Y_<=+s9;1B<=&07J1Bc?21FG-2@BFa@B1325+X@gPR),4@B1B4B/?'51B/0432*@Y>"9;&?DIN<=1Bcb),&0L=FJ[V254BFsPR25I 9;-0-043)*a<=+s9;1B<C),&?@A);PvD?9;1:91FG-2*@

6,HW B$+"A8(ES')34;2576PN'68($+*-E-ES*S6%,@9I;U"AE-L(9+*-"A, 9+576Q94*-;I876%;U'K& L/BD", $+'=&('/,/*-,/.9+5/'XB($+"8/E-'=3 '=,H9+*-$+')E-W9EG8/L9 9+5/6%96B(B($+"N6%R 5V*S;F,("9 PN')$UWX3P6%$+MA')9!68(ES'< '="AB(E-' 6Q$+'0,/"%9F.A'=,(')$!6E-E:W ,("9CYF*-E-ES*-,(.P9+" $+'=E-'K6%$+, G ,6 ;UL($ PN')WP8HWIKJ2MmE "%1?6E-E7PA6%E-* &Q R >R!5/'=3P6 ; 'DC(634*-,/'=&PY#')$+' "1 6 ES6,(.AL/6.A'0R)E 6%;U;C9+576%9 R="AL(E &6; Y#'=E-E

576PN' 8D'='=, 'DCB($+'=;U;U'K&*-, A 'ETE-'K6A&*S,(.9+"P9+5/'@L('=; 9+*-"A,YF5/')9+5(')$ 9+5('28D')9U9+')$ 'DCB($+'=;U;U*KPN'),/'=;U;0"%1lQ R >R!5/')3P6P*-;.A'=,(')$!6E-E:W ,("9F,('='K&('=& E(,/"9FL(,7&')$+; 9+"H"@& E("$O8D"9+5 G '05("ABD' 9+5/6%9C9+5/' 6%,/; Y#')$O*S;,/"%9CWH')9FL(,7&(' $+; 9+"H"@& GU PN'=,V*:1dQ R6B(B/E-*-RK6%9+*-"A,&'=;U*-.A,(')$+; ;U5("AL(E &X1"$O9+5/'034"; 9OB76%$U9O,("9O,/'='=&V6 PN')$UWX; 9U$+",/.4ES6,(.AL76%.A' R=ES6;U;BE/9+5/')W

YF*-ESE 8D' ,/')'K&(*-,/.2,7634');UB76R)' ;UL/B(BD"$U9C1"%$O*S,H9+')$+"BD')$!68(*-ES*:9W9E76%,7&3P6%,HWX6B/B(E-*SR=6%9+*-"A,(;FYF*-E-EL(,7&"AL/89+'K&(E:WP8D'0&'=;U*-.A,('K&9+"2Y "%$+MXYF*:9+5 ;U"34' "1 9+5('*Q0> ;UBD'=R=*27'=&X3P6%*S,(; 9U$+'K63 &(6%9!6 1J"$+3P6Q9O6B/B(E-*SR=6%9+*-"A, E-*-MN' 9+576Q9F"1 V*-R)$+";U"1J94R='FG @ 9 *-;2,("9 'K6; W ;+6KW 6,HW@9+5/*-,/.&'7,(*-9+*KPN'P6%8D"AL9 9+5('P1JL(9+L$+'FEG6,7& 9+5('41L(9+L$+'P;UR 5('=3P6 ;U*:9+L76%9+*-",*-, B/6%$U9+*-R=L/ES6Q$G

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

Q<w

Applicability

Performance

Precision

\ve;:]8. ;6#&3$!cN "Q .8#*8$x : $e;*:d-$!&$!& \A 9&J#"8$5 );N "QWm]$!*EN OBQ ""9:; H 9&G-"&$c$!*E 9&Gg-2'):;$!"6?

• 254yPR),4B+ 9,'*'*25-01:9;p0L=F`<=&`1B<=+X2W9;&?D`+X25+X),4BFV> 25[V25&`PR),4NLU9;4B7V2@B1tF_LC2*@Bc?2*2513@$9;&?DLU9;4B7V2@3'3c?25+s9,@j

• - 9;4B1P^43),+[,9;L=<CDa<=1FV>a9;LC@:)W@B/0-0-0L=FX),1Bc?254K[,9;L=/ 9;p0LC28>_&?),&T1B4B<=[_<U9;L"<=&0-0/01f@3':c?25+s9Qt@325&?@B<=1B<=[V2m'*)_D029,@3@B<C@B1g<=&aPR),4B+s9;1B<C),&j

E2IN<=L=L@32*25Mq13).@3c?)YI 1Bc0<C@Y> 9;&?Du

•A25[V25LC),-o9d2_-0LC),4:9;13),4BFEkw_n_x 2*Da<=13),4.9;-0-0L=<C'Y9;1B<C),&>D025+X),&?@31B4:9;1B<=&071Bc 9;1i1Bc?2q132*'3c0&0<CG/?2q<C@-04:9,'51B<C'Y9;Lj

• 254yPR),4B+> 9;& 9;L=F Y2W9;&?D`25[89;L=/ 9;132132*@B14B/0&?@),&b432Y9;L@B1tF_LC2*@Bc?2*2513@Yj

•?),4NPR2Y9;1B/0432*@NINc0<C'3c9;432m&?),1<=&b'*),+.+X),&/?@32mFV251Y> '*),&?@B1B4B/?'51132*@B1$'Y9,@:2*@Yj

£*#¤ & &

va-0L=<C'5<=1$&?),&a7V)V9;LC@A9;4328

• PR),4B+s9;Lu-043)G);P);Pv1Bc?2'*),4B432*'51B&?2*@3@$);P),/04|9;-0-043)V9,':c

• '*),+.-0LC25132q1B/013),4B<U9;Lf<=&H9;L=L1Bc?2q132*'3c0&?),LC),78<C2*@i<=&G[V),L=[V2*DuXxgc?2X432Y9,D0254i<C@e9,@3@3/0+X2*DE13)M_&?)YIp 9,@B<C'KkAlnz>QkAln6AxNS9;&?Dikw_n_x Q jkAlnw_'3c?25+s9a>8kw_n_x xz2543@B<C),& ¨ ':c 9;&07V2*@z9;&?Dek 9;1Bcxz2543@B<C),& ¨ 9;432<=&G1B43)GDa/?'*2*Dbp04B<C2 ?FV>01Bc?),/078cj

• '*),+.-0LC25132-043)_Da/?'51B<C),&atG/ 9;L=<=1tFkw_nGx2*Da<=13),4<=+.-0LC25+X25&T1:9;1B<C),&j

•A251:9;<=LC2*Db'*),&?@B<CD0254:9;1B<C),&d);P25[V254BF9,@B-"2*'51);P25[V254BFqPr2Y9;1B/0432);Pv1Bc?2LU9;&078/ 9;7V2*@$<=&T[V),L=[V2*Duj

¨

£* 7 ''% ' %

xgc?2$432*@B1);Pu1Bc?2If),4BMi-043)_'*2*2*D0@g9,@PR),L=LC)YI@Yv<=43@B1Y>V1Bc?2+X)8@B1z<=+.-),4B1:9;&T1f132*'3c0&?),LC),78<C2*@g),&s1Bc?2Nkmln9;&?DZkw_n_x @:'*25&?2d9;432p04B<C2 ?Fo<=&G1B43)GDa/?'*2*Du>IN<=1Bc@3),+X2d25+.-0c 9,@B<C@q),&kAlnw_':c?25+s9a>@B<=&?'*2b1Bc0<C@|2*'*),+.+X25&?D?9;1B<C),&O<C@e@3)`c 9;43Dh13)'*),+.-04325c?25&?DO1Bc 9;1WIf2.IN<=L=L1B4BF13)b'Y9;-01B/0432s<=13@+X2Y9;&0<=&07<=&),/04)IN&Pr4:9;+X25IK),4BM> 9*[V),<CDa<=&0769;&TF6432PR254325&?'*213)1Bc?2mPR),4B+W/0LU9;1B<C),&?@|<=&1Bc?2|2*'*),+.+X25&?D?9;1B<C),&jkmldnW) @)IN&s@3'3c?25+s9LU9;&078/ 9;7V28>TmxN>,c 9,@9;LC@3)p2*25&.<=&?'5L=/?D02*D.<=&.1Bc?2gPr4:9;+X25IK),4BM~R9;&?D.<=&.1Bc?2N2a-0LC),4:9;13),4BF9;-0-0L=<C'Y9;1B<C),&h-043),784:9;+q>IN<=1Bch9s'*),&?'*25-01B/ 9;Lv+X)_D025Lv1Bc 9;1A'*)[V2543@mp"),1BcjAxgc?2W432Y9,D0254A<C@9,@3@B/0+X2*Dd13)M_&?)YI p 9,@3<C'kAln9;&?D`kmln +A9;+X2*@3- 9,'*2*@Yj

xgc?2KLU9;4B7V2*@B1@:2*'51B<C),&e<C@D02*Da<C'Y9;132*DW13) `3c 0o/10 =bn\4DF 4>Qp"2*'Y9;/?@32f9N432*D02*@B<=78&);P?1Bc0<C@If9,@),&?2K);P01Bc?2K+X)8@B1<=+.-),4B1:9;&T1'*),&T1B4B<=p0/01B<C),&?@m);Pz1Bc0<C@|IK),4BM> 9;&?Db<=1$If9,@|c?25432i@3),+X2<=&T1325432*@31B<=&07J&?25IDa<C@3'*)Y[V254B<C2*@AIf25432+s9,D028E2mc 9*[V2<=+.-043)[V2*D1Bc?2p2*@B1gM_&?)YIN& )I 9;L=7V),4B<=1Bc0+ @3<=78&0<] 'Y9;&T1BL=F`<=&b9;L=L+s9aSB),4$9,@B-2*'513@Yj

@32*'51B<C),&eIf9,@D025[V),132*D13)gPR),L=LC)YIN<=&07A/0-e),&1Bc?2KDa<;:254325&G1 0 g g1=]F^6 0 #_F^` / 4f);Pa1Bc?2432*@B/0L=1);P )YI9;& 9;L=F_@3<C@K ?43@B1N9;&?DsPR),4325+X)8@B1f[,9;L=<CD?9;1B<C),&>09;&?D`9;LC@3)9;L=L 1Bc?2A@B+s9;L=LC254N9;L=7V),4B<=1Bc0+X@fPr),4g2*Da<=13),4N25&0c 9;&?'*25+X25&T13@Yj

<=& 9;L=L=FV>?If2-0432*@325&G1$25[,9;L=/ 9;1B<C),&D?9;1:9.9;&?Db9.'*),&?'5L=/?@B<C),&j

!51

.

E2f@B1:9;4B1v),/01pGF<=&T1B43)_Da/?'5<=&07m1Bc?2kmldnJ132*':c0&?),LC),78<C2*@z9;&?DW+X)_D025LG/?@:2*Du>V9;&?DW1Bc?25&i-0432*@325&T19$/0&0<] 2*D+X)_D025L );Pu1Bc?21IK)e+X)8@B1IN<CD025L=F./?@:2*Ds@3':c?25+s9LU9;&078/ 9;7V2*@Y>amxN 9;&?DXkmldnhw_'3c?25+s9a>_-043)[G<CDa<=&07i1Bc?2&?2*'*2*@3@9;4BF6@:'3c?25+s9<=&aPR),4B+s9;1B<C),&PR),4N1Bc?2'*25&T1B4:9;Lkw_n_x )I 9;& 9;L=F_@3<C@$9;L=7V),4B<=1Bc0+-0432*@325&G132*D&?2a1Yj

V rz

v ^ NPOBQ ""9-:;@#&$J&g5"\FG\!^-5&FGI&2`3FG"9_$g*E-*E&2@]=p-p<-.$cFG-$cE5*E G')\$,c:]? l"!WEFGI$]$-^=X &!#&25* =4 &&-&-?

Q 5? O<"9gJ/

wG<=&?'*2ikmldnH<C@yS /?@31A9s+s9;4BMG/0-h@BF_&T1:9QPR),4m),43D025432*Du>LU9;p"25LC2*D9;&?D/0&04:9;&0MV2*Dd1B432*2*@AIN<=1Bch'3c 9;4:9,'513254D?9;1:9a>a1Bc?2ADa<;:254325&G1N@3'3c?25+s9iLU9;&078/ 9;7V2*@gc 9Y[V2A),&?2|1Bc0<=&07<=&J'*),+.+X),&xgc?25Fq9;432$4325-0432*@:25&T1:9;1B<C),&?@);P@3),+X2W'5LU9,@3@);P1B432*2LU9;&078/ 9;7V2*@Yjgw_'3c?25+s9.LU9;&078/ 9;7V2*@$PR2Y9;1B/0432'*),&?@B1B4:9;<=&T13@A),&@325[V254:9;Lv9,@B-"2*'513@>0@3),+X27V),<=&07Xp25FV),&?D`1B432*2LU9;&078/ 9;7V2*@

•wG1B4B/?'51B/0432);P 20 EN> m gK D02513254B+.<=&?2*@1Bc?2s~^1B432*2g@31B4B/?'51B/0432);P<=&?@31:9;&?'*2D0)G'5/0+X25&G1$+s9;4BM_/0-

¨<Q

•wG/0p0LU9;&078/ 9;7V2*@.PR),4 A 0 # 0 K D02513254B+.<=&?21Bc?29;L=LC)YIg9;p0LC2bD?9;1:91FG-2*@PR),4132_1s9;&?DZ9;1B1B4B<=p0/0132LC2Y9*[V2*@$<=&`<=&?@B1:9;&?'*2D0)_'5/0+X25&T13@

•f),&?@B1B4:9;<=&T13@),& F / #p' I E>F_#_n K @3-"2*'5<]PrF\432PR254325&T1B<U9;LW),4J/0&0<CT/?25&?2*@:@`'*),&?@B1B4:9;<=&T13@`<=&S<=&?@B1:9;&?'*2D0)G'5/0+X25&G13@

• #&%.'>Ei'*),&?@31B4:9;<=&T13@Y> );P^1325&b'Y9;L=LC2*DRtp0/?@B<=&?2*@3@N4B/0LC2*@UT

E2IN<=L=LPr)_'5/?@),&1Bc?2m+s9;4BM_/0-b@B1B4B/?'51B/0432i9;&?DD?9;1:9LU9;&078/ 9;7V2e9,@3-"2*'513@Nc?254328> 9;&?D`<=78&?),432<=&T1325784B<=1F9;&?D),1Bc?254X'*),&?@B1B4:9;<=&G13@X25&T1B<=4325L=Fq<=43@B1BL=FV>z1Bc?2sPR),4B+X254X9;-0-0L=F/0&0<=[V2543@:9;L=L=FO<=&kAlnz>INc?25432Y9,@.1Bc?2LU9;1B13254m9;432m4:9;4325L=FJ/?@:2*Du>?9;&?D@32*'*),&?DaL=FV>01Bc?2LU9;1B13254A9;432&?),13),4B<C),/?@BL=F6c 9;43D`13)X9;& 9;L=F Y2@B1:9;1B<C'Y9;L=L=FVj

M ä¨\P -043)Y[_<CD02*@J9PR),/0&?D?9;1B<C),&Pr),4X1Bc?2bD02?&0<=1B<C),&?@69;&?D\-043),-"254B1B<C2*@J);P1Bc?2 Ef' Iom = 0 E #_Ei' '= 0o/JIom(0QI 'D4@B/0p?@:251z);P 1B432*2fLU9;&078/ 9;7V2*@Yj M ¨<Q>P <C@z9;&X2Y9;4BL=Fe':c 9;4:9,'513254B<9;1B<C),&J);P"1Bc?2K+X)8@31z'*),+.+X),&X@3'3c?25+s9m'5LU9,@3@:2*@Y>9;LC),&07eIN<=1Bcs'5LC)8@B/0432N-043),-254B1B<C2*@f9;&?Dd~^&?),&at@B1:9;1B<C'$D0)_'5/0+X25&T1[,9;L=<CD?9;1B<C),&69;L=7V),4B<=1Bc0+X@PR),4z1Bc?25+jxgc?29;4B1B<C'5LC2A9;LC@3)@B/0787V2*@B13@f9;&X<=&T1325432*@31B<=&07?>T-)YIf254yP^/0L9;&?Ds2As'5<C25&T1KFV251z/0&?2a-0LC),<=132*Dq'5LU9,@3@);P432578/0LU9;4K1B432*2LU9;&078/ 9;7V2*@A'Y9;L=LC2*DEf'D4>#_E 0 F / 'iAo@U6f` 2 g.'7#_F_#_F_` / = 03/CIom.0<I 'D45j

M Q %\P 78<=[V2*@9|&0<C'*28>,p04B<C2P"9;& 9;L=F_@3<C@);P 1Bc?2-043),-254B1B<C2*@);P @3),+X2f);P 1Bc?2f+X)8@B1-"),-0/0LU9;4@3':c?25+s9$LU9;&078/ 9;7V2*@'5LU9,@3@:2*@Y>|9;&?D(-043),-)8@32*@`9;&9;L=13254B& 9;1B<=[V2h':c 9;4:9,'513254B<9;1B<C),& );PW432*@31B4:9;<=&?2*D_t'*),+.-"251B<=1B<C),& LU9;&078/ 9;7V2*@>` / '>@ g 0 4 4,g1Ef'>@BòEiA '>Eq#_nDg.' 0 G>F&=]F_#_n8>ap 9,@32*Dq),&61Bc?2|LU9;4B7V2*@B1N'5LU9,@3@f1Bc 9;1f'Y9;&6p2|2As'5<C25&G1BL=Fq[89;L=<CD?9;132*D`9;&?D1FG-2*Duj

E2eIN<=L=L4325LU9;132e1Bc?2?&?Da<=&07V@m);Pz1Bc?29;p")[V2W- 9;-2543@|13)X1Bc?2eIf9*Fb<=&bINc0<C'3cIf2W/?@32W1Bc?25+>"<=&T1B43)_Da/?'*29q'*),&?@B<C@B1325&G1A13254B+.<=&?),LC),78FVjWxgc?25432Pr),4328>"IK2iIN<=L=Lvp2578<=&dpGFd9;& 9;L=F *<=&0761Bc?2e-043),-"254B1B<C2*@);PmxN 9;&?DV kmldn w_'3c?25+s9h1Bc 9;1sIN<=L=Lp"26/?@:2P^/0LNLU9;13254J),&><=&\1B432*2LU9;&078/ 9;7V213254B+X@Yj\<=& 9;L=L=FV>fIK2bIN<=L=L<=&G1B43)GDa/?'*2eD02?&0<=1B<C),&?@PR),4$9i/0&0<] 2*DmxN9;&?D`kmldnOw_':c?25+s9.+X)_D025L> 9;LC@3)iPR),4NLU9;13254/?@328j

%&ZD02*@3'54B<=p0<=&07Ekmln'*),&T1325&G1q<=&o1Bc?2`Pr),L=LC)IN<=&07?>gIK2IN<=L=L$<=78&?),432b9;L=L$),1Bc?254XM_<=&?D0@s);Pm&?)GD02*@X1Bc 9;&25LC25+X25&G13@YjZE2IN<=L=L+s9;MV2`/0-oPR),4X1Bc 9;1XINc?25&\432<=&G1B43)GDa/?'5<=&07H1Bc?25+ LU9;13254Yjxgc0<C@.<C@X&?),1sc 9;&?D0@yIg9*[_<=&07q9;1N<=& 9,D02*T/ 9,'5<C2*@$);P1Bc?2m+X)_D025L"IN<=1Bc`432*@3-"2*'51N13)[Rt432Y9;L TmkAlnh@3'3c?25+s9'5LU9,@:@32*@ 8 K /?@B<=&07s9LU9;4B7V2.25&?),/078chc 9;+.+X254Y>9;L=Lv&?)_D02iMG<=&?D0@'*),/0LCDp2e@3LU9;+.+X2*D<=&T13)6<=1 K p0/019,@mIf2.@Bc 9;L=L@32*28>"<=1m<C@&?),1&?2*'*2*@:@:9;4BFVj

NuΣ '% *

E2ep"2578<=&dIN<=1Bc9XIf9YFb2_-0432*@:@B<=&07s1Bc?2i@B1B4B/?'51B/0432W);PK9X1B432*28>"9;&?Dd<CD025&T1B<]PrF_<=&07q<=13@|&?)GD02*@j$wG<=&?'*2WIf29;432.D02Y9;L=<=&07ÌN<=1BcE@3':c?25+s9,@Y>D02*'5LU9;4B<=&07d9s?&0<=132&G/0+Wp254W);PK& 9;+X2*@Y>LC251

Σp2.9X?&0<=132X9;L=-0c 9;p251);P

& 9;+X2*@Yj

n251TΣ

p"2m1Bc?2@:251);PΣ1B432*2*@Y

Q jNLC2Y9QPyσ ∈ Σ⇒ σ ∈ TΣ

mH ')ESE E 6%ES34"; 9G #'=RK6%L/;U'X"1O*:9+; ;UL(8(9W(B(*-,/.V1J'K6%9+L$+'XYF*:9+5 cV_ X T!NW,b EQ R >R!5/'=3P6*S; "A,(E-W ;U*-,/.AE-' 9W(BD'P*:1O6%9 9U$+*-8/L(9+');CR="A,(;U*S&(')$+'K&7G 'GYF*SE-E@$+'=; 9U$+*-R)9?9+5/'#&(*-;UR=L/;U;U*-",21"%$ Q R >@R 5('=3P6O8HW 6%;U;UL/34*-,/. ,/" ;UL(8(9W(BD'G;UL/8(; 9+*-9+L9+*-"A, E6,/&$+'=B76%*:$ ES6Q9+')$G

ä¨

¨ jN<=&T13254B& 9;L&?)GD028σ ∈ Σ

9;&?Dt1, · · · , tn ∈ TΣ ⇒ σ(t1, · · · , tn) ∈ TΣ

j

E2D0)X&?),1N&?2*2*D`13)XDa<C@B1B<=&078/0<C@Bcbp"251IK2*25&b&?)_D02*@$9;&?D`1Bc?2@3/0p01B432*2*@1Bc?25FJ43)G),1Yj

+A2_1'*),+X2*@$1Bc?2:AO` 20 F / );Pz9i1B432*2 t ∈ TΣ9,@$9@B1B4B<=&07q);P& 9;1B/04:9;L&G/0+Wp2543@Y

Dom : TΣ → N∗

Dom(t) = ε ∪ iu|i ∈ 1, · · · , n, u ∈ Dom(ti)

xgc 9;1A<C@Y> 1Bc?243)_),1|&?)_D02W);Pt<C@<CD025&G1B<] 2*DpTF`1Bc?2i@B1B4B<=&07

ε> 1Bc?2

Dom9;-0-0L=<C2*@A432*'5/043@B<=[V25L=F13)q2Y9,'3c

':c0<=LCDu>9;&?Dh2Y9,'3cE':c0<=LCDti) @m),43Da<=& 9;L

i<C@m-04325-25&?D02*Dh13)`9;L=L+X25+Wp2543@);P

Dom(ti)j L=Lv':c0<=LCDa4325&);P

2Y9,':ch&?)GD02@Bc 9;432.9J'*),+.+X),&h-04320>9;&?D@3<=p0L=<=&07V@2Y9,'3chc 9*[V2X9q/0&0<CG/?28> Q t@BF_+Wp),Lv@3/ .j%&1Bc?2PR),L=LC)YIN<=&07?> IK2IN<=L=L&?),1|Da<C@B1B<=&078/0<C@Bcp251tIf2*25&9i&?)_D02W9;&?D6<=13@<CD025&G1B<] 254|@B1B4B<=&07?j

9,':cb&?)_D02c 9,@$9 /1032 ' _PR),4NkAln25LC25+X25&G13@Y>0<=1<C@ Sy/?@B1g1Bc?225LC25+X25&G1$& 9;+X28

namet : Dom(t)→ Σ

xgc?2tT/ 9;L=<] 254$<=&1Bc?2AP^/0&?'51B<C),&d& 9;+X2<=&?Da<C'Y9;132*@1Bc 9;1$<=1N[,9;4B<C2*@NIN<=1Bcd2Y9,'3cb1B432*2m<=&?@31:9;&?'*28j

?),42Y9,':ce&?)_D02u<=&91B432*2

t>;If2K+s9YFWD02?&?2K<=13@ 03/ 6 'D47#HòE,4>#_E>F /CI xgc?2f@B1B4B<=&07m);P & 9;+X2*@N~^432*'Y9;L=LG1Bc 9;1Y>

PR),4$),/04-0/04B-)8@328> 9& 9;+X2<C@|9@BF_+Wp),L<=&1Bc?2W9;L=-0c 9;p251Σ>a&?),1A9.@B1B4B<=&07Gg25&?'*),/0&G1325432*Db1Bc043),/078c9

D02*@3'*25&G1Pr43),+ 1Bc?243)_),1);Pt13)

u

anst : Dom(t)→ Σ∗

anst(n) =

namet(ε)<]P

n = εanst(n0 · · ·n|n|−2).namet(n)

),1Bc?254BIN<C@:2

f),+.-0LC25+X25&G1:9;4BF13)`9;&?'*2*@B13),4@B1B4B<=&07V@> 1Bc?2r6>%CF = A 4>#_E>F /CI );P&?)_D02 v<C@|1Bc?2@B1B4B<=&07`);P1Bc?2i& 9;+X2*@m);P

<=13@|'3c0<=LCDa4325&

chst : Dom(t)→ Σ∗

chst(v) = namet(v1). · · · .namet(vn)

%1@Bc?),/0LCD`p22Y9,@BFJ13)X@32*2m1Bc 9;11Bc0<C@N<C@$@B/ s'5<C25&T1|13).D02*@3'54B<=p"21Bc?225LC25+X25&T13@|<=&`kAlnE1B432*2*@Yj

#t !# $ '

|2*@B1B4B<C'51B<=&07bPr43),+ 03/ n Σ1B432*2*@W13)b1B432*2*@W<=&H@3),+X2X1B432*2qLU9;&078/ 9;7V28>v&?2*2*DH9If9YF);P$D02*@3'54B<=p0<=&071Bc?2

-254B+.<C@3@B<=p0LC24325LU9;1B<C),&?@Bc0<=-?@p"251IK2*25&E&?)_D02*@Y>1Bc?25<=4& 9;+X2*@Y>9;&?Dh),1Bc?254&?)_D02*@9;&?D1Bc?25<=4& 9;+X2*@Yj Rt1B432*2.9;/013),+s9;13),&(Te-2543@B-2*'51B<=[V2i9,@|pTF M ääP 9;&?D9R2a1325&?D02*D'*),&T132a1yRP^432*2i784:9;+.+s9;4UTe-2543@B-2*'51B<=[V2pGF M ¨<Q>P p"),1Bcic 9*[V2g<=&'*),+.+X),&.1Bc 9;1z9z47# 0 #p' 0 4 4DF Io/h2 ' / #<C@-"254yPR),4B+X2*D),&i1Bc?2f&?)_D02*@v);P"9;&e<=&?@31:9;&?'*21B432*28jzxgc?2e9;/013),+s9;13),&b-2543@B-"2*'51B<=[V2<C@2Y9,@B<C254N13).432Y9,@3),&9;p"),/01gPR),4B+s9;L=L=F"

¨

8:L6;D;FH]IK/UxFDIbK6CQb;DLZ@aQb;DB%IbMJ;

m2?&?2W9;&d9;L=-0c 9;p251Σ′ );P,4># 0 #p'D45j / ` / A 'j#p'>E 2 F / F 4>#_F^6zEf' Iom = 0 Ed#_Ef'f' 0om #H` 20 #H` / <C@$91B/0-0LC2

A = (Σ′,Σ, δ, F )

INc?25432Σ

<C@69,@sp2PR),4328>F ⊆ Σ′ <C@J9O@3251q);P /10 = 47# 0 #p'D4>9;&?D δ

<C@69Pr/0&?'51B<C),&ZPr43),+ 9E&?)GD023) @~^1325&G1:9;1B<=[V25L=F0g9,@3@3<=78&?2*Ds@B1:9;132A9;&?Ds<=13@K& 9;+X28>T13)9432578/0LU9;4g2a-0432*@3@B<C),&q)[V254K1Bc?2|-254B+.<C@3@B<=p0LC2$@31B4B<=&07V@)[V254$<=13@':c0<=LCD`&?)GD02*@Q) 9,@3@B<=78&?2*D`@B1:9;132*@

δ : Σ′ × Σ→ Reg(Σ′)

+A)YI>0<]Pv1Bc?254322a<C@B13@$9ePr/0&?'51B<C),&λ> 9,@3@B<=78&0<=&07X@B1:9;132*@$13)X9;L=L&?)GD02*@

λ : Dom(t)→ Σ′

@3)1Bc 9;1Pr),425[V254BF6&?)_D02vIN<=1Bc

n':c0<=LCDa4325&

∈ Dom(t)

λ(v1) · · · λ(vn) ∈ δ(λ(v), namet(v))

1Bc?25&E1Bc?2X1B432*2.<C@ 0 6f6D'pgX#p'iAOpTF1Bc?2X9;/013),+s9;13),&jJ%t&E@:),+X2432578/0LU9;4W1B432*2.LU9;&078/ 9;7V2*@Y>1Bc?25432.+s9*Fp2+X),4321Bc 9;&d),&?2'3c?),<C'*2e);P

λPr),4N1Bc?2@9;+X2m1B432*28j

l)8@B1kmldnZ@3'3c?25+s9LU9;&078/ 9;7V2*@W2a-0432*@3@432578/0LU9;4W1B432*2XLU9;&078/ 9;7V2*@432Pr),4B+e/0LU9;1B<=&07d1Bc?2XD02*@:'54B<=-01B<C),&@BL=<=78cG1BL=F6<=&1Bc?2mPR),L=LC)YIN<=&07s@32*'51B<C),&>?<=1p"2*'*),+X2*@$2Y9,@B<C25413).@32*28j

#¤ & % % ) )% #*% #" ''0

@BL=<=78cG1BL=FDa<;:254325&G1-2543@B-2*'51B<=[V2),&e432578/0LU9;41B432*2LU9;&078/ 9;7V2*@/?@:2*@2a1325&?D02*De'*),&G132_1yRPr432*2784:9;+.+s9;43@13)XD02?&?21Bc?25+

G = (Σ′,Σ, S, P )

INc?25432Σ′ 9;&?D Σ

9;4329,@m<=&1Bc?2X9;/013),+s9;13),&E-2543@B-2*'51B<=[V28>9;&?DE9;432c?25432'Y9;L=LC2*D1Bc?2 / ` / #p'>E 2 F /X0 = 49;&?D(1Bc?2 #p'>E 2 F /10 =]4>432*@B-"2*'51B<=[V25L=FVj xgc?2@:251J);P?& 9;L@B1:9;132*@6<C@J&?)I 'Y9;L=LC2*D

S>$1Bc?2@:251J);P47# 0 E7#

/ ` / #p'>E 2 F /10 =]4>9;&?Dd1Bc?2Pr/0&?'51B<C),&δ<C@$4325-0LU9,'*2*DpTF9s@3251

P);P g1EU`QA m 6<#_F_` / 4.);Pz1Bc?2WPR),4B+ q → σr

>INc?25432

q ∈ Σ′ > σ ∈ Σ9;&?D

r ∈ Reg(Σ′)

%1'Y9;&p29,@3@B/0+X2*D`1Bc 9;11Bc?25432e9;432m&?).1tIf)X-043)_Da/?'51B<C),&?@<=&PIN<=1Bc1Bc?2@9;+X2

σ9;&?D

q>aL=<=MV28

q → σ r1, q → σ r2 ∪ Pmore

@B<=&?'*21Bc 9;1- 9;<=4$);Pv-043)GDa/?'51B<C),&?@$IN<=1Bc?),/01LC)8@3@);Pv7V25&?254:9;L=<=1tF'Y9;&p2m4325IN4B<=1B1325&13)

q → σ(r1|r2) ∪ Pmore

&F / #p'>Epg1Ef'7# 0 #_F^` / );P9W1B432*2 t9;7T9;<=&?@B1g1Bc?2|784:9;+.+s9;4

G<C@f@B1B<=L=Lu9W@31:9;132e~^&?),&T13254B+.<=& 9;L 9,@3@B<=78&0+X25&T1

¨

spersonsperson 11

spersons

email sales email salesname

111 112

211 212

sales spersons1

12

customer

name

customerssales2

customer

customer amount customer

emailname

customer customeramount amount amount

contact

121 122

2221sales customers customer

213113

1131 11331132 1134 1231 1232 1233 1234

221

123

222

2132

sales spersons spersonhomepage

salesepsilonsales

2131

name

name

homepage

K-[! GVΣTUHgFG <!>#=XUHi*:;$B$!*<&:]>$!"65&3P&3$&WFG2$B-?k! >&k

NPOBQL:]$,G-P' m?k#"6 !k$!"-&2W&2$&W*;$W$! *,-E*-$,')E$*5& ')W6:d!H !/V $*5&G' &-&2TX9&2$!&G`!/. &:]J$!"-&2G&2$!!? Qk:;$E#=X#&WP$ *!H@?\-\&W""-*E=,KJ:d:;^$<d?

Σ′ = D / 1, /l'b

, $(6 /l

,/ "

, $b 6 / 1, d6 /

, 6>[!,` / 2, $b 6 / 2, 6 / /

, a

, 6g $b

Σ =

*,()$)

,()$

," 7) +$ ()

,"'7 $)(

,)

,)5

,+$ )*G

,"$+"

, $7

S =

` / 1P = ` /l 1 ::=

(/ " (

, $b 6 / "

),/ "b::=

+()*$ (1, , /l

), $b 6 / "::=

"'7 $)() (0, , $b6 / 1),/ "

::= +()*$

( d6 /, 6g[!

,

(1, , D / 2)), $b 6 / 1 ::="'7 $)( !#"$"

( d6 /, 6 /%b /

, a

),` /l 2 ::=

( $b 6 / 2, 6g$

), ::=

"$+"' ( d6 /

, 6g[!

), d6 /

::=)

ε, 6g[!::=

5ε,

6 / /::=

$)+Gε, $b 6 / 2 ::=

"'7 $)(ε, 6g$

::= $7

ε

Z V # -k:d:;-H,""$!>k-k$EZ5[?v c&:] #[i-H4 G"$K=X\&-$ =XK+*,.8$,>FGb NPOBQ ""9-:;<$ ! DHl&2^*$_$x:]-$9&Hl$!*xh$!<"9"\' 4:]-$G 4V! ?

¨

λ13).2Y9,'3c&?)_D028>?@B/?':c1Bc 9;1Y

λ : Dom(t)→ Σ′, λ(root(t)) ∈ S

?),4|2Y9,'3cv ∈ Dom(t) :

xgc?254322a<C@B13@$9i-043)_Da/?'51B<C),&b4B/0LC2r ∈ P :

λ(v)→ labt(v) r>0@B/?':c1Bc 9;1

λ(v1). · · · .λ(vn) ∈ L(r)

1B432*2t<C@ I ' / '>E 0 #p'iAbpTF9i784:9;+.+s9;4

G>0<]P1Bc?25432<C@$9;&<=&T13254B-043251:9;1B<C),&);P

t9;7T9;<=&?@B1

Gj

7 % % . *) D&

xgc?269;/013),+s9;13),&9;&?D1Bc?2s432578/0LU9;4e1B432*2s784:9;+.+s9;4i-2543@B-"2*'51B<=[V2*@9;4328>v);P'*),/043@328>1Bc?2s@:9;+X2s1Bc0<=&07?9,':cO-043)_Da/?'51B<C),&

q → σr'Y9;&Op"2s1B4:9;&?@BLU9;132*DE13)9

δ+s9;-0-0<=&07

δ(q, σ) = r>v9;&?DhPR),4e9;L=Lg9;p?@325&T1

(q, σ)- 9;<=43@Y>

δ+s9;-?@e13)

∅>v9;&?DH9;/013),+s9;13),&HD02?&0<=1B<C),&?@i1B4:9;&?@BLU9;132s13)784:9;+.+s9;43@iIN<=1Bc1Bc?2q@:9;+X2

2Y9,@328jK%P),&0L=F6'*),&?@B<CD0254B<=&07q@B1B4B/?'51B/0432 T> 9;&kmldnED0)_'5/0+X25&T1|<C@[89;L=<CD6IN<=1Bcb432*@B-2*'51N13)s9.@:'3c?25+s9<]P<=1<C@|9,'*'*25-0132*D`pTF`@3':c?25+s9() @1B432*2W9;/013),+s9;13),&'Pyjv1Bc?2@:'3c?25+s9() @784:9;+.+s9;4Yj

8g),1BcemxN\9;&?DWkAlnJw_':c?25+s9|9;432KD02*'5LU9;4:9;1B<=[V28>hA 'i67= 0 E>F /CI 25LC25+X25&T13@Y>V9;1B1B4B<=p0/0132*@v9;&?D1Bc?25<=4'*),&T1325&T1Yjm2*'5LU9;4:9;1B<C),&?@z<=&1Bc?2*@32g@3':c?25+s9mLU9;&078/ 9;7V2*@1B4:9;&?@BLU9;132g13)9;/013),+s9;13),&s@31:9;132*@Y>8),4v&?),&T13254B+.<=& 9;LC@Yxgc?25F9;-0-0L=F13)J&?)GD02*@);PN9q'*254B1:9;<=&h& 9;+X2<=&E9J'*254B1:9;<=&E'*),&T132a1Y>9;&?D1Bc?25F@B-"2*'5<]PrF9J@3251);Pf9,'*'*25-01:9;p0LC2'*),&G1325&T1$@32*G/?25&?'*2*@fPR),4f2Y9,':c`&?)GD028jvE2m'Y9;L=L9;L=LuD02*'5LU9;4:9;1B<C),&?@N<=&69i@3':c?25+s9

Σd

>09;&?DJ<=1KIN<=L=Lp2*'*),+X225[_<CD025&T1|1Bc 9;11Bc0<C@N<C@ Sy/?@B1$9;&2a1325&?@B<C),&b);P

Σ′ j

kmldnd-254B+.<=13@+X)8@B1Y>Gp0/01f&?),1f9;L=L ':c 9;4:9,'5132543@g<=&s1Bc?2 ?$&0<C'*)_D02|9;L=-0c 9;p251Yn251 b p"2$1Bc?2-043)_Da/?'1B<C),&-043)_Da/?'51B<C),&d);Pv1Bc?2@:9;+X2& 9;+X2<=& M \P >?9;&?D

char∗p29;&TF6kAlnE@B1B4B<=&07?j

LC25+X25&G16 ` / #p' / # 2 `<A '>=]4dK +X)_D025LC@);Pg1Bc?2s9;L=LC)YIf2*DO':c0<=LCDE25LC25+X25&T1'*),&T1325&G1e);PN25LC25+X25&T13@qK 9;432432578/0LU9;4|<=&`p"),1BcbmxN 9;&?D`kmldnHw_'3c?25+s9a> 9;&?D1Bc?2432578/0LU9;4$2a-0432*@3@B<C),&`LU9;&078/ 9;7V2

::=

!#" "( +)

|

( ∗)

| (

+)|

(min,max,

)

| q ∈ Σ′

| ε

INc?25432min ∈ N0

>?9;&?Dmax ∈ N0 ∪ j

'Y9;&XD02*@3'54B<=p2g1Bc?2g'*),&T1325&G1+X)_D025LC@);P p),1BcmxN9;&?DikAlnbw_'3c?25+s9s~ <C@'Y9;43Da<=& 9;L=<=1tFV>G+X2Y9;&0<=&07min · · ·max

4325-251B<=1B<C),&?@Yjx2a1Y>V'*),+.+X25&T19;&?Di-043)_'*2*@3@B<=&07,<=&?@B1B4B/?'51B<C),&X'*),&G1325&T1c 9,@vp2*25&eLC2Pr1),/01Y>9;&?D`IN<=L=Lp"29,D0D02*D`LU9;13254j

8g),1Bc@3':c?25+s9`LU9;&078/ 9;7V2*@e'Y9;&Ec 9*[V2s1Bc?25<=4 0 #^#_E>F^G m #p' 2 `<A '>=]4J9,D02*G/ 9;1325L=FD02*@:'54B<=p"2*DhIN<=1Bc1Bc?2.LU9;&a78/ 9;7V2 ;C"B/BD";U'K&9+"46%ES;U"4R)"A,/;U*S&')$+*-,/.4&(6%9!6'P6E-L/');BE($+')1J')$+'=,H9+*S6E R="A,(; 9U$!6*-,H9+; ')9+RNG?'DCB($+'=;U;U'K&*S,X9+5/' ;UR!5/')3P6,G

¨3

::= (q ∈ Σ′, S ∈ Reg(char))| " (q ∈ Σ′, S ∈ Reg(char))| (q ∈ Σ′, s ∈ char∗)

pGFO9,@3@3)_'5<U9;1B<=&07E9@3251);P|9;1B1B4B<=p0/01326/?@32*@Y>v2Y9,'3cIN<=1Bco9;&AtD02*@3'54B<=-01B<C),&>zIN<=1Bc2Y9,'3co25LC25+X25&G1D02*'

LU9;4:9;1B<C),&j%t&HmxN9;&?DkmlnSw_':c?25+s9a>z'3c 9;4:9,'513254vA 0 # 0 2 `<AC'>= 4`9;432s432578/0LU9;4Y>),49;-0-043)*a<=+s9;1325L=F432578/0LU9;4YjgKc 9;4:9,'513254|D?9;1:9X9;-0-2Y9;4<=&b9;1B1B4B<=p0/0132[89;L=/?2*@Y>?9;&?D`<=&25LC25+X25&G1|'*),&G1325&T1Yj

%&skmldnhw_'3c?25+s9a>a1Bc?2|'*),+Wp0<=&?2*D6'*),&T1325&G1Y>0D?9;1:9e9;&?D69;1B1B4B<=p0/0132|+X)GD025LC@f);P9;&q25LC25+X25&G1gD02*'5LU9;4:9;1B<C),&<C@'Y9;L=LC2*Dh9 #_nDg.'5>9;&?D13)`9*[V),<CDh'*),&aPr/?@B<C),&>IK2IN<=L=Lz9;LC@3)q/?@32i1Bc?2iIK),43DIN<=1Bc1Bc 9;1m+X2Y9;&0<=&07~r25[V25&PR),4$mxNj

E2KIN<=L=La/?@32z1Bc?2K13254B+ AC'i67= 0 Ei'fA / `<A ' #_n gh'~r5+|x$uPr),41Bc?2&?)_D02*@1Bc 9;1v9;432fD02*'5LU9;432*Di<=&eD02*'5LU9;4:9;1B<C),&?@Y 5+|x<C@9.& 9;+X2W9,@3@3)_'5<U9;132*D6IN<=1Bcd9i1tF_-28jz%t&G1B43)GDa/?'*21Bc?2mP^/0&?'51B<C),&?@

Cm : Σ′ → L(M)

Ad : Σ′ → 2Σ′

Am : Σ′ → L(A)

9;&?D

Dd : Σ′ → Reg(char)

1Bc 9;143251B/04B&`1Bc?2'*),&G1325&T1|+X)GD025LPR),4$9i&?)GD02X~ PR),49;&TF6),1Bc?254&?)_D02*@g1Bc 9;&43)G),1$9;&?D`25LC25+X25&G1&?)_D02*@Y><=1.43251B/04B&?@

∅>z1Bc?2`@:251);PmD02*'5LU9;432*D\9;1B1B4B<=p0/0132*@PR),425LC25+X25&G13@b~

∅PR),4i&?),&at25LC25+X25&G13@>N9;&?Do9dD?9;1:9

+X)_D025L>0432*@B-2*'51B<=[V25L=FVj

xgc?2mPr/0&?'51B<C),&m

@B<=+.-0L=F`2a1B4:9,'513@N1Bc?2@BF_+Wp),LC@N+X25&T1B<C),&?2*Db<=&d9;&Mt2_-0432*@3@3<C),& 8

m(!#" "

(M1 · · ·Mn)) =⋃n

i=1 m(Mi)m(

(M1 · · ·Mn)) =

⋃ni=1 m(Mi)

m( (M1 · · ·Mn)) =

⋃ni=1 m(Mi)

m(

(min,max,m′) =

∅<]P

max = 0m(m′)

),1Bc?254BIN<C@32m(q ∈ Σ′) = qm(∅) = ∅

1Bc?2mPr/0&?'51B<C),&Cd : Σ′ → 2Σ′ 43251B/04B&?@$1Bc?2D02*'5LU9;432*Db'3c0<=LCDa4325&);P95+Ax

Cd(q) = m(Cm(q))

9;&?D`1Bc?2P^/0&?'51B<C),&PD : Σ′ → 2Σ′ 43251B/04B&?@N1Bc?2-)8@3@B<=p0LC2m- 9;4325&G1|5+|x@gPR),4$9.5+|x

Pd(q) = q′ : q ∈ Cd(q′) | q ∈ Am(q′)

) (., 0, .)

3P6=WX6%B/BD'K6Q$ *-, 62&(')$+*KP6%9+*-"A,8@WP$+'=; 9U$+*-R)9+*-", G

¨ON

#£ % % %

k`<6 mJ2 ' / #hn gh'Yk' / F&#_F^` / ~rmxN<C@J~R9,@WP9;4i9,@W25LC25+X25&G13@X9;432s'*),&?'*254B&?2*D i9`L=<C@31i);P25LC25+X25&T1D02*'5LU9;4:9;1B<C),&?@Y

LC (d6 / U/l &

INc?25432 U/l <C@9;&),&?2/0& 9;+Wp0<=78/?),/?@A432578/0LU9;4$2a-0432*@3@B<C),&)Y[V254|25LC25+X25&T1& 9;+X2*@Y>0D02*'5LU9;4B<=&07q1Bc?2'*),&G1325&T1.IN<=1BcO'Y9;43Da<=& 9;L=<=1FH9;&?DO),43D0254i'*),&?@B1B4:9;<=&G13@Yj L=13254B& 9;1B<=[V25L=FV> U/l <C@i9L=<C@B1e);P25LC25+X25&T1& 9;+X2*@Y>Tc?2Y9,D02*D.pTF.9m@B-2*'5<U9;L013),MV25&4 - Z >81Bc 9;1),&0L=Fi432*@B1B4B<C'513@1Bc?29;L=LC)IK2*DX& 9;+X2*@);P':c0<=LCD25LC25+X25&G13@s~^&?)s432*@31B4B<C'51B<C),&?@9;-0-0L=Fd),&'Y9;43Da<=& 9;L=<=1tF),4A),43D0254>9;&?Dh9;L=LC)YI@':c 9;4:9,'513254D?9;1:9s'*),&G1325&T13@<=&G132543@B-"2543@:2*Ddp251tIf2*25&E'3c0<=LCDh25LC25+X25&G13@Yjxgc?25432i<C@m9;LC@:)J9;& 4 13),MV25&>9;L=LC)YIN<=&07`&?)J'*),&T1325&T19;1g9;L=L>T&?),1f25[V25&J9'*),+.+X25&G1N),4f9m-043)_'*2*@3@B<=&07e<=&?@B1B4B/?'51B<C),&~^1Bc?2*@:2|9;432$),1Bc?254BIN<C@:2A9;L=LC)IK2*DJ13)e9;-0-2Y9;49;&GFGINc?25432.),/013@B<CD02e1:9;7V@ 8>9;&?Dh9;& -6 13),MV25&>1Bc 9;1|If),4BM_@mL=<=MV29 4 ] IN<=1Bch9XL=<C@31A);P25[V254BF A 'i6j= 0 Ef'iA25LC25+X25&T1|& 9;+X28j

%1K<C@N),&0L=FJ9;L=LC)YIK2*D13)Wc 9Y[V2),&?2AD02*'5LU9;4:9;1B<C),&6PR),4g2Y9,'3c25LC25+X25&T1N& 9;+X2A<=&9eAxNja%&?D02*2*Du>G<=&`mxN>PR),4v9;&GF25LC25+X25&T1&?)_D02z<=&.9;&W<=&?@B1:9;&?'*2fD0)_'5/0+X25&T1Y>81Bc?2f),&0L=F1Bc0<=&07AD02513254B+.<=&0<=&071Bc?2f9;L=LC)YIf2*D.'*),&T1325&T1);Pv1Bc?2&?)_D02<C@g1Bc?2& 9;+X2);Pv1Bc?225LC25+X25&T1|&?)GD028j

xgc?2K2F:2*'51);P01Bc?2*@32K@B1:9;132<=&?@325&?@3<=1B<=[V28>C= `<6 0 =?D02*'5LU9;4:9;1B<C),&?@);P?25LC25+X25&T1v'*),&T1325&G13@<C@u1Bc 9;11Bc?2KD02?&0<=1B<C),&);PA1Bc?2`'*),4B432*@B-"),&?Da<=&07h1B432*29;/013),+s9;13),&\'Y9;&op2J432*@B1B4B<C'5132*DuwG<=&?'*261Bc?254326<C@209,'51BL=FH),&?26432578/0LU9;42a-0432*@3@B<C),&)Y[V254

Σ′ PR),4|2Y9,':cd& 9;+X2i<=&σ′ > IK2i'Y9;&D0)J9*Ig9*FIN<=1Bc@B1:9;132i9,@3@B<=78&0+X25&G1m25&G1B<=4325L=FV>9;&?D

Sy/?@B1N/?@32m& 9;+X2*@Y

δDTD : Σ′ → Reg(Σ′)

[89;L=<CD?9;1B<C),&d4B/0&b),&9.mxN|tD02*'5LU9;432*Dbkmldn<=&?@B1:9;&?'*21B432*2W<C@Y>01Bc?25&> ),&0L=Fb9+s9;1B13254|);Pz'3c?2*':MG<=&07?>PR),4$2Y9,'3cb&?)GD02

v>?1Bc 9;1Y

chst(v) ∈ δDTD(namet(v))

*)

&skmldn@3':c?25+s9q~^kw_<=&?@B1:9;&?'*2A'*),&?@B<C@B13@K);P9&G/0+Wp254g);Pe4j6>%(' 20 A `<6 mJ2 ' / #&4>a2Y9,'3c6'*),&T1:9;<=&0<=&079&G/0+Wp254|);P,476>%.' 20 6 ` 2 g(` / ' / #&4j @3'3c?25+s9X'*),+.-"),&?25&G1$<C@Y

• 1:9;4B7V251& 9;+X2*@3- 9,'*2

• &G/0+Wp254|);PD02*'5LU9;4:9;1B<C),&?@

= ' 2 ' / # A 'i67= 0 E 0 #_F_` / 4i9,@3@3)_'5<U9;13225LC25+X25&T1|& 9;+X2*@IN<=1Bc`1FG-2D02?&0<=1B<C),&?@ BA 5/*-;C;U'=')34; "aPN')$+E:WP; 9U$+*-R)9E(6,7&4YC6%;CB($+"8768(E:W49+5/' $+');UL/E:9C"1 6 ;UE-*-BV*-,P9+5/' Q R ;UBD')R=*27RK6Q9+*S", GI NMTY#'=,H9F6 E-",/.

YC6=W9+"P6E-*S&/6Q9+'IR="A3434'),@9+; 6,/& B$+"HR='=;U;U*-,/. *-,(; 9U$+L/R)9+*-"A,(; BD'K&(6,H9+*-RK6E-E:W Y '2YF*-E-E 8D'I6E-*:9U9+E-'I34"$+' $+'=ES62C'K& "A, 9+5(';UL/8! '=R 9E7,/"%9FR="A,(;U*S&(')$+*-,/.4R)"A3434'=,H9C6%,7&VB$+"HR='=;U;U*-,/.4*-,(; 9U$+L/R)9+*-"A,(;F"AL(9+B(L(9C*-, P6E-*S&/6Q9+*-"A, G

¨ %

#^#_EDFHG m #p'A 'i67= 0 E 0 #_F_` / 4i9,@3@3)_'5<U9;1329;1B1B4B<=p0/0132& 9;+X2*@IN<=1Bc1tF_-"2WD02?&0<=1B<C),&?@ #&%('>EA 'f67= 0 E 0 #_F^` / 4e1Bc 9;1|9;432m&?),14325LC25[89;&T1$<=&`1Bc0<C@1B432Y9;1B+X25&T1

• &G/0+Wp254|);PD02?&0<=1B<C),&?@

V F 2 gX= '[#_nDg.'A ' / F_#_F^` / 4D02?&?2WD?9;1:9i+X)_D025L1tF_-"2*@ ` 2 g1= ' :#_nDg.'dAC' / F_#_F_` / 4mD02?&?2W'*),&T1325&T1A+X)_D025L9;&?Db9;1B1B4B<=p0/0132+X)_D025L1tF_-2*@ t `<A '7= I Ei` m g AC' / F_#_F_` / 4mD02?&?2J~^- 9;4B13@);Pf'*),&T1325&G1$+X)_D025LC@ #^#_EDFHG m #p' I EU` m g A ' / F&#_F^` / 4D02?&?2@:2513@);P9;1B1B4B<=p0/0132eD02*'5LU9;4:9;1B<C),&?@ #&%('>EA ' / F_#_F_` / 4A1Bc 9;1|9;432&?),14325LC25[,9;&G1<=&1Bc0<C@N1B432Y9;1B+X25&G1

• &G/0+Wp254|);PyF / 67= m A '1F 2 g(`oE7#1Ei'fA ' / '432Pr254325&?'*2*@$13)X),1Bc?254$@3':c?25+s9.D0)G'5/0+X25&G13@

•w_),+X2Rtc?25L=-"254UT'*),+.-),&?25&T13@~R9;&0&?),1:9;1B<C),&?@Y> 2513'8j=j=j

f),+.-0LC2J1tF_-"2|D02?&0<=1B<C),&?@~r@B1B<=L=L"'*),&?@3<CD0254B<=&07),&0L=FX25LC25+X25&G1'*),&T1325&G1K9;&?DJ+X)_D025L 7843),/0-?@N9;432A'*),+-)8@32*D);PB

•VL' l7m ' / 6 '.'*),+.-")8@B<=13),43@>01B4:9;&?@BLU9;1B<=&07X13).1Bc?2 &?),&T13254B+.<=& 9;Lv);Pv),/04

MLU9;&078/ 9;7V2

• %J`oF^6 ''*),+.-)8@B<=13),43@Y>?1B4:9;&?@BLU9;1B<=&07s13)1Bc?2 &?),&T13254B+.<=& 9;Lv);Pv),/04 MLU9;&078/ 9;7V2

•k'i6j= 0 E 0 #_F^` / 45>0-")8@:@B<=p0L=F69,@432Pr254325&?'*2*@Y>?1B4:9;&?@BLU9;1B<=&07s13).@BF_+Wp),LC@N<=&

Σ′

• F = AO6 0 EiA\4V 4 4325-0432*@325&T13@9;&GFb25LC25+X25&T1mIN<=1Bch9;&TF`& 9;+X2.9;&?Dd9;&GFb'*),&T1325&G1YjA%1<C@|13)q@:),+X2D02578432*2-)8@3@B<=p0LC2m13)L=<=+.<=11Bc?2W9;L=LC)IK2*Dd& 9;+X2*@B- 9,'*2*@$);Pv1Bc?2m4325-0432*@325&G132*Db25LC25+X25&T13@j

• 0 EUA3F /10 =]F_#_n:E 0o/CI '>4>"1tIf)q&G/0+Wp2543@ 5 ""'7() 9;&?D "" 7( +s9*Fp2e9;-0-0L=<C2*D13)q9;&GFb);P1Bc?29;p")[V28j 5 ""'7() 4:9;&07V2*@gPr43),+W13)i<=&a?&0<=1FV> 9;&?D )""'7( Pr43),+ e13)i<=&a?&0<=1tFV>?-0L=/?@1Bc?2z@B-2*'5<U9;LV[89;L=/?2 jxgc?2*@32z1B4:9;&?@3LU9;132z13)N1Bc?2 &?),&T13254B+.<=& 9;La);P?),/04 M

LU9;&078/ 9;7V2

•t `<A '>= I Ei` m gEf'&?<'>Ef' / 6 'D45>g432Pr254B4B<=&07h13)h9+X)_D025Lg7843),/0- ~^1Bc?25FO'Y9;&op262_- 9;&?D02*Do@BF_&T1:9,'51B<]'Y9;L=L=F0

•wG-"2*'5<U9;L =&='*),+.-)8@B<=13),43@Y>u1Bc 9;14325-0432*@325&G1W9;&TF-"254B+e/01:9;1B<C),&);Pg1Bc?25<=4'*),&T1325&T13@jixgc?2*@:2X9;432c?2Y9*[_<=L=Fh432*@B1B4B<C'5132*DH13)d9;-0-2Y9;4i),&0L=FEDa<=432*'51BL=F/0&?D025491tF_-"2qD02?&0<=1B<C),&~R9QPr13254i+X)GD025LK7843),/0-2_- 9;&?@3<C),& >f9;&?D\),&0L=F'*),&T1:9;<=&(D02*'5LU9;4:9;1B<C),&?@Y>N9;&?Do),&0L=FOIN<=1Bc(9'Y9;43Da<=& 9;L=<=1tFPr43),+ 13) Q jxgc?25Fq1B4:9;&?@3LU9;13213).1Bc?2 !#" " &?),&T13254B+.<=& 9;Lv);Pv),/04

MLU9;&078/ 9;7V2

?),4e@3),+X2432Y9,@3),&E),4e9;&?),1Bc?254Y>),&0L=F'*),+.-)8@B<=13),43@W9;&?Dh&?),1g 0 E>#_F^67= 'D4XL=<=MV2XD02*'5LU9;4:9;1B<C),&?@i9;&?DIN<=LCD_'Y9;43D0@Y> 9;432W9,'*'*25-01:9;p0LC2e9,@N1Bc?2),/013254B+X)8@31|'*),+.-),&?25&T1|);Pz9i+X)_D025L7843),/0-b),4$9.'*),+.-0LC2`1tF_-28j

xgc?2& 9;+X2*@);PN25LC25+X25&T1eD02*'5LU9;4:9;1B<C),&?@Y>1Bc?2& 9;+X2*@);PN9;1B1B4B<=p0/0132XD02*'5LU9;4:9;1B<C),&?@Y>1Bc?2& 9;+X2*@);PK1FG-2D02?&0<=1B<C),&?@Y>T1Bc?2g& 9;+X2*@);P +X)_D025L07843),/0-.D02?&0<=1B<C),&?@K9;&?Di1Bc?2g& 9;+X2*@z);P"9;1B1B4B<=p0/0132N7843),/0-XD02?&0<=1B<C),&?@9;L=L p"25LC),&07<=&qDa<C@B1B<=&?'51 4>n 2 Gi`3=h4Hg 0 6 'D45>T-04325[V25&G1B<=&07i& 9;+X2$'*),& ?<C'513@p251tIf2*25&J),&?2NM_<=&?Ds9;&?DJ9;&?),1Bc?254Yj A 5/' $+' *-;06I,(*-R=' Y 6=W 9+"4576%,7&(E-'09+5/')3 34"%$+' ')ES').N6,H9+E:WT< #"A,(;U*S&(')$+*-,/.P9+5/')3 ,("A,H9+')$+34*-,76%E-;OYF*:9+5/"L(9 629+')$+34*-,76E

*-,V9+5/'=*:$OB($+"@&L/R)9+*-", G ,"AL$ *-34B(ES')34'=,H9!6%9+*-"A, EH9+5/')W6%$+' ! L/; 9O'DCB76%,7&'K&X; W,H9!6R 9+*SR=6E-E:W9E(9+5("AL/.5 G

¨3w

contain,

refer

refer

contain,

refer

refer

contain, refer

attribute groups

attribute decls

model groups

element decls

contain, refer

complex types

simple types

refer

contain

extend

restrict

refer

refer

contain,

contain, refercontain

contain

restrict

extend,

refer

compositors

K5m GVW$ 2-:]kE&kkd"6$')!&2$E:>!*>' "$,$!:d-$, $!*_6')--$!"6Z&3!"6-&'kN OBQ ""9-:]!? *-&d*5&"=gc<#8$g&2D=X63F^-$bc&"9!:;B"6:]g$$,d> 9a'G5*H$g*>!8^8l!G-*`y')l6:]H,"6:d!>34gW*6h!$$g& :;/ 64$!*]&:]G34gW*6h!$$g&? /V T V R V HR YR V $!* 4 ? W#"6k"6$,$:]$, "4" H $!* !! " HX:] $K=9;$-&2$]'!&\&"9-:]d"6:]g$$,&-?

m2*'5LU9;4:9;1B<C),&?@m9;&?DD02?&0<=1B<C),&?@+s9YF`9;-0-2Y9;4|9;1Da<;:u254325&T1|-0LU9,'*2*@Y

• # = ` G 0 = =bn8>f9;1v#H`>g1@p= ' Z '>=m<=&9@:'3c?25+s9hD0)_'5/0+X25&T1Y>f+X2Y9;&0<=&071Bc 9;1.1Bc?25F\9;4326& 9;+X2*DZ9;&?D9,''*2*@3@B<=p0LC2i1Bc043),/078c?),/011Bc?2@3'3c?25+s9ajixgc?2i& 9;+X2);Pg9q78LC),p 9;LD02*'5LU9;4:9;1B<C),&E<C@A1Bc?2& 9;+X2i);Pf1Bc?225LC25+X25&T1),49;1B1B4B<=p0/0132<=1AD02*'5LU9;432*@>9;&?Dd1Bc?25432i+s9YFp"29;1m+X)8@B1m),&?2e78LC),p 9;LD02*'5LU9;4:9;1B<C),&h-254@BF_+Wp),Lg@3- 9,'*2sPR),4X9;&TFO& 9;+X28jOxgc?2J& 9;+X2`);PA9d78LC),p 9;L=L=FD02*'5LU9;432*D1tF_-"26c 9,@i&?)h@325+s9;&G1B<C'@B<=78&0<] 'Y9;&?'*28jxgc?2& 9;+X2*@B- 9,'*2W);Pv1Bc?25+ 9;L=L<C@$9;L=Ig9*Fa@1Bc?21:9;4B7V251$& 9;+X2*@B- 9,'*2W);Pv1Bc?2@3':c?25+s9~r25[V25&`PR),4$9;1B1B4B<=p0/0132*@j

•LC25+X25&T1),4N9;1B1B4B<=p0/0132mD02*'5LU9;4:9;1B<C),&?@g+s9*FJ9;-0-2Y9;4= `<6 0 = =bn8>*6f` / # 0 F / 'fAYF / 6f` 2 g1= ' :#_nDg.'[A ' / F @#_F_` / 4j L=13254B& 9;1B<=[V25L=FV>u1Bc?25432i<C@m9Ef'&?<'>Ei' / 6 's+X2*'3c 9;&0<C@B+ 9Y[,9;<=LU9;p0LC2iPR),4m432Pr254B4B<=&07613)`9s78LC),p 9;LD02*'5LU9;4:9;1B<C),&bpGFq<=13@N& 9;+X28j

•xzF_-"2D02?&0<=1B<C),&?@`+s9*FS9;-0-"2Y9;4 = `<6 0 =&=]n8>d6f` / # 0 F / 'fA F / '7= ' 2 ' / #`oE 0 #^#_E>FHG m #p'"A 'i67= 0 E 0 #_F^` / 4j L=13254B& 9;1B<=[V25L=FV>1Bc?25432<C@9;&?),1Bc?254Ef'&?j'7Ei' / 6 'q+X2*'3c 9;&0<C@B+ 9*[89;<=LU9;p0LC2Pr),4m432PR254B4B<=&07`13)9q78LC),p 9;LD02?&0<=1B<C),&bpGFq<=13@N& 9;+X28j -$Pv'*),/043@:28>01Bc?21tF_-2D02?&0<=1B<C),&b/?@32*D6PR),4$9;&b9;1B1B4B<=p0/0132WD02*'5LU9;4:9;1B<C),&+W/?@B1$p"2@B<=+.-0LC28j

•ld)_D025LK9;&?D9;1B1B4B<=p0/0132q7843),/0-OD02?&0<=1B<C),&?@9;432X/0&0<CG/?25L=F& 9;+X2*D v1Bc?25F+s9YF9;-0-"2Y9;4i),&0L=FE9;113),-aLC25[V25L> 9;&?D`+s9YFJp2m432PR254B432*D`13)Pr43),+ IN<=1Bc0<=&d9;&TF61tF_-2),47843),/0-bD02?&0<=1B<C),&j

xgc?2f-)8@3@B<=p0<=L=<=1tF13)A),-01p"251IK2*25&78LC),p 9;L0),4LC)_'Y9;L_D02*'5LU9;4:9;1B<C),&?@z9;&?DiD02?&0<=1B<C),&?@LC2Y9*[V2*@vkmldn`w_'3c?25+s99;/01Bc?),43@mIN<=1Bc1Bc?2Pr432*2*D0),+ ~R9;&?Dbp0/043D025& |);PKD02*'5<CDa<=&076INc?25432e13)s-0/01m1Bc?25+j xgc?25432i<C@Y> c?)YIf25[V254Y>9@BL=<=78cG1gp0/01p 9,@B<C'A@325+s9;&T1B<C'mDa<;:u254325&?'*2$p251tIf2*25&61Bc?2$1IK)0 LC25+X25&G1gD02*'5LU9;4:9;1B<C),&?@N'*),&G1:9;<=&?2*DJ<=&q1FG-2

8

D02?&0<=1B<C),&?@'Y9;&S432tD02*'5LU9;43225LC25+X25&T1`& 9;+X2*@>|25[V25&(<]PW1Bc?)8@32& 9;+X2*@9;432D02*'5LU9;432*D25LC@325INc?25432o~R9,@),-0-)8@32*D`13).78LC),p 9;LD02*'5LU9;4:9;1B<C),&?@Y>?INc?25432W9;&GF6& 9;+X2<=&d9@BF_+Wp),L@B- 9,'*2m+s9YFJp2D02*'5LU9;432*Db9;1$+X)8@B1),&?'*2j

x)6p"2i+X),432.@B-2*'5<] '8>LC251/?@9,@3@B/0+X2i1Bc 9;1m+X)GD025L7843),/0-?@9;432.D02Y9;L=1IN<=1BcPR),4A&?)YIpGFd2a- 9;&?Da<=&071Bc?25+@BF_&T1:9,'51B<C'Y9;L=L=FV>1Bc 9;1W1FG-2sD0254B<=[89;1B<C),&O<C@W&?),1W/?@32*Du>v9;&?DELC)_),ME9;1W1Bc?2q@3251W);P$9;L=LA~^78LC),p 9;LN9;&?DLC)_'Y9;L .'*),+.-0LC2Z1FG-2D02?&0<=1B<C),&?@Yjxgc?2d9;& 9;LC),78Fo13)),/04JD02?&0<=1B<C),&?@6);Pm432578/0LU9;4J1B432*2LU9;&078/ 9;7V2*@&?)Ip2578<=&?@13)b1:9;MV2s@Bc 9;-28><]PNIf2XLC251

Σp"2.1Bc?2s& 9;+X2*@W);P1Bc?2X25LC25+X25&G13@D02*'5LU9;432*D<=&O9b@3'3c?25+s9a>

9;&?Db9,@:@B<=78&),&?2@BF_+Wp),Lu<=&Σ′ 13)X2Y9,'3cb25LC25+X25&G1|D02*'5LU9;4:9;1B<C),&~^432*@3),L=[G<=&07X25LC25+X25&G1$432PR254325&?'*2*@m &25LC25+X25&G1|D02*'5LU9;4:9;1B<C),&bp2*'*),+X2*@|9i1B4B<=-0LC2W);P

(<=13@$@B1:9;132

q ∈ Σ′,<=13@25LC25+X25&T1|& 9;+X2

σ ∈ Σ, Cd(q))

1Bc 9;1A'Y9;&p"2mIN4B<=1B1325&d<=&T13)J9i+s9;-0-0<=&07q);P9δP^/0&?'51B<C),&>?),4A9;&b2_1325&?D02*Dd'*),&T132a1yRP^432*2W-043)GDa/?'51B<C),&>

<=&1Bc?2W),pT[_<C),/?@If9YFVj

xgc?25432W<C@|9.),-0-),4B1B/0&0<=1tF6PR),4$'5LU9;4B<] 'Y9;1B<C),&'Y9;L=L=<=&07J9;1/?@$c?254328E2+.<=78cG1A9,@$IK25L=L/?@:21Bc?225LC25+X25&T1D02*'5LU9;4:9;1B<C),&?@m9,@N1Bc?2@3251);P@B1:9;132*@'PBjv&?),&T13254B+.<=& 9;LC@9,@N1Bc?2@31:9;132& 9;+X2*@Y

q 7→ eiσ|q

<C@N1Bc?2i) 1BcdD02*'5LU9;4:9;1B<C),&H~^<=&b@3),+X2),43D0254);P9;&25LC25+X25&G1$& 9;+X2*D

σ

9;&?DD02?&?2e9iP^/0&?'51B<C),&µ1Bc 9;1$+s9;-?@D02*'5LU9;4:9;1B<C),&?@$13)1Bc?2& 9;+X2);P1Bc?2&?)GD02m1FG-2D02*'5LU9;432*Du

µ : Σ′ → Σ :µ(ei

σ) = σ , µ(aiσ) = @.σ , µ(root) = root

µ(pi) = pi , µ(comment) = comment , µ(pcdata) = pcdata

%&d'*),&G132_13@mINc?254329.[89;4B<U9;p0LC2W4:9;&078<=&07`)[V254Σ′ <C@|/?@32*Du>9;&?Db1Bc?2i@BF_+Wp),LC@

σ),4

i9;432W&?),1Ap),/0&?D

),4c 9Y[V2W9;&TF`@B<=78&0<] 'Y9;&?'*28> IK2IN<=L=L@B1B<=L=Lu/?@32,Sy/?@B1N1Bc?2& 9;+X2qj

mxN<C@gLC)G'Y9;L]1FG-2 K kAlnOw_':c?25+s9<C@g&?),19,@gL=<=+.<=132*Duz%t&`@3),+X2mkmlnw_'3c?25+s9<=&?@B1:9;&?'*2*@>a1Bc?254329;432s+X),432X1Bc 9;&O),&?2qD02*'5LU9;4:9;1B<C),&OIN<=1BcO1Bc?2s@:9;+X2s25LC25+X25&T1i& 9;+X28jr-|&O1Bc?2s),1Bc?254ec 9;&?Du>'Y9;432sc 9,@p2*25&\1:9;MV25&ZpGFO1Bc?2bD02*@B<=78&?2543@s);Pkmldn w_':c?25+s9h13)h+s9;MV2d25LC25+X25&T13@s1tF_-"2Y9;p0LC29;L=432Y9,DaFo9,@X1Bc?25<=4),-25&0<=&07X1:9;7V@|9;43225&?'*),/0&G1325432*DbpGF9;&`kAlnh- 9;43@3254Yj

xgc?2|kAlnw_':c?25+s9W|2*'*),+.+X25&?D?9;1B<C),&*M ¨3P @B-2*'5<] 2*@z1tIf)VL6>%(' 20 ` 2 g(` / ' / # ` / 47#_E 0 F / #y@z),&q'*),&a1325&G1$+X)_D025LC@W~^432*@B1:9;132*D`c?25432<=&9@B<=+.-0LC254LU9;&078/ 9;7V21Bc 9;&`<=&b1Bc?2$2*'*),+.+X25&?D?9;1B<C),&

• = ' 2 ' / # k'i67= 0 E 0 #_F_` / 4 ` / 4DF 4>#p' / # k a%tP1Bc?25432m<C@Y>_IN<=1Bc0<=&`1Bc?2@:9;+X2m1tF_-2AD02?&0<=1B<C),&> 9- 9;<=4|);PD02*'5LU9;4:9;1B<C),&?@m);Pz25LC25+X25&T13@AIN<=1Bc1Bc?2W@:9;+X2W& 9;+X28> 1Bc?25&dp"),1BcD02*'5LU9;4:9;1B<C),&?@m+W/?@B1|/?@321Bc?2@:9;+X278LC),p 9;L1FG-28j

• / F l7m ' 0 E>#_F^67= ' #^#_EDFHG m #_F_` / ?%1+e/?@B1p2-")8@:@B<=p0LC2m13)XD02513254B+.<=&?28> INc?25&[,9;L=<CD?9;1B<=&07<=& D0)G'5/0+X25&G1b),43D0254d9@32*G/?25&?'*2h);Pi25LC25+X25&G13@d9;7T9;<=&?@B19H1tF_-"28>$Pr),42Y9,':c25LC25+X25&T1d<=&1Bc?2@32*G/?25&?'*28>uIN<=1Bc?),/01WLC)_),MG<=&07b9;1W9;1B1B4B<=p0/0132*@i9;&?DhIN<=1Bc?),/01LC)_),MG<=&07b9;c?2Y9,Du>INc0<C'3cO- 9;4B1B<C'5LC2.<=&1Bc?2J1tF_-"2JD02*'5LU9;432*@1Bc?2625LC25+X25&T1Yjxgc0<C@ip 9,@B<C'Y9;L=L=FO+X2Y9;&?@1Bc 9;11Bc?2J'*),&G1325&T1.+X)_D025Lg432578/0LU9;42_-0432*@:@B<C),&?@N+W/?@31p"2` / '>@ mJ/10o2 G>F Iom ` m 4j

Q

E2`@Bc 9;L=L@:2*261Bc 9;1.1Bc?2J?43@B1.'*),&?@B1B4:9;<=&T1qIN<=L=LNp"2*@B13)I25[V254BFOkmlnw_'3c?25+s9<=&?@B1:9;&?'*2IN<=1Bc\@3),+X2-043),-254B1B<C2*@A1Bc 9;1A9;432[V254BF`/?@:2P^/0LPr),4$),/04|kw_n_x 9;& 9;L=F_@B<C@>?INc0<=LC21Bc?2i@32*'*),&?Dd'*),&?@B1B4:9;<=&T1A<C@$/?@:25LC2*@3@PR),4f),/04g-0/04B-)8@32*@~R9;&?Ds<C@f<=&?D02*2*DJ&?),1g25[V25&J&?2*'*2*@:@:9;4BFq9;1N9;L=L PR),4f2As'5<C25&G1N- 9;43@321B<=+X2A[,9;L=<CD?9;1B<C),&`);Pkmldn<=&?@B1:9;&?'*2*@

4DF /CI = '>@ #_nDg.'e432578/0LU9;4$1B432*2LU9;&078/ 9;7V2<C@$9432578/0LU9;4$1B432*2LU9;&078/ 9;7V28>0PR),4NINc0<C'3c`PR),4|9;&GF(q, σ)

eiσ, ej

σ ∈ m(δ(q, σ)) ⇒ i = j

xgc?2 zH'*),&?@B1B4:9;<=&G1+s9;MV2*@vkAlnw_'3c?25+s9m@B<=&078LC21FG-28>8/0&?D0254),/04z9,@3@B/0+.-01B<C),&.1Bc 9;1v1tF_-"2gD0254B<=[89Q1B<C),&`<C@f&?),1g/?@32*Du>09;&?DJIN<=1Bc6),&?2m20'*25-01B<C),&(<=LCD0'Y9;43D0@Yj%t1f<C@g-)8@3@B<=p0LC2|<=&Jkmlnhw_':c?25+s9i13)D02?&?2'*),&?@B1B4B/?'513@$L=<=MV28

7 "&), -' 4*5'+G(- &4,) +"* +(G " &

*7+ "&

!A254328>V1Bc?2g?43@3125LC25+X25&T1fD02*'5LU9;4:9;1B<C),&qIN<=L=L?p2N4325-0432*@325&G132*DXpGFi1Bc?2432578/0LU9;4K2a-0432*@3@B<C),&ai PR),4@3),+X2 i

>INc?25432Y9,@|1Bc?2mLU9;1B13254$IN<=L=L>0<=&d),/0413254B+X@Y>ap24325-0432*@325&T132*DbpTF

(e1σ1|e2

σ1|e···σ1|e1

σ2|e2

σ2|e···σ2| · · · )

>01Bc 9;1<C@Y>9;&GFi& 9;+X2i~^L=<=+.<=132*DX13)m1Bc?2N1:9;4B7V251K& 9;+X2*@B- 9,'*2<=&.1Bc0<C@K209;+.-0LC2z9,@3@3)_'5<U9;132*D.IN<=1Bcq9;&TF1FG-28> 0o2 ` /JI#&%J`o4j'

aj , j 6= ij`?),4e),/04e-0/04B-")8@:2*@Wc?)IK25[V254Y>vINc0<C'3cHIN<=L=Lp2.13)b1tF_-"2s&?)GD02*@e@B1:9;1B<C'Y9;L=L=FE<=&),43D0254

13)X2*@31B<=+s9;1321Bc?2-)8@3@B<=p0LC2),/013'*),+X2e);P9;&bkw_n1B4:9;&?@yPr),4B+ 4B/0&b),&1Bc?2&?)_D028>0If2IN<=L=L78<=[V2W/0-d9;&TF9;& 9;L=Fa@B<C@g),&q1Bc?2A432*@B/0L=13@g);P1B4:9;&?@yPR),4B+s9;1B<C),&?@N);PIN<=LCD0'Y9;43D0@Y>09;&?DSy/?@B1f9;-0-043)Y_<=+s9;132m1Bc?2m),/013'*),+X2A13)R 9;&GFJIf25L=L]RPr),4B+X2*DbkAlnEINc 9;13@:)G25[V254UT:j

CPB%;`@aIbK6Lz TFZCOJH]F/OJ;I(~]Qb; F]S%MrTMNI&~

E2iIf9;&G1m13)J@3c?)YI1Bc 9;1Y?),49;L=Lv9,'*'*25-0132*D1B432*2i@B1:9;1329,@3@B<=78&0+X25&G13@);Pf9s@3<=&078LC21tF_-"2i432578/0LU9;4m1B432*2LU9;&078/ 9;7V28

<j?),4b9;&TFS5+|xq>$1Bc?2h@:2516);Pi-")8@:@B<=p0LC2h9;&?'*2*@B13),4b@B1B4B<=&07V@`);Pi&?)GD02*@61FG-2*D

q<C@9H432578/0LU9;4

LU9;&078/ 9;7V28j<=<j?),4$9;&TFJ5+|x@

q1, q2>_<]P

q1 6= q2>a1Bc?25&61Bc?2mLU9;&078/ 9;7V2);P-)8@3@B<=p0LC29;&?'*2*@B13),4@31B4B<=&07V@N);P&?)_D02*@

1tF_-"2*Dq1

<C@$Da<C@_Sy),<=&G1IN<=1Bc1Bc 9;1$);Pv&?)_D02*@N1tF_-"2*Dq2j

wG<=&078LC21FG-2iLU9;&078/ 9;7V2*@|LC251A/?@AD02513254B+.<=&?2e1Bc?2i5+|x );PK9.& 9;+X2*D$6>% F&= Ab25LC25+X25&G1m);PK9s5+|x> 78<=[V25&1Bc?2':c0<=LCD ) @& 9;+X2W9;&?D1Bc?2- 9;4325&T1<) @|+Ax

δsingle−typechild : Σ′ × Σ→ Σ′

δsingle−typechild (q, σ) = ei

σ : eiσ ∈ m(δ(q, σ))

¨

"'+ *))-BHHJ9I$(G 2210 L"'+ '&),)-'1'& !0&

"$ C4&" $5"&

,+ )*8- 4-B-0'& !'80& ,(+.-"+'&

+"'$+5"&+"$C4+&

+&

),)-"+ 4+ '& !"0&

+"$ C4+ + 0'&* 71"&

+ 4*B & ! &*7 "&

"$+C4&

+"$ C4+ + '&" $+5"&

+ 4*B-0 & !9"& + (- 4*B !'(0&

5 +""'7()/2'&+"'+$5"&

"$+C4&" )&

1

12

1

1

3

comment

pi

r

ca

r

a

b

a

a

c

a

c

a

b

r

a

a a

r

root

&kmldnOw_':c?25+s9.IN<=1Bc1FG-2m432*'5/043@B<C),&jzxgc?2W'*),+.+X25&T13@A'*),&T1:9;<=&b1Bc?2W+AxS& 9;+X2*@N/?@32*DujLC25+X25&G13@$& 9;+X2*D 9;432D02*'5LU9;432*Dd),&?'*278LC),p 9;L=L=FV> 9;&?D61IN<C'*2LC)_'Y9;L=L=FK 1Bc?2m78LC),p 9;LD02*'5LU9;4:9;1B<C),&/?@32*@|9iLC)G'Y9;Lu1FG-2D02?&0<=1B<C),&> 9;&?D`<=&`1Bc 9;1Y>?9;&25LC25+X25&G1$432PR254325&?'*2<C@g/?@32*DJPR),4N1Bc?2 " 25LC25+X25&T1YjKxgc?2),1Bc?254$25LC25+X25&G1|D02*'5LU9;4:9;1B<C),&?@|432Pr254$13)1Bc?25<=41tF_-"2pTFJ<=13@N& 9;+X28jKwG<=&?'*21Bc?25+Ax@

a19;&?D

c19;432

78LC),p 9;L> 25<=1Bc?254 ),4 " 'Y9;&`p"2m1Bc?2WD0)G'5/0+X25&G1|25LC25+X25&T1A);PvD0)_'5/0+X25&T13@$[,9;L=<CDIN4B1Yj1Bc0<C@@3':c?25+s9aj%&1Bc?2 )I 9;L=7V),4B<=1Bc0+-0432*@:25&T132*DLU9;13254Y>?IK2W9,@3@3/0+X21Bc?2),&?2D02*'5LU9;4:9;1B<C),&b<C@$'3c?)8@325&d9,@[#&%('D0)_'5/0+X25&T1A25LC25+X25&T1|D02*'5LU9;4:9;1B<C),&>"9;&?D2*Da7V2*@NPr43),+ "`[ 13)1Bc?2),1Bc?2543@A9;4324325+X)Y[V2*DujKFa'5LC2*@<=&`1Bc?2m <=&?Da<C'Y9;1321Bc 9;11Bc?2@3':c?25+s9() @<=&?@B1:9;&?'*21B432*2*@c 9*[V2/0&0L=<=+.<=132*Dc?25<=78cT1i~^<=1<C@1FG-2432*'5/043@B<=[V2>0INc?25432Y9,@$&?),1Bc0<=&07s<=&`1Bc?2m 432 2*'513@1Bc 9;1|9':c?),<C'*2W'*),+.-)8@B<=13),4If9,@/?@32*D`<=& ) @'*),&T1325&G1|+X)_D025L>0p0/01@32*G/?25&?'*2If9,@$/?@32*D6<=&1Bc?2),1Bc?2543@Yjxgc?2 5 ""'7()2 'Y9;43Da<=& 9;L=<=1F),&1Bc?2Rt4UTm- 9;4B1B<C'5LC2LC2Y9Y[V2*@&?)1B4:9,'*2);Pv<=13@325L]P<=&`1Bc?2WA >025<=1Bc?254Y>0p0/01NIN<=1Bc?),/011Bc 9;1Y>01Bc?25432IK),/0LCD`p2&?)?&0<=132<=&?@B1:9;&?'*2D0)_'5/0+X25&T1|);Pv1Bc?2@3':c?25+s9~R9;&?D`<]P@B/?'3c9i&?);<=&?@B1:9;&?'*2W@3':c?25+s9<C@gPR2*D613)s9If),4BMG<=&07J@B1:9;1B<C'[89;L=<CD?9;13),4Y> 9;&TF6[89;L=<CD?9;1B<C),&432*@B/0L=1<C@'*),4B432*'51 K &?).<=&?@B1:9;&?'*2*@|9;1$9;L=L+X2Y9;&?@&?)<=&G[,9;L=<CDb<=&?@B1:9;&?'*2*@jxgc?2W9;&?'*2*@313),4LU9;&078/ 9;7V2*@|);Pv1Bc?25+|x@|9;4328anld(a

1) = a anld(a2) = a(ba|cr∗aa)(1r∗aa)∗

anld(a3) = a(c|ba)r∗a(ar∗a) anld(b

1) = ab

anld(c1) = ac anld(r

1) = a(c|(b|c)a(aa)∗)r+

8

~^< zf),&?@B<CD0254N9;&J9;/013),+s9;13),&JINc?)8@32$@31:9;132@3251<C@Σ′ >V<=13@K<=&0-0/01LU9;&078/ 9;7V2|<C@@B1B4B<=&07V@f)Y[V254 Σ

>G9;&?DX<=13@1B4:9;&?@B<=1B<C),&Pr/0&?'51B<C),&d<C@

δsingle−typechild

j5-|pG[G<C),/?@3L=FV> <=1A<C@m9Xm >9;&?Db1Bc?2eLU9;&078/ 9;7V2i);P<=&0-0/01A@31B4B<=&07V@1Bc 9;1+s9;MV2*@$1Bc?2W9;/013),+s9;13),&b432Y9,':cd9;&TF6- 9;4B1B<C'5/0LU9;4A@B1:9;132m<C@N432578/0LU9;4Yj

~^<=< 5+A)YI'*),&?@B<CD0254W9;&GFd1IK)`&?)_D02*@v1, v2 ∈ Dom(t)

<=&E9;&9,'*'*25-01B<=&074B/0&h);Pg96@B<=&078LC21FG-21B432*29;/013),+s9;13),&),&d9i1B432*2

t>aINc?25432

λ(v1) 6= λ(v2)9;&?D

ans(v1) = ans(v2)

8f/01J<=1sc 9,@qp"2*25&S@Bc?)YIN&(1Bc 9;1s1Bc?2@B1:9;132λ(v)

);PW9;&TF\&?)_D02v<C@q1Bc?2b@B1:9;132);P@3),+X2A 4B/0&

),&O<=13@e9;&?'*2*@B13),4i@B1B4B<=&07O~r@B-2*'5<] 'Y9;L=L=FV>1Bc?2s@B1:9;132.<C@(δsingle−type

child )∗(ans(v), λ(root(t)))>z9;&?DE1Bc 9;1

@B1:9;132<C@N432Y9,'3c?2*DdD02513254B+.<=&0<C@B1B<C'Y9;L=L=FVjK%1N<C@N1BcG/?@&?),1-)8@3@B<=p0LC2m1Bc 9;1λ(v1) 6= λ(v2)

INc0<=LC2ans(v1) =

ans(v2)j

!m9*[_<=&072*@B1:9;p0L=<C@Bc?2*D1Bc 9;1<=&h@B<=&078LC21tF_-2e432578/0LU9;41B432*2LU9;&078/ 9;7V2*@>u&?)GD02*@A+s9YFdp2W1FG-2*DpTFd1Bc?25<=49;&?'*2*@B13),4A@B1B4B<=&07V@$9;LC),&?28>0If2IN<=L=LD02?&?2W9;& 0o/ 6 'D47#H`oEq= 0o/CIom.0<I 'WPr/0&?'51B<C),&1Bc 9;1If2IN<=L=L/?@32mLU9;13254Y

anld : Σ′ → Reg(Σ)

mxN<C@g@B<=&078LC21tF_-"28>a13)_)0>GPr),4g1Bc?2@B<=+.-0LC2A432Y9,@3),&61Bc 9;1N1Bc?25432'Y9;&6p2m9;1g+X)8@B1N),&?2m1FG-2|Pr),4N9;&25LC2+X25&G1N& 9;+X28wG<=&078LC21tF_-"2A432578/0LU9;4N1B432*2|LU9;&078/ 9;7V2*@'*),&T1:9;<=&`1Bc?2|LC)G'Y9;L]1FG-2A432578/0LU9;4g1B432*2|LU9;&078/ 9;7V2*@>9;&?D`1Bc?2W'5LU9,@3@N<C@@B1B4B<C'51BL=FJLU9;4B7V254e~^1Bc?2@3<=&078LC21tF_-"22?9;+.-0LC2W9;p)Y[V2Ig9,@&?),1LC)_'Y9;L]1tF_-2j

#* *) & % '

kmldnw_'3c?25+s9b+s9;MV2*@96[,9;L=<U9;&G19;1B1325+.-019;1W+.<=+.<C':MG<=&07<=&0c?254B<=1:9;&?'*2s+X)_D025LC@W);P$),p(SB2*'51yt),4B<C25&T132*D-043),784:9;+.+.<=&07hLU9;&078/ 9;7V2*@Y>vIN<=1Bc#_nDg.'A '>E>F Za0 #_F^` / .xFG-2*@e+s9*FEp2sD0254B<=[V2*DP^43),+),1Bc?254i1tF_-"2*@epTFEf'D4>#_E>F^6j#_F_` / >;432 2*'51B<=&07m9N@3+s9;L=LC254'5LU9,@3@ ' 3#p' / 4DF^` / ~^1Bc?2@3251);Pa-0c?25&?),+X25& 9$+X)_D025LC2*DpTF1Bc?2K'5LU9,@3@>;),4pGF' 3#p' / 4>F_` / >V432 2*'51B<=&07.9mLU9;4B7V254 F / #p' / 4DF^` / ~^1Bc?2|@3251);Pu+X)GD025LC2*Ds-043),-"254B1B<C2*@K);P2Y9,'3cs-0c?25&?),+X25&?),&);P"1Bc?2N'5LU9,@3@jWV m Gj#_n gh' 4 m G>4>#_F_# m #_F^` / <C@),&?2g);P"1Bc?2fP^/0&?D?9;+X25&G1:9;LC@z);P 1Bc?2N),p(SB2*'51yt),4B<C25&T132*D.- 9;4:9,Da<=78+>+X2Y9;&0<=&07X1Bc 9;19;19;&TFJ-0LU9,'*2mINc?25432),p(SB2*'513@N);P9i'*254B1:9;<=&'5LU9,@3@9;432m2_-2*'5132*Du>0),p(Sy2*'513@N);P9iD0254B<=[V2*D'5LU9,@3@|9;432W9,'*'*25-0132*Dd9,@NIf25L=Lj

=H]S@aIbMrIbH]IbMNK6COJLK/HJQb@

kw_ c 9,@q1tIK)Da<;:u254325&T1JFV251q4:9;1Bc?2546@B<=+.<=LU9;4sPr2Y9;1B/0432*@sPr),4J25& 9;p0L=<=&07o@B/0p01tF_-0<=&07?>NINc0<=LC2d43251:9;<=&0<=&071FG-2Y9;p0<=L=<=1tFs9;11Bc?2N1B<=+X2|9A- 9;43@3254z432Y9,'3c?2*@<=13@z),-25&0<=&071:9;7? -|&?2<C@ 4 m GD4>#_F_# m #_F_` /I Ei` m g 4>GINc0<C'3cs<C@9Ig9*F);P 9;L=LC)YIN<=&07m9;&W25LC25+X25&T1v5+|x13)$9;-0-2Y9;4<=&-0LU9,'*2K);P09;&?),1Bc?254Y>;MV2*25-0<=&07|1Bc?21tIf)|Da<C@B1B<=&078/0<C@3c 9;p0LC2pGFd432*G/0<=4B<=&0761Bc 9;11Bc?25Fbp),1Bch9;432D02*'5LU9;432*Dh78LC),p 9;L=L=FV>IN<=1BcDa<;:u254325&T125LC25+X25&G1& 9;+X2*@Yjexgc?2i5+Ax1Bc 9;1X+s9YFOp2`@B/0p?@B1B<=1B/0132*D<C@s'Y9;L=LC2*D1Bc?2 %(' 0 A\);P|1Bc?2`@B/0p?@B1B<=1B/01B<C),&Z7843),/0->f9;&?DZ9;&GFH5+Ax 1Bc 9;1+s9YF@B/0p?@31B<=1B/0132<=1K <=&?'5L=/?Da<=&071Bc?2c?2Y9,D<=13@325L]P9K <C@9 2 ' 2 Gf'>E`);Pf1Bc?27843),/0-jf),&?'543251325L=FV>v9;&9;1B1B4B<=p0/0132 78) 5'715$*(+$7 <C@A9,D0D02*Dd13)X1Bc?2eD02*'5LU9;4:9;1B<C),&h);P2Y9,'3c+X25+Wp254Yjxgc?25FOIK),4BMH1B4:9;&?@B<=1B<=[V25L=F f<]PA9d+X25+ep"254X);P|),&?26@B/0p?@31B<=1B/01B<C),&o7843),/0-H<C@1Bc?2Jc?2Y9,D);Pm9;&?),1Bc?254Y>f9;L=L+X25+ep"2543@g);Pu1Bc?2$LU9,@31z7843),/0-69;LC@:)p2*'*),+X2+X25+Wp2543@g);Pu1Bc?2N?43@B1K7843),/0-jxgc?2$1FG-2*@);P1Bc?2$+X25+Wp254

D02*'5LU9;4:9;1B<C),&6+W/?@31Kp2$D0254B<=[V2*DsP^43),+1Bc?2$1FG-2$);P1Bc?2$c?2Y9,Ds<=& Y2543)e),4K+X),432|@31325-?@A~R9;-0- 9;4325&G1BL=FV>a1Bc0<C@@3254B[V2*@13)L=<=+.<=1N1Bc?2@B/04B-04B<C@32mINc?25&b9@B/0p?@B1B<=1B/01B<C),&`7843),/0-bc?2Y9,D6<C@N@B/0p?@B1B<=1B/0132*D K 1Bc?2m1tF_-2m<C@N@B1B<=L=L'*),+.- 9;1B<=p0LC2j

wG/0p?@B1B<=1B/01B<C),&7843),/0-?@$'Y9;&bp"2D02*@3/07T9;432*Dd9*Ig9*F`pGF`4325-0LU9,'5<=&07q25[V254BF6432Pr254325&?'*2W13)s97843),/0-c?2Y9,DbpTF9 "'$+5" '*),+.-)8@B<=13),4e)[V254i9;L=LK1Bc?2X+X25+Wp2543@i);Pg1Bc?2s7843),/0->p0/01WD0),<=&07@:)`IK),/0LCDp"2./0&aP9;<=1BcaPr/0L13)Wk 9;1Bc ¨ ) @f+X)GD025L");P25LC25+X25&T1gD02*'5LU9;4:9;1B<C),&?@Y>_INc0<C'3c6<=&?'5L=/?D02*@K@3/0p?@B1B<=1B/01B<C),&q7843),/0-69(XL=<U9;1B<C),&>?9;&?D/?@32*@1Bc 9;1<=&h1Bc?2 " ) ) Pr/0&?'51B<C),&jX%tPK<=&?@B<C@B1B<=&07),&4325+X)Y[_<=&07b@B/0p?@B1B<=1B/01B<C),&E7843),/0-?@>1Bc?2mPr/0&?'51B<C),&b'*),/0LCD`p29;-0-043)*a<=+s9;132*Du> 1Bc?),/078cj

\;DL6Mt5FDI(McK/CwS~R;l<ZIb;DCP@aMNK6C

xgc?2`),1Bc?254.+s9aSB),41tF_-"26D0254B<=[89;1B<C),&Pr2Y9;1B/04326<=&kw_<C@rA '>E>F Za0 #_F^` / G>n"' O#p' / 4DF^` / >INc0<C'3co<C@.),&0L=F-)8@3@B<=p0LC2INc?254321Bc?2fD0254B<=[V2*DW1FG-2z<C@'*),+.-0LC2u>,9,@),&0L=F1Bc?2*@32f'Y9;&Wc 9Y[V2K+X),4321Bc 9;&9$@B<=&078LC2K+X25+Wp254Yj(<=1BcE1Bc0<C@APR2Y9;1B/04328>uPR),42Y9,'3cD0254B<=[89;1B<C),&EpTF2a1325&?@B<C),&);Pg96'*),+.-0LC2h1FG-2

t>9;L=Lz5+Ax@D02*'5LU9;432*D

IN<=1Bc1tF_-2t<=+.-0L=<C'5<=1BL=FO@3- 9*IN&o9&?25I 25LC25+X25&T1X5+Ax>IN<=1Bc1Bc?2v4 0o2 'J25LC25+X25&T1.& 9;+X269;&?DIN<=1Bc

1Bc?2D0254B<=[V2*DJ1tF_-28>?9;&?DqIN<=1Bc9;&6<=+.-0L=<C'5<=1D02*'5LU9;4:9;1B<C),&);Pv9W432*G/0<=432*D9;1B1B4B<=p0/01328> )5 J4* PR),4mDa<C@B1B<=&078/0<C@Bc 9;p0<=L=<=1tFVjd-|&?2'*),&?@32*T/?25&?'*2);P1Bc?2*@:2e<=+.-0L=<C2*D5+Ax@A<C@A1Bc 9;19;1B1B4B<=p0/0132*@+e/?@B1W@3),+X25c?)I '*),&T1B4B<=p0/0132s13)`25LC25+X25&T1& 9;+.<=&07?><=&E),43D0254mPr),4/?@m13)64325+s9;<=&O@B<=&078LC21tF_-"28j.n9;13254Y>INc?25&64325L=F_<=&07i),&`9;&?'*2*@B13),4yLU9;&078/ 9;7V2m1tF_-2Y9;p0<=L=<=1tFs);P25LC25+X25&G13@Y>_IK2AIN<=L=L"c 9*[V2|13)?&?D69W@:),L=/01B<C),&sPR),41Bc 9;1Yj

xFG-2*@'Y9;&`p2YG7= `<6V>o'iAPr),4ND0254B<=[89;1B<C),&pTFJ/?@B<=&07s9 8$"'N 9;1B1B4B<=p0/0132),&`1Bc?25<=4D02?&0<=1B<C),& ?1Bc?22F:u2*'51<C@13)@3IN<=13'3cq)5:J<=+.-0L=<C2*Ds@B/0p01FG-2N@B/0p?@B1B<=1B/01:9;p0<=L=<=1FPr),41Bc?)8@:2g1tF_-"2*@Yjvm254B<=[89;1B<C),&s);P &?25I\1FG-2*@vPr43),+p0LC)_'3MV2*Db1tF_-"2*@N<C@$@B1B<=L=Lu-")8@:@B<=p0LC28>a1Bc?),/078cj

&h2_1325&?@B<C),&y);PN9J'*),&T1325&T1W+X)GD025L

x<C@A<=13@325L]PN9J'*),&T1325&T1W+X)GD025L>9;&?D<=1m<C@'*),+Wp0<=&?2*DEIN<=1Bch1Bc?2

2a1325&?D02*Dh'*),&T1325&G1+X)GD025Lx@3<=+.-0L=Fd9,@

(x, y)>u&?),12a'*2*2*Da<=&078L=FdP9;<=1BcaP^/0Lv13)J1Bc?2/?@B/ 9;Lv<CD02Y9J);P

),p(SB2*'51yt),4B<C25&T132*Do'5LU9,@3@:2*@Y>INc?25432q-043),-254B1B<C2*@i9;432s& 9;+X2*Du>v&?),1e),43D025432*Duj M Q P c 9,@e9,Da[_<C@32*DO9;7T9;<=&?@31/?@B<=&07h2a1325&?@B<C),&Z9;1X9;L=L~R9;&?D9;7T9;<=&?@31.+s9;&TFO),1Bc?254PR2Y9;1B/0432*@.);P$kmldnw_':c?25+s9V>f9;&?DH/?@32J+X)_D025L7843),/0-?@g<=&?@B132Y9,Dq13)i),p01:9;<=&J1Bc?2A@:9;+X2A2F:2*'51Y>GIN<=1Bc?),/01g1Bc?2|'*),+.-0L=<C'Y9;1B<C),&?@$);P9;/013),+s9;1B<C'AD02*'5LU9;4:9;1B<C),&7V25&?254:9;1B<C),&9;&?D )5 J4+ j

&q/0-0-254p),/0&?DsPr),4K1Bc?2|@3251f);P5+|x@K+X25&G1B<C),&?2*DJ<=&q1Bc?2A'*),&T1325&G1g);P9e5+|x>TIN<=1Bc?),/01KM_&?)YINLC2*Da7V2);Pv1Bc?2-0432*@325&?'*2),4$[,9;L=/?2);Pv<=13@ )5 =4+ 9;1B1B4B<=p0/0132e'Y9;&b@B1B<=L=Lup2m+s9,D028>078<=[V25&d9.@3':c?25+s9a

Wd : Σ′ → 2Σ′

Wd(q) = m(Cm(q)) ∪⋃

q′∈9;L=L1FG-2*@@B/0p?@31B<=1B/01:9;p0LC2<=&),&?2D0254B<=[89;1B<C),&b@B1325-`Pr43),+

q Wd(q′)

K INc0<C'3cb<C@|9.@3251$);P9;L=L5+Ax@+X25&G1B<C),&?2*Db<=&b1Bc?21B4:9;&?@B<=1B<=[V2W'5LC)8@3/0432W);PD0254B<=[,9;1B<C),&dpTF`2_1325&?@3<C),&>9;&?D'*254B1:9;<=&0L=F.9;&i/0-0-254vp"),/0&?Dujxgc?2KP^/0&?'51B<C),&

Cm

@B<=+.-0L=Fi2_1B4:9,'513@v1Bc?2g'*),&G1325&T1+X)_D025La);P9|5+Axj 9+5/' ,76%34'=;UB76%R=' B($+'/5C cV_ "%$ YF576Q9+'BPN')$B($+'/5C *-; L/;U'K& *-,/; 9+'K6& 32L(; 9 8D' 8D"L/,7&9+" 9+5(',76%34'=;UB76%R='

SUTVTXZYVY2[V[F[\m[.\ gNjVkUY aY9eaS,bBh F_^ aTN^5eNb G

I(9;DL_^J;DL6Mt5FDI(McK/Cwz5;DFDI(HJL6;`@

k'>E>F Za0 #_F_` / G>nrEf'D4>#_E>F_6<#_F_` / <C@m&?),1T/0<=132.9,@mc 9;43D13)6D02Y9;LvIN<=1Bc9,@A2a1325&?@B<C),&je%t1m<C@m@B<=+.-0L=F9qIg9*F);P432*@B1B4B<C'51B<=&07E9b'*),&T1325&T1.+X)_D025L~^4325-0LU9,'5<=&07<=1epTFO9b@B/0p0LU9;&078/ 9;7V2>9dD?9;1:9+X)_D025LA~^<=&H1Bc?2J@:9;+X2Ig9*F?> ),4|9;&b9;1B1B4B<=p0/0132W+X)GD025L~^4325-0LU9,'5<=&07 15$ 'Y9;43Da<=& 9;L=<=1B<C2*@$pGF 7 5 (A ),4 *(+$ 5 8 5 A ><=&h),43D0254m13)J+s9;MV2e[89;L=<CD?9;1B<C),&h+X),432'54B<=1B<C'Y9;LjW%1A'Y9;&<=&?D02*2*Dp2i@:),/0&?DaL=F<=78&?),432*D\~R9,@AIK2IN<=L=LD0)TINc?25&2*@B1B<=+s9;1B<=&07E9;&/0-0-254Wp),/0&?DO);PNPR),4W1Bc?2sLU9;&078/ 9;7V26);P9d@3':c?25+s9a>z9;&?DE<=13@e1B4:9;&?@yPr),4B+.%tP$95+Ax ~r25LC25+X25&T1),4e9;1B1B4B<=p0/0132/?@32*@e91tF_-"2X1Bc 9;1W<C@WD0254B<=[V2*DOpTF432*@B1B4B<C'51B<C),&>v<=13@e@3251W);PN-254B+.<=1B132*D[89;L=/?2*@<C@W96@B/0p?@:251);Pf1Bc 9;1);Pg1Bc?2.D0254B<=[V2*D_RP^43),+ 1tF_-"28>9;&?Dh1Bc?2.'*)8@B1);PgIN<CD025&0<=&07<C@1Bc?25&Sy/?@B1W9@B+s9;L=LLC)8@3@|);Pz-0432*'5<C@B<C),&j?),4m@B<=+.-0LC21FG-2*@Y> c?)YIf25[V254Y> 1Bc 9;19;432e9;L=LD0254B<=[V2*DpTF`432*@B1B4B<C'51B<C),&dP^43),+ 9@B<=+.-0LC25Rt/04y1tF_-"2>Ts~^1Bc?21FG-2);P

char∗>a432*@31B4B<C'51B<C),&"ceF&= =p"2'*),&?@B<CD025432*Duj

xgc?2 / F&=&= 0 G7= '`Pr2Y9;1B/04328>INc?25&o/?@32*Do),&\9'*),+.-0LC2G1FG-2*Do5+|x>v-254B+.<=13@X9@3)D02*'5LU9;432*Do25LC25+X25&T113)c 9Y[V26&?)'*),&G1325&T1q9;1s9;L=L>z<]P|<=1<=&?@B132Y9,Dc 9,@X9;&\9;1B1B4B<=p0/0132 )5 = 5*(7+ jEnu<=MV2`D0254B<=[89;1B<C),&pGFE2_1325&?@B<C),&>1Bc0<C@PR2Y9;1B/0432.p0432Y9;Ma@e9;&?'*2*@B13),4yt@31B4B<=&07d1FG-2Y9;p0<=L=<=1tFhpGF2F:u2*'51B<=[V25L=FED02*'5LU9;4B<=&079`&?25I>25+.-01FTt'*),&G1325&T1q5+AxPR),4i1Bc?2q),4B<=78<=& 9;L$9;&?'*2*@B13),4LU9;&078/ 9;7V28j @WIN<=1BcoD0254B<=[89;1B<C),&pTF432*@31B4B<C'51B<C),&>9,@LC),&07b9,@),&?2<C@@9;1B<C@y 2*DIN<=1Bch/0-0-"254p),/0&?D0@),&E5+Ax@m+X25&T1B<C),&?2*D<=&9J'*),&T1325&T1e+X)GD025L>1Bc0<C@PR2Y9;1B/0432'Y9;&p2m<=78&?),432*Duj

GD47#_E 0 6j#'>= ' 2 ' / #AC'i67= 0 E 0 #_F_` / 49;432b25LC25+X25&G1JD02*'5LU9;4:9;1B<C),&?@q1Bc 9;1q'Y9;&\&?),1sp"2`<=&?@31:9;&T1B<U9;132*Du>),&0L=F@B/0p?@31B<=1B/0132*Dujxgc?25F\9;432`[V254BF/?@32Pr/0LNPR),4X@B<=+W/0LU9;1B<=&079h'*),&T132a1yRP^432*2d@B-2*'5<] 'Y9;1B<C),&);P@X@3':c?25+s9 @B/0p?@31B<=1B/01B<C),&`7843),/0-Jc?2Y9,D0@f1:9;M_<=&071Bc?2|-0LU9,'*2m);P&?),&G13254B+.<=& 9;LC@Y>0IN<=1BcJ&?),&ac?2Y9,D67843),/0-6+X25+Wp2543@9,@13254B+.<=& 9;LC@Yj

'%B( $ "! #"

1B1B4B<=p0/0132*@m<=&kAlnHc 9*[V2e&?)q),43D0254Y>u9;&?Dd<=&mxN 9;&?Dbkmldn\w_':c?25+s9a>9;1B1B4B<=p0/0132e+X)_D025LC@A'Y9;&dp29,D02*G/ 9;1325L=F`D02*@3'54B<=p"2*Dd9,@ S /?@31$9@3251);P9;1B1B4B<=p0/0132W/?@32*@gPR),42Y9,'3c25LC25+X25&T1|D02*'5LU9;4:9;1B<C),&j

%&7V25&?254:9;L> 9;&d9;1B1B4B<=p0/0132eD02*'5LU9;4:9;1B<C),&9,@3@:)G'5<U9;132*@$9.& 9;+X2IN<=1Bcd9.D?9;1:9;1FG-28> 9;&?Db9;& 0 #^#_EDFHG m #p' m 4j'~r),/04)IN&X13254B+q9,@3@:)G'5<U9;132*@9;&J9;1B1B4B<=p0/0132D02*'5LU9;4:9;1B<C),&sIN<=1Bcq9;&X25LC25+X25&G1KD02*'5LU9;4:9;1B<C),&>a9'Y9;43Da<=& 9;L=<=1tFV>-)8@3@B<=p0L=F9ND02P9;/0L=1[,9;L=/?2z9;&?D-")8@3@3<=p0L=Fm9N@31:9;1325+X25&T11Bc 9;11Bc?29;1B1B4B<=p0/0132[89;L=/?2<C@002*D13)N1Bc?2D02P9;/0L=1[89;L=/?28j

%&mxNi> 9;1B1B4B<=p0/0132WD02*'5LU9;4:9;1B<C),&?@|9;&?Dd9;1B1B4B<=p0/0132/?@32*@$9;432mIf),/0&?D/0-<=&),&?28

J3CCC /% / 6 /l bd6 /(3"!# %$&U/ (d6 /-3¢!# $(U/ N1/ / - /%

)∗&

9;L=1Bc?),/078cS<=&@:),+X2b'Y9,@32*@Y>g25&G1B<=1B<C2*@~R9@B<=+.-0LC2+s9,'543)HD02?&0<=1B<C),&9;&?DZ2a- 9;&?@B<C),&+X2*':c 9;&0<C@B+qX<C@/?@32*DoPr),4X4325-2Y9;132*D9;1B1B4B<=p0/0132b/?@32*@d~r2a-0LU9;<=&0<=&07c?)I mxNm@s'Y9;&Z'*),&G1:9;<=&Z+s9;&GFo+X),432b25LC25+X25&T13@9;&?DH9;1B1B4B<=p0/0132qD02*'5LU9;4:9;1B<C),&?@i1Bc 9;&o9;-0-"2Y9;4B<=&07d<=&1Bc?2s@:'3c?25+s9`132a1 j !U/"21"/ <C@e),&?2s);P25<=78cG1s432578/0LU9;4s1FG-2*@sD02?&?2*DZ<=&M aP >N9;&?Do1Bc?2 / -# /$ '*),&T1:9;<=&?@q1Bc?2<=&aPR),4B+s9;1B<C),&D02513254B+.<=&0<=&07INc?251Bc?254i1Bc?2J9;1B1B4B<=p0/0132q<C@ + 7 5'(+A > 5$+ ),4 K 5'*A ~R9;&?DO13)INc0<C':cH@31B4B<=&07Gj%&6kAlnEw_'3c?25+s9a>?9;1B1B4B<=p0/0132*@N+s9YFsp2|D02*'5LU9;432*D678LC),p 9;L=L=FV>?9;&?DJ432PR254B432*Dq13)ePr43),+ 9e1FG-2|D02?&0<=1B<C),&>9,@3@3<=78&0<=&07q9'Y9;43Da<=& 9;L=<=1tFd9;&?D9XD02PR9;/0L=1002*D`[89;L=/?2mPr),4N1Bc?2m432PR254325&?'*2W),&0L=FVj

E2IN<=L=Lz@B1B<=L=Lv-0432*@3'54B<=p2.9;&?'*2*@B13),4LU9;&078/ 9;7V2*@PR),49;1B1B4B<=p0/0132*@Y>u1Bc?),/078c>9,@m1Bc?25FdIK2IN<=L=Lp2i&?2*2*D02*DLU9;13254Yjix)9;L=LC)I Pr),4@3),+X22a-"254B<=+X25&G1:9;1B<C),&<=&p 9;LU9;&?'5<=&07`-"254yPR),4B+s9;&?'*2.[a@Yj-0432*'5<C@B<C),&>9;1B1B4B<=p0/0132/?@32*@IK25432|D02*@B<=78&?2*Dq9,@p"25<=&079;p0LC2N13)W@B/0p?@31B<=1B/0132|9;1B1B4B<=p0/0132$D02*'5LU9;4:9;1B<C),&?@jE2g?43@B1z&?2*2*Ds13)W2a1325&?DΣp25FV),&?D25LC25+X25&T1|& 9;+X2*@Y> 9;&?D

Σ′ p25FV),&?D25LC25+X25&G1|D02*'5LU9;4:9;1B<C),&?@Y

anld(aiσ) = anld(Pd(a

iσ)).σ

INc?25432Pd

<C@$9iPr/0&?'51B<C),&Σ′ → 2Σ′ 1Bc 9;1Y>?Pr),4|9;&9;1B1B4B<=p0/0132/?@328>043251B/04B&?@|1Bc?2@B<=&078LC2e25LC25+X25&T1AD02*'5LU9Q

4:9;1B<C),&d1Bc 9;1N/?@32*@N<=1Y>?),4Y>_PR),4$9;&d9;1B1B4B<=p0/0132WD02*'5LU9;4:9;1B<C),&> 43251B/04B&?@|9;L=Lu1Bc?225LC25+X25&G1|D02*'5LU9;4:9;1B<C),&?@$1Bc 9;1/?@32<=1Y>?9;&?D

anld<C@2a1325&?D02*D`13).43251B/04B&>aPR),4$9.@3251

Q ⊆ Σ′ >a1Bc?2/0&0<C),&LU9;&078/ 9;7V2 ⋃

q∈Q anld(q)j

@mIN<=1Bc9;1B1B4B<=p0/0132+X)GD025LC@>mxN 9;&?DkmldnZw_':c?25+s99;432i&?),1[V254BFd2a-0432*@3@B<=[V2<=&c?)YI'*),&G1325&T13@9;&?DED?9;1:9'Y9;&E'*),+Wp0<=&?28j8g),1BcEc 9Y[V2.&?)6If9YF);Pg<=+.-)8@B<=&07b9;&TF- 9;4B1B<C'5/0LU9;4W),43D0254W),4D025-25&?D025&?'5Fp251tIf2*25&b1Bc?2m1tIf)0> 25& 9;p0L=<=&07q9'*),+.-0LC25132W@325- 9;4:9;1B<C),&b);P1Bc?2WD?9;1:9i+X)GD025LPr43),+ 1Bc?2'*),&T1325&G1$+X)_D025L>9,@ Sy/?@B1$9iPr/0&?'51B<C),&43251B/04B&0<=&07q9.432578/0LU9;4$@B/0p0LU9;&078/ 9;7V2W);P ! ∗ j%&Z9;L=432Y9,DaFH@31:9;132*Du>mxN ),&0L=FOc 9,@X9dPR25I -0432*D02?&?2*D\D?9;1:91tF_-2*@.1Bc 9;1X'Y9;&\D02*@3'54B<=p29;1B1B4B<=p0/0132'*),&G1325&T1Y>aINc?25432Y9,@f'3c 9;4:9,'513254ND?9;1:9<=&J25LC25+X25&T13@f<C@ R 9;L=L"),4&?),1Bc0<=&07oT: <=1Bc?254g9;&TF.kmldn@B1B4B<=&07i9;1g9;L=L>+.<]02*D`IN<=1BcbD02*'5LU9;432*Dd25LC25+X25&T13@Y>?),4$&?).'3c 9;4:9,'513254mD?9;1:9X9;1$9;L=Lj

kmldn(w_'3c?25+s9)5:u2543@W9J+e/?'3c+X),432.?&?2784:9;<=&?2*D'*),&T1B43),LK);PgD?9;1:9;1FG-2*@1Bc 9;&mxN &TF@B<=+.-0LC21FG-2s'Y9;&Op"2./?@:2*Du>9;&?Dh1Bc?25432J9;432X+X),432s1Bc 9;& T);PN1Bc?25+ p0/0<=L=1W<=&T13)b1Bc?2XLU9;&078/ 9;7V2 z9;L=LK432578/0LU9;4),4s9;-0-043)Y_<=+s9;1325L=F432578/0LU9;4 + jOkAlnw_'3c?25+s9c 9,@s@3),+X2JL=<=+.<=1:9;1B<C),&?@X<=&o<=13@X9;p0<=L=<=1tFH13)hD02*@3'54B<=p2+.<]a1B/0432*@m);P25LC25+X25&T19;&?DdD?9;1:9q'*),&T1325&G13@Y$%1|'Y9;&432*@B1B4B<C'51mD?9;1:9s'*),&G1325&T13@);P25LC25+X25&G13@),&0L=F<]Pz1Bc?2D02*'5LU9;4:9;1B<C),&H<C@W@B<=+.-0LC2~rD02*'5LU9;432*@W&?)b25LC25+X25&T1'*),&T1325&T1jb%Pg1Bc?2s25LC25+X25&G1eD02*'5LU9;4:9;1B<C),&H<C@W'*),+.-0LC2u>D?9;1:9'*),&G1325&T1fD02*'5LU9;4:9;1B<C),&s<C@R 9;L=L ),4&?),1Bc0<=&07oT:>TL=<=MV2NAxN z<=1Bc?254K9;&TFikAln@B1B4B<=&07'*),&G1325&T1g9;19;L=L0<C@D02*'5LU9;432*D9,@ND?9;1:9i'*),&T1325&G1e~^1Bc?2 5 A 9;1B1B4B<=p0/0132);P1Bc?2D02*'5LU9;4:9;1B<C),&`<C@ (7 >a),4g&?)D?9;1:9i'*),&T1325&T19;1|9;L=L<C@ND02*'5LU9;432*DO~ 5 *A@.* j

7T9;<=&>TIf2$'Y9;&q7V251f9*Ig9*FXIN<=1Bcq/?@B<=&07e9W@B<=+.-0LC2NPr/0&?'51B<C),&~Dd

p"25LC)I|),&qD02*'5LU9;4:9;1B<C),&?@f1Bc 9;1z43251B/04B&?@9432578/0LU9;4J2_-0432*@:@B<C),&)[V254 ! 1Bc 9;1J9;432D02*'5LU9;432*D(9,@q9&?)_D023) @sD?9;1:9E'*),&T1325&T1E~r),4X1Bc?2b25+.-01tFLU9;&078/ 9;7V28> <]P&?)XD?9;1:9X'*),&T1325&T1|<C@D02*'5LU9;432*D j

kmldnw_':c?25+s9c 9,@9iD02*'5LU9;432*D`IN<=LCD0'Y9;43D6&?)_D02m1tF_-"2|PR),4N9;1B1B4B<=p0/0132*@> 43(15'87 j%1g4325-0432*@325&T13@9;&GFq&G/0+Wp254);P9;1B1B4B<=p0/0132*@Y>0IN<=1Bc9;&TFq& 9;+X29;&?D`9;&TFq'*),&G1325&T1Y>"9;&?DqL=<=MV2 4 >_<=1g<C@f13)@3),+X2mD02578432*2-)8@3@B<=p0LC2J13)dL=<=+.<=1i1Bc?2`9;L=LC)IK2*D& 9;+X2*@B- 9,'*2*@X);P|1Bc?2q4325-0432*@:25&T132*D\9;1B1B4B<=p0/0132*@Yj LC@3)dL=<=MV2 4 >1Bc?2-043),p0LC25+);P?1B1B<=&07X<=1g<=&T13).1Bc?2@:'3c?25+s9+X)_D025L<C@'5<=43'5/0+W[V25&G132*DpTFJLC2Y9*[_<=&07X<=1N),/01);P1Bc?29;&?'*2*@313),4LU9;&078/ 9;7V2W+X)GD025L> 9;&?DLC251<=1p29,'*'*2*@3@B<=p0LC2@325- 9;4:9;1325L=FzE2&?2*2*D`&?),1+X)_D025L<=13@2F:u2*'51$),&b@3':c?25+s9@B1B4B/?'51B/04328> ),&0L=Fq<=13@$2F:2*'51$),&`1B4:9;&?@BPr),4B+s9;1B<C),&d432*@B/0L=13@Yj

@ ,X'DC(634B(E-' "1?6 9 WBD' ,/')'K&(*-,/.26B(B($+"C*S3P6Q9+*-"A,V*-;F8D"AL(,7&'K&/"N6%9+*-,(. BD"A*-,H9F,@L/328D' $+;=< >L(R 562,@L/3 8D')$CRK6%,V8D'YC$+*:9U9+'=,J='UE J ' JNE J %' ')9+RNG E6%,7&29+5(' B(L/34B/*-,(. E-'=343P6 CR=6,4B($+"aPN'F9+576Q9#ES6%,/.AL/6.'=; "aPN')$G9+5/'=3 6%$+' ,/"%9G$+'=.L/ES6%$

N

! #"%$'&'()

*+-,/.10243657583:9<;7+>=@?>0BADCFE/;7G>,/;836+H3I2J,/.10A/,DKI,/;8CLKI+KI57MNA/;8AOKI57=P36E/;7,/.>QOASRUTWV<TXKI+1?ZYW[]\_^NCD.10FQK@KIE`0a +>;cb0B?d;7+e,`3O36+10f?>0BADCFE/;7G>,/;836+hg

V.10Yi[!\TjKI,DKk[]3N?>0F5P+13N?>0lN;7+1?>A nmomop $ KI+1? rq G>E`3sCB0BAÀ`;7+>=6tu;7+1A/,/E a CF,/;836+nvrKI+1?wKIE`0K6ADA a QO0B?,`3yx)0;7QzG>57;8CF;7,/57M-?>0BCF5KIE`0B?|R9<;7,/.+13yCB36+e,`0F+s,36EKI,/,/E/;7x a ,`0BA:RKI+1?-,/.10 char∗

?1KI,DK!QO3N?>0F5u~-V.10 1m@ps ep +13N?>0WlN;7+1?;8A?>0FG>E`0BC:KI,`0B?]KI+1? a +1A a G>G36E/,`0B?L;7+dYj^N\NVRA`3w;7,<;8A+136,J?>0BCF5KIE`0B?|~V3zA a QzQKIE/;7:0W,/.10k2 a +1CF,/;836+1AJK:6KI;75KIx>580i2436EK6CBCB0BAÀ/;7+>=w;7+2436E/QKI,/;836+236EKA`C`.10FQK d

Rs,/.10i243657583:9<;7+>=2 a +1CF,/;836+1AiKI575r.KBP0KOA`0F, Σd

3I2UKI575r?>0BCF5KIEDKI,/;836+1ASR;7QzG>57;8CF;7,i?>0BCF5KIEDKI,/;836+1AJ;7+1CF5 a ?>0B?|R3I2KOA`C`.10FQKK6A,/.10F;7EJ?>36QKI;7+hg

Σd = Ed ∪Ad ∪ root, text, comment,pi

9<.10FE`0EdKI+1?Ad

KIE`0j,/.10j0F580FQO0F+s,iKI+1?L,/.10KI,/,/E/;7x a ,`0?>0BCF5KIEDKI,/;836+1AJ3I2 d~

@0y9<;7575KI58A`3A a G>G>580FQO0F+e,,/.10y;7+2436E/QKI,/;836+_;7+x36,/._TWV<TKI+1?YW[]\^NCD.10FQKA`C`.10FQK6A9<;7,/.,/.10?>0BCF5KIEDKI,/;836+H3I2iK!C`.13AD0F+ZE`3N36,z0F580FQO0F+e,w2436E,/.10A`CD.10FQKg36,/.-A`C`.10FQK!5KI+>= a KI=P0BAw.K:P0+132uK6CF;757;7,M2436EJA/G)0BCF;c2MN;7+>=O,/.>;8A:R1x a ,J;7,;8AiKw+KI, a EDKI5r;7,`0FQX3I2;7+2436E/QKI,/;836+],`3K6AÀ`3NCF;KI,`0j9<;7,/.!KI+YW[!\KIG>G>57;8C:KI,/;836+hRKI+1?o;7+KI+eM@C:K6A`0Rr,/.10O;7+2436E/QKI,/;836+o9<;7575x0z+10B0B?>0B?>I~*+oKI+o;7QzG>580FQO0F+s,DKI,/;836+hR,/.102 a +1CF,/;836+C:KI+x)0<;7QzG>580FQO0F+e,`0B?K6AKI+K a ,`3It?>0F,`0BCF,/;836+hR1K6AKjG>E`36=EDKIQGKIEDKIQO0F,`0FE:R36EUxeMK6A/ls;7+>=,/.10a A`0FEJ,`3zA`0F580BCF,,/.10f?>0BCF5KIEDKI,/;836+d2E`36QK57;8A/,:~

Rd : → Ed

V.10 +13N?>0WlN;7+1?L;8AJKI58A`3z?>0BCF5KIE`0B?d;7QzG>57;8CF;7,/57MPR19<;7,/.,/.10jCB36+s,`0F+e,iQO3s?>0F5

(

(0, , (comment,pi)).Rd().(0, , (comment,pi)))

• Cm

E`0F, a E/+1A,/.10CB36+e,`0F+e,kQO3s?>0F53I2KwTWiVjRK6AJKI+0G>E`0BAÀ/;836+;7+L,/.10 Mtu5KI+>= a KI=P0~

• Cd

E`0F, a E/+1A,/.10kAD0F,U3I2hG3ADA/;7x>580JCB36+s,`0F+e,<TWkVA3I2rKfTWiVj~e136E RP;7,E`0F, a E/+1A Rd(Σd)Re2436E

0F580FQO0F+e,À:Rn;7,E`0F, a E/+1Ak,/.10f0F580FQO0F+e,:AW?>0BCF5KIE`0B?]C`.>;758?E`0F+hR ;c2',/.100F580FQO0F+s,k;8Ak?>0BCF5KIE`0B?,`3jCB36+e,DKI;7+O,`0,:ReKI+1? nmomop $ KI+1? ;c2,/.100F580FQO0F+e,U;8A+136,?>0BCF5KIE`0B? ¡ ;7+OTWV<Tw~136EJ36,/.10FE+13N?>0WlN;7+1?>A:R;7,E`0F, a E/+1A,/.10j0FQzG>,MA`0F,:~

• Wd

E`0F, a E/+1A,/.10JAD0F,3I2|G3ADA/;7x>580JCB36+s,`0F+e,<TWkVA3I2rKfTWiVjRP9<;8?>0F+10B?,`3fE`0FQKI;7+6KI57;8?0FP0F+;c2,/.10j,MNG)0f3I2,/.10TWkV_;8AA a x1A/,/;7, a ,`0B?dxeMKI+eM?>0BCF5KIE`0B?|RA a x1A/,/;7, a ,DKIx>580,MNG0~136E+136+tuYf^NTA`C`.10FQK6Ak36E<+136+t0F580FQO0F+e,WTWkVA:R,/.>;8A;8A'¢ a A/, Cd

~

• Pd

E`0F, a E/+1AJ,/.10A`0F,J3I2G)3AÀ/;7x>580jGKIE`0F+s,Àk3I2KOTiiVj£0FP0FE/ML+13N?>0j,/.KI,k.K6AJ,/.10KIE/= a QO0F+e,jK6AKG3ADA/;7x>580jC`.>;758?]36EJKI,/,/E/;7x a ,`0R36EJK6AJKzCB36+s,DKI;7+10B? R nmomop $ 36E ~

• Ad

E`0F, a E/+1AJ,/.10KI,/,/E/;7x a ,`0fQO3N?>0F5h3I2KzTWkVjR1K6AJKwAD0F,J3I2'TWiVrA:R9<;758?>C:KIE`?>AJ+136,;7+1CF5 a ?>0B?|~¤¥¦I§S¨4©uªI«¬¨D®6D¯±°S²4³±²³±²<´6µ²4«·¶¸®©uªI«W¹:®º¸`»h¯±«/¶S¼«W¸D½'©uª6`©/¾¿©<À·¸§º¯Á¶´«iü«·Âº¯ÁµÀ·«/¶´B°²4«¬©J¸µ½À/µ®I¶º³Á¶I`©u«iü¸B¸µ©

«·¯±«·Ã<«·®B©u²·ÄS©uªI¸§º¼ªe¾

ÅÆ

• Am

0NG>E`0BADA/;836+1AJKI,/,/E/;7x a ,`0j;7+243z;7+L,/.10 Atu5KI+>= a KI=P0j2436EJKI+]KI,/,/E/;7x a ,`0fTWkVj~

• Dd

E`0F, a E/+1ACD.KIEDK6CF,`0FE?1KI,DKkQO3s?>0F5>3I2KkTWkVj£º;7,;8AKkE`0F= a 5KIE'5KI+>= a KI=P03:P0FE ! RKI+1?|R69<;7,/.,/.10w57;7Qz;7,DKI,/;836+1A;7+,/.10zADC`.10FQK5KI+>= a KI=P0A/G0BCF;cbC:KI,/;836+1ASRh;7,j;8Aj;7+1?>0FG)0F+1?>0F+e,3I2,/.10zTWiVjACB36+e,`0F+s,JQO3N?>0F5u~

• S∗d

E`0F, a E/+1Ai,/.10E`00N;7P0,/EDKI+1A/;7,/;7P0CF583A a E`03I2,/.10A`0F,i3I2U?>0BCF5KIE`0B?!A a x1A/,/;7, a ,`0TWiVrAJ236EWKTWkVj~kx1A/,/EDK6CF,TiiVrAKIE`0E`0FQO3:P0B?|~36EKI+eMj36,/.10FETiiVrA,/.KI+.10:K6?>A3I2>Yj^NTA a x1A`,/;7, a ,/;836+=E`3 a G1A:R136+>57M,/.10KIE/= a QO0F+e,iTWkV;8A<;7+d,/.10jA`0F,<E`0F, a E/+10B?|~

• anldE`0F, a E/+1A,/.10iE`0F= a 5KIEJKI+1CB0BA/,`36E<TWiV 5KI+>= a KI=P0i2436E<KTWiVj~s36E0:K6CD.TWkV q

RNKI+1CB0BA/,`36E5KI+>= a KI=P0BA3I2)KI5751TWiVrA',/.KI, q

QKBMwA a x1A/,/;7, a ,`0,/.>E`3 a =.O,/.10<A a x1A`,/;7, a ,/;836+z=E`3 a GzQO0BC`.KI+>;8A/QKIE`0j;7+1CF5 a ?>0B?;7+yK a +>;836+d5KI+>= a KI=P0~*+L,/.10f;7QzG>580FQO0F+s,DKI,/;836+hRn,/.105KI+>= a KI=P0f;8Ak?>0BA`CFE/;7x0B?]K6AKI+dK a ,`36QKI,`36+h~

V.102 a +1CF,/;836+ Tt

,DKIlP0BA,93i,MNG0BAK6A'KIE/= a QO0F+e,À:RNKI+1??>0BCF;8?>0BA9<.10F,/.10FE',/.10A`0BCB36+1?QKBMA a x1A`,/;7, a ,`0,/.10b1EÀ/, KI+1?oE`0F, a E/+1A p R;c2,/.10AD0BCB36+1?KIE/= a QO0F+e,w;8AKI+oYW[]\ ^NC`.10FQKd,MNG0R'?>0FE/;7P0B?;7+:0FE`3w36EQO36E`0iA`,`0FG1A2E`36Q ,/.10Jb1EÀ/,<KIE/= a QO0F+e,:RKI+1?+13A/,`0FG a AD0B?;7+,/.10W?>0FE/;76KI,/;836+;8A N0B?O2436E,/.10f?>0FE/;7KI,/;836+dlN;7+1? a A`0B?|~k,/.10FE/9<;8A`0R :p ;8A<E`0F, a E/+10B?|~V.102 a +1CF,/;836+ Td : Q×Ed → true, false

,DKIlP0BA',/.10iiKIQO0<3I2|Kk,MNG0<KI+1?OKiTWkVjRPKI+1?E`0F, a E/+1Arp ;c2<,/.10O,MsG)0zE`0240FE/E`0B?@,`3LxsM!,/.10Ob1EÀ/,KIE/= a QO0F+s,;8AE`0FG>5K6CB0:KIx>580OxeM,/.10O,MNG0O3I2<,/.10A`0BCB36+1?KIE/= a QO0F+s,:R1K6AG)0FE Tt

RKI+1?O,/.10b1EÀ/,KIE/= a QO0F+s,;8AU+136, s0B?O236EU?>0FE/;7KI,/;836+;7+;7,ÀYW[!\!^NC`.10FQK?>0BCF5KIEDKI,/;836+h~k,/.10FE/9<;8A`0R Sp ;8A<E`0F, a E/+10B?|~V.10w2 a +1CF,/;836+ Te : Ed × Ed → true, false

236E/9KIE`?>Af,`3Td

R)b1EÀ`,W0,/EDK6CF,/;7+>=,/.10w+KIQO0z3I2,/.10?>0BCF5KIE`0B?d,MNG0j3I2';7,Àb1EÀ/,kKIE/= a QO0F+s,:~

^N36QO0j,/E/;7N;KOKIG>G>57;80BAJ,`3wYi[!\o?>0BCF5KIE`0B?L+13N?>0j,MsG)0BA:g

• 580FQO0F+e,ÀO?>0BCF5KIE`0B?Z9<;7,/.HKd=5836xKI5,MsG)0E`020FE`0F+1CB0.K:P0KI+0,/EDK !#" $% &(')+*-,/.10 23 KI,·t,/E/;7x a ,`0?>0BCF5KIE`0B?|Rn9<;7,/.Kz,MNG)03I2|¢ a A/,,/.104iiKIQO03I2,/.10f,MNG)0~5J575r;7QzG>57;8CF;7,W?>0BCF5KIEDKI,/;836+1AA/GKB9<+10B?!xsM]?>0b1+10B?0,`0F+1A/;836+!?>0FE/;7KI,/;836+1Af3I2U,/.10,MNG)0wKIE`0QK6?>0w0G>57;8CF;7,:RhKI+1?!0:K6CD.y.K6AKI+0N,/EDK76" 8:9<; q>=?@BA#CEDFGCEHAJILK/M:A<H1CONQPSRTA v ')1*U,/.10 23 KI,/,/E/;7x a ,`0f?>0BCF5KIE`0B?|~

• 580FQO0F+e,Àz?>0BCF5KIE`0B?WV * 1X 3ZY . [ \3 .KBP0LKI575?>0BCF5KIEDKI,/;836+1AwE`0FG0:KI,`0B?Z,9<;8CB0£36+1CB0A`0F,.K6A,/.10?>0BCF5KIE`0B?ZCB36+e,`0F+s,QO3N?>0F5KI+1?ZKI+0,/EDK?>0BCF5KIE`0B?Nt] !^" $% & KI,/,/E/;7x a ,`0 '_):`, V * 9<;7,/.-K,MNG0j3I2',/.10fA/;7+>=580F,`36+d6KI5 a 0baX )Z3 £,/.10j36,/.10FEkA`0F,9<;7,/.L,/.10f?>0BCF5KIE`0B?]CB36+e,`0F+e,c %:d ; (0, eS$SfeS$ ; 9<; , cUg " h<9 (comment,pi))KI+1?Ki6" 8:9<;j . [1\3k')+*-, V * KI,/,/E/;7x a ,`0?>0BCF5KIEDKI,/;836+h~ +>;757580B?+10BADA2 a +1CF,/;836+ Nd

;8AJ?>0b1+10B?dK6A:g

Nd(q) =

true;c2

q.K6AkKwE`0<l a ;7E`0B? ')1*U, V * OKI,/,/E:~U?>0BCF5KIEDKI,/;836+d9<;7,/.,/.10WKI5 a 0 . [1\3

false otherwise

V.10BA`0KI,/,/E/;7x a ,`0BA= a KIEDKI+e,`0B0,/.KI,0F580FQO0F+s,ÀUCB36G>;80B?OK6A·tu;8A2E`36Q ;7+>G a ,,`3j3 a ,/G a ,xeMzKI+Yf^N\NViG>E`3ItCB0BAÀD36Er?>3<+136,h583A`0E`0<l a ;7E`0B?KI,/,/E/;7x a ,`0BAr;7+3 a EA/,DKI,/;8CA/;7Q a 5KI,/;836+h~ Nd

;8Ah236E|,/.10 ) m 3n Xo 3 3:n3 V .qprYsKI,/. 3 3n3 V .tp<r ;7,`0FQ,`0BA/,?>0BA`CFE/;7x)0B?L5KI,`0FE:~

ÅZu

V.10JYi[!\]*+243A`0F,A/G)0BCF;cbC:KI,/;836+G>E`3Ss;8?>0BAKjCB36+1A/;8A/,`0F+s,?>0BADCFE/;7G>,/;836+KI+1?KIx1A`,/EDK6CF,/;836+xK6A/;8A236E a A`0;7+d36,/.10FEkA/G0BCF;cbC:KI,/;836+1ASg

•*,JKIG>G>57;80BA<,`3O90F575ct42436E/QO0B?|R1x a ,+136,+10BCB0BADADKIE/;757MKI57;8?LYW[]\

•*,KIx1A`,/EDK6CF,À?>3NC a QO0F+e,ÀLKI+1? +13s?>0BA3 a ,3I2W,/.10F;7ECB36+e,`0,:g k+! "#$ &%' ;8AKI+KIx1A/,/EDK6CF,/;836+3I2Kj+13s?>0Rs9<.>;8C`.;8AU=;7P0F+KIx1A/,/EDK6CF,)(*+(,%-' ".%/k,/.KI,QKBMzx)05l a 0FE/;80B?z2436EKI5 a 0BAE`0F580F6KI+s,236E,/.10;7,`0FQg H?>3NC a QO0F+e,;7+2436E/QKI,/;836+z;7,`0FQRI236E'01KIQzG>580R.K6AKG>E`36G)0FE/,M+KIQO0B?10>Sp3254 6 RG>E`3:N;8?;7+>=iK<xK6A`0879J*1,`3E`0BA`3657P0E`0F5KI,/;7P0:79J*¬A);7+j,/.10?>3NC a QO0F+e,'KI=eKI;7+1A/,:~ P0F+0F580FQO0F+e,k;7+236E/QKI,/;836+;7,`0FQOAJ;7+L,/.10f?>3NC a QO0F+e,J.K:P0j,/.10jG>E`36G)0FE/,MKIx1A/,/EDK6CF,/57M;7+>.10FE/;7,`0B?|~

•iKIQO0BA/GK6CB0BAKIE`0iA a G>G36E/,`0B??;7E`0BCF,/57M q +KIQO0B?+13s?>0BA.K:P0iK<; 01mope=>0,?Pp ; 01m@p G>E`36G0FE/,M>v

•*,.K6AG>E`36G)0FE/,/;80BA236EwK6CBCB0BAÀ/;7+>=]A a xtu;7,`0FQOA3I2kKI+;7+236E/QKI,/;836+-;7,`0FQg ?1@GA>Bºp ; q CD.>;758?-0F5ct0FQO0F+e,À3I20F580FQO0F+e,ÀKI+1?y,/.10O?>3NC a QO0F+e,0F580FQO0F+s,3I2<K?>3NC a QO0F+e,µvR 0DCCB@FEHGIC:pedq 3I2KI+@0F5ct0FQO0F+e,µvRKI+1?J; 01mope=>0,?PpK0DCCB@E>GIC:pe!q 236EfK6CBCB0BAÀ`;7+>=L,/.10 'Zn ZV )q,MLMLNL YPOLMLNL'O +KIQO0BA`GK6CB0Q %+R-ST+! "#,/R3I2U0F580FQO0F+e,Àv~J*+d,/.10 a Gs9KIE`?y?;7E`0BCF,/;836+hR|KI575r;7+2436E/QKI,/;836+];7,`0FQOAW0>CB0FG>, A>U?VGmop ; C .K:P0]K =>0,Bºp ; C G>E`36G0FE/,M q 236E 0DCCB@E>GIC:p ASRU,/.10L+KIQO0;8A UXW ; pNB-p1psmop ; C v2436EK6CBCB0BAÀ/;7+>=L,/.10F;7EfCB36+s,DKI;7+>;7+>=d;7,`0FQ~wV.>;8AjQO3N?>0F5;8Aj0<l a ;7KI580F+e,f,`3,/.10wYs'KI,/.LTjKI,DK[]3N?>0F5q ,`3wx0WG>E`0BAD0F+e,`0B?vR0>CB0FG>,<2436EJK240F9 +KIQz;7+>=CB36+eP0F+s,/;836+1A:~

•*,WQO3N?>0F58AfK?>3sC a QO0F+s,K6AW.KBN;7+>=]K BYUUC +13s?>0OKIx)3:P0w,/.10wE`3N36,j0F580FQO0F+e, q KI58AD3C:KI57580B?@,/.10Q R-ZX[%' \%'S]%'[%' `vR10<l a ;76KI580F+s,/57ML9<;7,/.Y s'KI,/.h~

•*,C:KI+136+>;8C:KI57;7:0BAW?;_^|0FE`0F+e,JE`0FG>E`0BAD0F+e,DKI,/;836+1AW3I2,/.10fADKIQO0f,/.>;7+>=1RnA a C`.!K6AJCB36+eP0FE/,/;7+>=5`Xa!bMcNdMcA`0BCF,/;836+1A:Rn0F+e,/;7,/;80BAfKI+1?dCD.KIEDK6CF,`0FEWE`020FE`0F+1CB0BAi,`3O,/.10C`.KIEDK6CF,`0FEÀW,/.KI,k,/.10FMLE`0FG>E`0BA`0F+e,:~W^s;7+1CB0Yj^N\NV E a +1Aj36+],`36G3I2U,/.10w*+23AD0F,kQO3N?>0F5uR90zK6AÀ a QO0;7+!,/.10243657583:9<;7+>=L,/.KI,W,/.10FE`0zKIE`0+13sfeT5V- A`0BCF,/;836+1A:R>0F+e,/;7,/;80BAi36EC`.KIEDK6CF,`0FEiE`0240FE`0F+1CB0BA5802,<;7+A/,MN580BA/.10B0F,À:~

YW[]\ *+23A`0F,?>3s0BA+136,A/G)0BCF;c2M@KI+sM;7QzG>580FQO0F+e,DKI,/;836+h£;7,36+>57My;8AKI+-KIx1A/,/EDK6CF,/;7+>=]?>0BADCFE/;7G>,/;836+Z3I2583NC:KI5KI+1?CB36+s,`0N,;7+2436E/QKI,/;836+!K6CBCB0BADA:~

g ihkjlm\n oqpsrutvw xltzy |psr~t8t |w5!i

<K6A/;8C:KI5757MPR,/.10fYWTi[ ;8AkKzE`0BA/,DKI,`0FQO0F+e,W3I2YW[!\o*+23A`0F,:R19<;7,/.]Kz?>0b1+>;7,/;836+y3I2 Q R-ZN[%'* Q %'RK?>0b1+>;7,/;836+@3I2+13N?>0 "(,%'/RhKI+1?],/.10K6?>?;7,/;836+3I2K,MNG0A/MA/,`0FQ 2436Ei6KI5 a 0BA:~iVMNG)0BAWKIE`0?>0b1+10B?!;7+,`0FE/QOAk3I2YW[]\Z^NC`.10FQK~

V.10iQO3A/,xK6A/;8Ck,`0FE/Q3I2r,/.10i,MNG0iA/MA/,`0FQ ;8A<KI+ &%-wRN9<.>;8CD..K6A;7,À+KIQO0k2E`36Q ,/.10i;7+2436E/QKI,/;836+;7,`0FQOAO3I2iYi[!\ *+23A`0F,:Rx a ,KIE`0.>;7=.10FE·tu580FP0F5k0F+e,/;7,/;80BA:gik+-;7,`0FQ;8A0F;7,/.10FEKI+ .|"RvSZ% q KE`0BA/,/E/;8CF,`0B?YW[]\^NC`.10FQKA`;7QzG>580O,MNG)0z;7+1A/,DKI+1CB0Svj36EwK* Q %F~*,`0FQOA.KBP0KI+ZK6AÀ`3NCF;KI,`0B? "(,%FR'K "(,% Q YSZ,%OKI+1?!K5/' "'FNSZ% q K6Ak;7,iKIG>G)0:KIEÀi;7+!KI+!Yi[!\Z?>3sC a QO0F+s,µvR)KI+1?],/.10,MNG0;8AiKOQKIG

M

x)0F,90B0F+,/.10,93>g36Ew01KIQzG>580RKI+0F580FQO0F+e,w+13N?>03I2J,MsG)0 ')U,^* V .33[ QKBMo.KBP0,/.10A/,/E/;7+>=KI5 a 0 !eDRUKI+1?o,/.10,MsG)0B?oKI5 a 0e~ J+Z;7+1A/,DKI+1CB00F580FQO0F+e,z3I2iK]CB36QzG>580,MsG)0?>0BCF5KIEDKI,/;836+.K6AWKOA/,/E/;7+>=6KI5 a 0,/.KI,k;8AkCB36QzG3AD0B?]3I2,/.10A`,/E/;7+>=KI5 a 0BAJ3I2;7,ÀJ,`0N,k+13s?>0?>0BA`CB0F+1?1KI+e,À q 9<.>;8CD..KIG>G)0F+1A,`3x0i,/.10WADKIQO0iA/,/E/;7+>=w6KI5 a 0i,/.KI,,/.10iYj^N\NV;7+1A/,/E a CF,/;836+X1 \3 o:Saw93 a 58?L0FKI5 a KI,`0W,`3>R=;7P0F+,/.100F580FQO0F+e,µvRnKI+1?,/.10j,MNG0B?KI5 a 0j;8A'¢ a A/,<,/.10jA/,/E/;7+>=6KI5 a 0~

V.10FE`0KIE`0jA`0FP0F+J* Q %YF Q /W;7+d,/.10f?1KI,DKQO3s?>0F5ug

U?MGm@p ; C ; UApe 0F+1C:KIG1A a 5KI,`0Yi[!\?>3sC a QO0F+s,À:~j@05KIx0F5',/.>;8Ai+13N?>0lN;7+1?K6A BYUUC ~iTW3NC a tQO0F+e,i+13s?>0BAkC:KI+d.K:P0KI+sML+ a Qx)0FEW3I2U0F580FQO0F+e,:R)CB36QzQO0F+e,:RG>E`3NCB0BAÀ/;7+>=6tu;7+1A/,/E a CF,/;836+y36EJ,`0,C`.>;758?E`0F+hRK6A36G>G)3A`0B?Z,`3dE`3N36,+13s?>0BA;7+ZYi[!\?>3sC a QO0F+s,À:£U,/.>;8A;8Ax)0BC:K a A`0Ys'KI,/. a AD0BA?>3sC a QO0F+s,+13N?>0BAK6ACB36+e,DKI;7+10FEÀ236Ej,`0FQzG)36EDKIE/M,/E`0B0BA:~ikG>G3A`;7,`00FEÀ/;836+ RYsKI,/.]KI58A`3A a G>G)36E/,ÀCB36QzG a ,DKI,/;836+1Ak36+LYW[!\2EDKI=QO0F+e,À9<.>;8CD.]KIE`0j+136,J?>3NC a QO0F+e,ÀS~

psm@p ; C ; UAps>0DCCB@E>GIC:p ; UApe KIE`0fK6A;7+Yi[!\~¡ pC ; UApe KIE`0jQO3N?>0F58A3I2,/.10j,`0N,<,/.KI,<QK:MKIG>G0:KIE<;7+1A/;8?>0j0F580FQO0F+s,J+13N?>0BA:~i3w,`0N,<+13N?>0W;7+

,/.10OQO3N?>0F5UE`0FG>E`0BA`0F+s,ÀzKI+0FQzG>,M@A`,/E/;7+>=1R'KI+1?o,`0N,+13s?>0BA+10FP0FE.K:P0A`;7x>57;7+>=d,`0,+13N?>0BA:~@0W5KIx0F5r,/.>;8A<+13s?>0fls;7+1?K6A =:?A10DC0 ~

01mope=>0,?Pp ; UAps KIE`0W,/.10j+KIQO0BA/GK6CB0f?>0BCF5KIEDKI,/;836+1Ak,/.KI,<90ADKB9 KIx)3:P0RA`0FGKIEDKI,`0B?2E`36Q ,/.10KI,/,/E/;7x a ,`0i+13s?>0BA,/.KI,,/.10FMKIE`0J;7+,/.10kYi[!\ ~ A`0F+1A`0~*,U9K6A243 a +1?Kº2,`0FEA`36QO0k0G)0FE/;80F+1CB09K6AYs'KI,/. AU?1KI,DKiQO3N?>0F5>,/.KI,+KIQO0BA/GK6CB0BAx>;7+1?;7+>=PAUKIE`0x0F,/,`0FEQO3N?>0F580B?OKIx1A/,/EDK6CF,/57M,/.KI+K6A<+13N?>0BA:R1KI+1?LE`0240FE`0F+1CF;7+>=O,`3z+KIQO0BA/GK6CB0j+13N?>0BA<.K6AJx0BCB36QO0j?>0FG>E`0BC:KI,`0B?d;7+Y s'KI,/.~

Umom@p ; C ; UApe>=>BYU?epe:@ ; @ ; CBG1?!C@U ; ; UApe KIE`0fK6A;7+Yi[!\~

V.10 Q R-ZX%- q Q %';8AKI+o36E`?>0FE/;7+>=d3I2KI575+13N?>0BAj;7+K?>3NC a QO0F+e,:R9<.>;8C`.@90OE`0BA/,DKI,`0w.10FE`0O;7+KA/;7QzG>57;cb0B?236E/Qg

•V.10WE`3s36,+13N?>0W;8A<,/.10Wb1EÀ`,<+13s?>0~

• P0FE/M+13s?>0j3NCBC a EÀ<x)0236E`0W;7,ÀkC`.>;758?E`0F+!KI+1?L?>0BADCB0F+1?1KI+e,À:~•iKIQO0BA/GK6CB0J+13s?>0BAU;7QzQO0B?;KI,`0F57Mz243657583:9 ,/.100F580FQO0F+e,+13N?>0<9<;7,/.9<.>;8CD.,/.10FMKIE`0iK6AÀ`3NCF;KI,`0B?|~,/,/E/;7x a ,`0+13N?>0BAk;7QzQO0B?;KI,`0F57M243657583:9 +KIQO0BA/GK6CB0+13N?>0BA:~<V.10E`0F5KI,/;7P036E`?>0FEi;8A a +1?>0b1+10B?;7+LYiTW[ZRx a ,;8AA/,DKIx>580~

•V.10E`0F5KI,/;7P0J36E`?>0FE3I2hA/;7x>57;7+>=PAU;8AU,/.10J36E`?>0FE;7+9<.>;8C`.,/.10FMO3sCBC a E;7+O,/.10bm * `S[3 VG>E`36G0FE/,M3I2,/.10F;7EJGKIE`0F+e,+13N?>0~

•e.>;758?E`0F+]KI+1??>0BA`CB0F+1?1KI+s,Àk3NCBC a E<x02436E`0W243657583:9<;7+>=A`;7x>57;7+>=PA:~

V.>;8A36E`?>0FE/;7+>=f;8A'C:KI57580B?w,/.10?>3NC a QO0F+e,36E`?>0FEx)0BC:K a A`0;7,'36E`?>0FEÀ'+13N?>0BA';7+OKk,/E`0B0;7+OKIx)3 a ,,/.10ADKIQO09KBMdK6A<,/.10F;7E580;8C:KI5|E`0FG>E`0BA`0F+s,DKI,/;836+1A5 A`,DKIE/,,DKI=PA0F,`C~U KIE`0f36E`?>0FE`0B?d;7+dKI+YW[]\@?>3NC a QO0F+e,:~

P0FE/MKI5 a 0W;7+LYiTW[ KI+1?YsKI,/.z;8AKAD0<l a 0F+1CB0gT A/;7+>=580W+13N?>0k;8AKwA`;7+>=580F,`36+A`0<l a 0F+1CB0j3I2,/.10+13N?>0£K]A`0<l a 0F+1CB03I2J+13N?>0BA;8A;7,ÀD0F5c2·RKI+1?Z,/.10AD0<l a 0F+1CB0BAw3I2JA`0<l a 0F+1CB0BA,/.KI,QK:MCB36+1CB0FG>, a KI5757M

! #"%$&(')*+'$,.-&/01)234"657"6'. 98:;*+')7<&)236)*=>)2<-;?A@B"65"'B!CD<)236)E*F,HGJILKMNOQPJRSKTVUXWZYE[\P^]`_a3.)b<5<;cd<&3%"+)2<A"6e)2fB3g&g"%$V05hi)j)2"65ESe*k"%$&3=,GJlEMmOQK+P^]`_IonGJlMmLOQK+P^]`_IRSKTVUXWZYp)6qhr5s<t<5vuw<S"%$AV3>E)E3ouw'=<(*=5<!hr65Ex)p;5;*FS<A"yuwz"'5;")<7)E36365;*Fe)v".3*+')"5"%$Vpz"jf$E,

KIG>G)0:KIE;7+ AD36QO0d0FKI5 a KI,/;836+1AKIE`0dCB36+1A`;8?>0FE`0B? nKI,/,`0F+10B?KI+1?H36E`?>0FE`0B?H;7+ ?>3sC a QO0F+s,36E`?>0FE:~_^N0tl a 0F+1CB0J,MsG)0BA<KIE`0JCB36QzG)3A`0B?3I2r;7,`0FQ ,MsG)0BAKI+1?C:KIE`?;7+KI57;7,/;80BA:R1K6A9<.KI,,/.KI,C:KI+x0kA/MN+e,DK6CF,/;8C:KI5757M0G>E`0BAÀ`0B?LxsMYs'KI,/.A( p| Gp ; ?Pp ¡ =p +136+e,`0FE/Qz;7+KI5ug p&| Grp ; ?Pp ¡ =p

::= ~J3n2 .10 o )S3; \3 V 3-p<rZk| (

6'C:psm ¡ =p ??MG1BYBIp ; ?PpN6 ; AH@F?M0DCUB ?)6C:pNm ¡ =p::= @ ; A ¡ peC | *.3:nTpr | CUnm @F? ¡ =Up|??NGIBBºp ; ?epM6 ; AH@?0DCUB::= | |

CUnmK@? ¡ =p ::= [email protected] |??NGIBIp ; ?PpM6 ; A>@?0DCU*B .K6A,/.10 a A a KI5UQO0:KI+>;7+>=2E`36Q E`0F= a 5KIE0NG>E`0BADA/;836+1A:~ ;7,/.13 a ,36+10RKA`0<l a 0F+1CB0z,MsG)0wx0BCB36QO0BAKA/;7+>=580F,`36+hRr0<l a KI5,`3;7,Àj;7,`0FQ~4 A`0<l a 0F+1CB0O;8AfKI+;7+1A/,DKI+1CB0O3I2<A`36QO0A`0<l a 0F+1CB0,MNG)0;c2WKI575;7,Àw;7,`0FQOAOKIE`0;7+1A/,DKI+1CB0BA3I2J;7,À 6'C:psm ¡ =p RUKI+1?-;7,À580F+>=,/.;8Aw9<;7,/.>;7+,/.10x)3 a +1?>AJA`0F,<xsM,/.10 |??NGIBIp ; ?PpM6 ; A>@?0DCU*B ~V.10jKIE/;83 a A,`0FE/Qz;7+KI58AkC:KI575|2436EA`36QO0j0NG>5KI+KI,/;836+hg

@ ; A ¡ peC QKBMG>E`3N? a CB0KI+eML3I2/g

e

3 3:n3 V .qpr , 3 3n_3 V .tpr :*,`0FQ ,`0BA/,2436EJKI+eML0F580FQO0F+e,

3 3:n3 V .qp 01m@p r :*,`0FQ ,`0BA/,2436E<+KIQO0B?d0F580FQO0F+e,À

3 3:n3 V .qp 01m@p ¡ =p 01mop r , :*,`0FQ ,`0BA/,À2436E0F580FQO0F+e,À:R,/.10W,MNG03I29<.>;8CD.

3 3:n3 V .qp ¡ =p 01m@p r :KIE`0j,/.10W+KIQO0B?d,MNG0j36EJKIE`0?>0FE/;7P0B?2E`36Q;7,:RKI+1?+136,<.KBN;7+>=,/.10V * 3Z` G>E`36G)0FE/,M

3 3:n3 V .qp 01m@p ¡ =p 01mop r , :*,`0FQ ,`0BA/,À2436E0F580FQO0F+e,À:R,/.10W,MNG03I29<.>;8CD.

3 3:n3 V .qp ¡ =p 01m@p r :KIE`0j,/.10W+KIQO0B?d,MNG0j36EJKIE`0?>0FE/;7P0B?2E`36Q;7,

) m 3n Xo 3 3:n3 V .qp 01mop r :*,`0FQ ,`0BA/,2436EA`C`.10FQKºt?>0BCF5KIE`0B?!0F580FQO0F+e,À:Rn36E,/.10F;7Ek?>0BCF5KIE`0B?A a x1A/,/;7, a ,/;836+tu=E`3 a GyA a x1A/,/;7, a ,`0BAX . .1[_* \ .3 p 01mop r :*,`0FQ ,`0BA/,2436E<+KIQO0B?]KI,/,/E/;7x a ,`0BAX . .1[_* \ .3 p 01mop ¡ =p 01m@p r :*,`0FQ ,`0BA/,À2436EJKI,/,/E/;7x a ,`0BA:R>,/.10j,MsG)0f3I2'9<.>;8C`.X . .1[_* \ .3 p ¡ =p 01mop r :KIE`0j,/.10W+KIQO0B?d,MNG0j36EJKIE`0?>0FE/;7P0B?2E`36Q;7,

) m 3n Xo:X . .1[_* \ .3 p 01mop r :*,`0FQ ,`0BA/,2436EA`C`.10FQKºt?>0BCF5KIE`0B?yKI,/,/E/;7x a ,`0BA

` \Zn_3 V . oV `+3-p<r :*,`0FQ ,`0BA/,2436EJKI+eML?>3sC a QO0F+s,J+13N?>0

` \Zn_3 V . oV `+3-p^3 3n_3 V .qp ... r r :*,`0FQ,`0BA/,236E?>3NC a QO0F+e,k+13s?>0BAJ3I2'?>3NC a QO0F+e,À9<.13AD0f?>3sC a QO0F+s,J0F580FQO0F+e,kGK6AÀ<,/.10f0F580FQO0F+s,J,`0BA/,

` \Zn_3 V . oV `+3 :*,`0FQ ,`0BA/,2436E?>3sC a QO0F+s,J+13N?>0BA3I2'?>3NC a QO0F+e,Àk9<.13A`0

p) m 3:n Xo 3 3n3 V .tp ... r r ?>3NC a QO0F+e,k0F580FQO0F+s,JGK6AÀ,/.10jA`C`.10FQK0F580FQO0F+e,J,`0BA`,.3'1.qpr , n n3 V .tp<r , V `3 p<r , :

Vr0BA/,À236E<,`0,:R1CB36QzQO0F+s,:R2 [ 3) )1* V o * V ).1[ \ ._* V p ... r :

KI+eMstulN;7+1?36EG>E`3NCB0BAÀ/;7+>=z;7+1A/,/E a CF,/;836+]+13s?>0BA*.3np<r ;8AJKI+;7,`0FQ ,`0BA/,2436EJKI+eM;7,`0FQ ,MsG)0 q +13N?>0f36EJKI,`36Qz;8Cf,MsG)0SvKI,kKI575u~

V.10 01mop ;7+,/.10 CUmK@? ¡ =p G>E`3s? a CF,/;836+!KIE`0 iiKIQO0BAk3I2\ .|"RjA`;7QzG>580j,MNG0BASgV.10FE`0!QKBM KIG>G0:KIE,`30;8A/,A`36QO0]CB36QzG)0F,/;7,/;836+x0F,90B0F+YWTi[ZAA`0<l a 0F+1CB0],MNG)0BA:RKI+1? YW[!\^NCD.10FQKA57;8A/,KI+1? a +>;836+t?>0FE/;7P0B?zA`;7QzG>580,MsG)0BA:gh*¬AKKI5 a 03I2KYf^NTH57;8A`,·t?>0FE/;7P0B?w,MNG0KJA`;7+>=580F,`36+A`0<l a 0F+1CB03I2n,/.1057;8A/,',MNG)0R36E;8A;7,KiA`0<l a 0F+1CB03I2n,/.1057;8A`,;7,`0FQ ,MsG)0V.10CB36+1;8CF,;8A'0F57;7Qz;7+KI,`0B?zxeM36+>57MG0FE/Qz;7,/,/;7+>=zYW[!\^NC`.10FQKl .|"RWA/;7QzG>580W,MsG)0BA:RN9<.>;8C`.!KIE`0jA/;7QzG>580W,MNG0BA,/.KI,?>3+136,<.K:P0K57;8A/,W36E a +>;836+yA`,`0FGKI+sMs9<.10FE`0w;7+!,/.10F;7EWYj^NT?>0FE/;7KI,/;836+!GKI,/.!2E`36Q ,/.10A`;7QzG>580 a E·tu,MsG)0~jV. a ASR36+>57M,/.10 u 3I2,/.10!OA/G)0BCF;cb0B?Yf^NT A/;7QzG>580W,MNG0BA,/.KI,JKIE`0 G>E/;7Qz;7,/;7P0jA`;7QzG>580W,MNG0BA / KIE`0fKI58A`3KI,`36Qz;8CW,MsG)0BA:~*+1A/,DKI+1CB0BA<3I2r+136+tKI,`36Qz;8Cj,MsG)0BA:RA a C`.dK6A*¬T 9 ^36E<V W^KIE`0WCB36+sP0FE/,`0B?L,`3A`0<l a 0F+1CB0j,MsG)0BA<;7+]KG>E`3NCB0BAÀC:KI57580B?K .|! ""!RNx02436E`0W,/.10FMx0BCB36QO0jG>E`36G)0FEYWTW[ KI5 a 0BA:~

YsKI,/.;8Ai;7+s,`0F=EDKI,`0B?y;7+e,`3Yj^N\NVLK6AjK 5KI+>= a KI=P0w;7+!,/.105KI+>= a KI=P0 D£h;7,ÀiG>E/;7QKIE/MdG a E/G)3A`0BAjKIE`0A`0F580BCF,/;836+ 3I2fA`0<l a 0F+1CB0BA3I2W+13s?>0BA;7+ ?>3NC a QO0F+e,À:RKI+1? 3 a ,/G a ,3I2fA`0<l a 0F+1CB0BA3I2j;7,`0FQOAO,`3oE`0BA a 57,,/E`0B0BA:~WYs'KI,/.C:KI+KI58AD3G)0FE·2436E/QXCB36QzG a ,DKI,/;836+1Af36+yKI5 a 0BA:R)A a C`.@K6AW0FKI5 a KI,/;836+@3I2Ux3N36580:KI+@KI+1?+ a QO0FE/;8C:KI5i0G>E`0BAÀ/;836+1A:£90L9<;75755KIE/=P0F57M-;7=+136E`0d,/.>;8AOlN;7+1?3I2jCB36QzG a ,DKI,/;836+1ASR<A/;7+1CB090]CB36+1CB0FE/+3 a EÀ`0F57P0BAJQO3A/,/57M9<;7,/.,MNG0BAkKI+1?L+136,9<;7,/.KI5 a 0BA:~

YsKI,/.i;8Af/- "sXS3 "(,% Q R9<.>;8C`.w;8A=P3N3s?+10F9A236E'A/,DKI,/;8CYj^N\NVjKI+KI57MA/;8A:R6CB36QzGKIE`0B?w,`3kA`;7, a KI,/;836+a +1?>0FEz,/.10?MN+KIQz;8CKI+1?ZEDKI,/.10FEwQO0BAÀ/Mo,MNG0A/MA/,`0FQ 3I2kY s'KI,/. gYs'KI,/.y0NG>E`0BAÀ`;836+1AC:KI+-x)0,MsG)0t?>0BCF5KIE`0B?d;7+]Yj^N\NVRnKI+1?d9<;7,/.dYsKI,/.Ai36G>,/;836+KI5f/' .! "#R " ( FN%+! "ZX+%BR;7,JC:KI+]x0fP0FE/;cb0B?¤4¤ ©u«¬üÃ-¶º«I®I«/¶J³Á®J©uªI« "!$#SÀªI«¬Ã&%r«·À·¸µÃ<Ã<«·®6¶ºD©u³±¸®('S©uªº«¬°JDü«®º¸®*)¯±³±²©rµ®I¶k®I¸µ®:§I®I³±¸µ®k©°SÂ«·²

Å

,/.KI,,/.100G>E`0BAÀ/;836+1AwKI579K:MNAwG>E`3N? a CB0E`0BA a 57,À,/.KI,wCB36+2436E/Q ,`3],/.10?>0BCF5KIE`0B?Z,MNG)0~!^s;7+1CB0,/.>;8AP0FE/;cbC:KI,/;836+LC:KI+x0iK6AÀ a QO0B?O,`3,DKIlP0kG>5K6CB0kKI,,/.10,/;7QO0i3I2h;7+>;7,/;KI57;7SKI,/;836+3I2KI+Yf^N\sVG>E`3sCB0BADA`36E:R36E:R;c2 a +1A a G>G)36E/,`0B?|R,/.KI,Yj^N\NV G>E`3NCB0BAÀ/;7+>=]9<;7575U,`0FE/Qz;7+KI,`0KI,f,MNG)00FE/E`36EÀR90+10B0B?@+136,583s36l;7+s,`3O;7,JKI+eML?>0B0FG)0FE.10FE`0~

iAKI+Z;7+e,`0F=EDKI,`0B?A a xtu5KI+>= a KI=P0RY s'KI,/.].K6AKJ/' . ""R5R ! &%! 4RUK6AwK]?>0b1+>;7,/;836+2436E.13S9A/,DKI,/;8CCB36+s,`0N,z;7+2436E/QKI,/;836+-;8AGK6ADA`0B?o,`3]YsKI,/.d2E`36Q ;7,Àw0F+eN;7E`36+>QO0F+e,:~@@09<;7575QKIlP0 a A`03I2,/.KI,?>0b1+>;7,/;836+!9<.10F+!KI+KI57MNB;7+>=Ys'KI,/.hR1;7+!KI+!K6AÀ a QzG>,/;836+!,/.KI,Yj^N\NVjAi;7QzG36E/,`0B?]A`C`.10FQK6Ai0F,`C~<KIE`0lN+13:9<+h~sKIE/,Àk3I2,/.10fCB36+s,`0N,iKIE`0g

C0DC@?0G ; UXW ; A>U?MGm@p ; C: RQKIG>G>;7+>=?>3NC a QO0F+e,k+KIQO0BA<,`3O?>3NC a QO0F+e,J,MsG)0BA6 ; VD?U=Up?rpNmJ0C =Upe V.10BA`0LKIE`0LA/G)0BCF;cb0B?Z,`3yx00<l a ;76KI580F+s,O9<;7,/.-,/.10,MNG0BAw,/.KI,w+13N?>0BA

KIE`0KI+>+136,DKI,`0B?]9<;7,/.!? a E/;7+>=YsKI,/.0F6KI5 a KI,/;836+-~@0wK6AÀ a QO0f,/.KI,k,/.10ADC`.10FQK6A a A`0B?L2436EA/,DKI,/;8CfKI+KI57MA/;8AJKI+1?L;7+,/.10WYs'KI,/.z;7+tA`CB36G)0jA`C`.10FQKO,MNG0BAkKIE`0j,/.10jADKIQO0~

6 ; VD?U=Up,0,B@0,Eq ps ^s,DKI,/;8C:KI5757Mls+13S9<+d,MsG)0BA3I2'Yj^N\NV KIE/;KIx>580BA G ; ?!C@U ; @ *; 0DCGIBIpe V.>;8ACB36QzG)36+10F+e,?>0b1+10BAYf^N\NVºt?>0b1+10B?_KI+1?HYsKI,/.ºt?>0b1+10B? 2 a +1Ct

,/;836+1Aw,/.KI,zC:KI+Zx)0C:KI57580B?Z2E`36Q 9<;7,/.>;7+HKI+0NG>E`0BADA/;836+h~ K6CD.2 a +1CF,/;836+A/;7=+KI, a E`0LC:KI+-x)0583s36lP0B? a GdxeM+KIQO0KI+1?KIE/;7,MPRKI+1?CB36+e,DKI;7+1AJGKIEDKIQO0F,`0FEiKI+1?LE`0F, a E/+d,MNG0BA

" ( !#"$%!&$

V.10YWTi[ ,MsG)0A/MNA`,`0FQ%;8Ak+136,WK6AW0G>E`0BAÀ/;7P0wK6AJYW[!\^NCD.10FQKCB36+e,`0F+s,jQO3s?>0F58A:~ iAJ90AµKB9fR;7,C:KI+36+>57MO0NG>E`0BAÀA`0<l a 0F+1CB0BA3I2|;7+1A/,DKI+1CB0BA3I2|,/.10JADKIQO0J,MNG0RKI+1?36+>57Mw9<;7,/.O243 a E?;_^|0FE`0F+e,C`.136;8CB0BA3I2 |??NGIBIp ; ?PpM6 ; A>@?0DCU*B RNA`3,/.10FE`0J;8A57;7,/,/580JCD.KI+1CB0i3I2rA a CBCB0BAÀU;7+,/E/Ms;7+>=,`3wK6C`.>;80FP0iA/,DKI,/;8CJYf^N\NVKI57;8?1KI,/;836+oA/;7QzG>57M!xeM]YiTW[dtu,MNG>;7+>=,`0FQzG>5KI,`0BAj;7+oKYf^N\sV ,/EDKI+1A·2436E/Q q ;7,j;8AWG)3AÀ/;7x>580'Ávo;7+36E`?>0FE,`3]QKIlP0A/,DKI,/;8C,MNG>;7+>=]20:KI, a E`0BA6KI57;8?1KI,`03 a ,/G a ,:~ k+Z,/.1036,/.10FE.KI+1?|RYi[!\^NCD.10FQK!CB36+e,`0F+e,QO3N?>0F58AJC:KI+0G>E`0BAÀA`36QO0fYiTW[ ,MNG0BA:R1K,/E/;8CDl90j9<;7575 a AD0W5KI,`0FE:~

VUMsG)0OKI+>+136,DKI,/;836+1Af;7+@A/,Ms580BA`.10B0F,Àj9<;7575uR|.13:90FP0FE:RrG>E`3Ss;8?>0 a Af9<;7,/.oKCD.KI+1CB0z,`3QKIlP0OKA/.KIE/G)0FE= a 0BAÀKI,i,/.10wG)3AÀ/;7x>580z3 a ,/G a ,f3I2Yj^N\NV Z 2 0 o:SaL;7+1A/,/E a CF,/;836+1Af,/.KI,j;7+sP36lP0K2 a +1CF,/;836+hR36EjCB36GeM,/.10fCB36+s,`0F+e,W3I2 a +>lN+13:9<+hR1x a ,,MNG0B?6KIE/;KIx>580BA36EJGKIEDKIQO0F,`0FEÀ:~

()*,+-".*/0#"12334

s65879:;=<>:@?>?>ACB6+D?E58<>:GF)9H587IF#5J?lN+DBKF<+5J?MLCBNK587ACB6+O;H5879D?EA7+oYsP5879 gRQ&9D:TSU?>:TLC:@NT7KVPWA73:F+5I+YW[]\X7<>:@:VH5R?>:<l a :F+DN@:MB8Y'+DB.Z=:@?:~[+ 79D:kYs65879IW<\58]^]_58<KVD58L`]GB?7):F3:T<Sa:b;=<>:@?>?ACB6+ a ?>:@?&79D:W 0DC =>B +DB6+.7>:T<]Â7+H58Lu£D:F3:F+79D:YsP5879c:b;=<>:@?>?ACB6+Xdbe AC?MAC?f?Ss+.7\5JNT7ACNK58L`L`SX5 ;H5879O:b;=<>:@?>?ACB6+ q 58]GB6+=Wg]_5I+hS ]GBJ<>:l.A7+DZ=?µv~U:F)A`L`L a ?>:E79D:I7>:T<]i;H5879:b;=<>:@?>?ACB6+jVkF)<A`77>:F+U5J? XPathpath

7>Ba]G:K5I+:;=<>:@?>?>ACB6+D?479H587,5JNT7 a 58L`L`S

!

?>:TLC:@NT7+DBZ=:@?MY <>BJ] 5I+Yi[!\7<>:@:V6A7+X] a N\9 79D:a?\58]G:aF#5KSU79H587I79D:Yf^N\.Q 9:@N@BJ]^]G:F+DZD587ACB6+Z=B:@?:~

;H5879 :;=<>:@?\?ACB6+A7+79=AC??>:F+D?>: AC?5+ a ]x:T<4B8Yf/' &%&(:;=<>:@?>?>ACB6+D?KV=:K5JN>9gN@B6+D?>AC?7A7+=WGB8Y 5I+K /TVD5* Q %< &%/' 5I+DZ 5w+ a ]x:T<4B8Y1(* % Q #R ! &%/P£HY BJ<:D58]^;=LC:V=79D:,;H5879g:b;=<>:@?>?ACB6+m * `,1, a+1 `+3+) 3 V ` XZV . o: [ o )S3 Za p<r-, , V `3 p<r m * `,1, X X .1. [* \1.3T, , X . .1[_* \ .3 p X [ r9H5J?I7F#B?7>:T;D?:£ 79D:bD<>?7 a ?>:@?E79D:m * ` 5ºbAC?KV5I+DZX9H5J?^5 a+1]+H58]G: q +DBZ=:Svf7>:@?7R5I+DZ 5g;=<>:@ZNtACNK587>:£f79D:?>:@N@B6+DZ ?7>:T; a ?>:@? 79D: X . .1[_* \ .3 5ºbAC? 5I+DZ 79D:!YsP5879A`7>:T] 7>:@?>77X . .1[_* \ .3 p<r ~[+ 79=AC?g:D58]^;=LC:VjxBJ79 m * `,1, 5I+DZ X . .1[_* \ .3t,1, N@B a LCZ 9H5B3:oxk:@:F+ BJ]Â`77>:@Z :F+h7A`<>:TL`S3VI5J?79D:@?>:O5ºb:@? 58<>:79D:UZ=: Y 5 a L`7xk: Y BJ<>:+H58]G:7>:@?>7>?g5I+DZ 5877<A7x a 7>:XA`7>:T] 7>:@?7>?:£E9DBKF#:F3:T<KVMF :XF)A`L`LF)<A`7>:dY s65879%:b;=<>:@?>?ACB6+D?_A7+ 79D:TA`<GY a L`L)Y BJ<] 7>BO5:3BJACZ-N@B6+bY a ?ACB6+h~ Q&9D: N@B6+h7>:F+.7B8Y 79D: ;=<>:@ZbActNK587>:V `3+) 3 V ` XV . o [ o )Z3 Za pr , V `3 pr m * `,1, XHV.N@B a LCZ58LC?>Bf9H5:3:Wxk:@:F+5Ix>x=<>:FA 587>:@Za7>Bk¢ a ?7L Xn~Jb:@?IZ=:@?>NT<A7x:aZbA`<>:@NT7ACB6+D?RB8Y+H5:.A`Wh587ACB6+ A7+ 5I+ZYW[]\7<>:@:V5I+DZONK5I+Zx:_Z=:@?>NT<A7x:@Z 5J?fY a +DNT7ACB6+D?Y <>BJ] +DBZ=:@?f7>Bc?>:<l a :F+DN@:@?EB8Y+DBZ=:@?:g ?7>:T;OBS3:T<E79D: 2 X [3 V . 5ºbAC?f<>:TL 587A73:a7>Bc5 R &%>! f+DBZ=::F58L a 587>:@?G7>B79D:g:T]^;=7S BJ<_?A7+=WLC:T7>B6+?>:<l a :F+DN@:gB8Y 79D: 2 X [3 V . ;=<>BJ;:T<7SB8Y 79D:+DB.Z=:£5U?7>:T;BS3:T<^79D: m * ` 5ºbAC?f<>:TL 587A73: 7>B5cN@B6+h7>:b7+DBZ=: :FJ58L a 587>:@?R7>Bc79D:+DB.Z=: ? m * `S[3 V;=<>BJ;:T<7S5J?,5G?\:<l a :F+DN@:V:T7>N~,( : Q 5ºb:@? LÀ7l3: 2 X [3 V . 5I+DZ XV 3). [ 58<<\5I+=W3:E79D:I?>:<l a :F+DN@:fA7+ %'%'/%Z=BN a ]G:F+h7BJ<>Z=:T<:£ Z=BKF<+.F#58<>Z ?7>:T;D?aLÀ7l3: m * ` 5I+DZ `3+) 3 V ` XZV . A7+ +DBJ<]_58L Z=B.N a ]G:F+.7BJ<>Z=:T<KV5I+DZ 21[3 3Z`_* V o )+* * V 5I+DZ7a 1 * V o )+* * V A7+<>:F3:T<>?>:M5I+DZL+DBJ<]_58L$BJ<>Z=:T<KV=<>:@?;:@NT7A73:TL`SP~X . . [* \ .3 BJ<>Z=:T<>?)A7+g5I+ a +DZ=:b1+D:@ZLx a 7?7\5Ix=LC:,BJ<>Z=:T<KV 5I+DZb1+H58L`L`S3V=79D:,?A7+=WLC:T7>B6+g5ºbAC? )Z3 Sa_:F58Lcta 587>:@?7>BG5^?>:<l a :F+DN@:,B8YPLC:F+=W79 VD5I+DZL+D:@:@Z=?<+DBJ79H5:3:E5I+ BJ<>Z=:T<:~ B.Z=:I7>:@?7>?M58<>:RZ=:T<A73:@Z Y <>BJ] 79D: UAp ¡ psC +DB6+h7>:T<]Â7+H58Lu~RQ&9D:TS 58<>:I79D: 6'C:psm ¡ psC ?f58L`<>:K5JZbSA7+.7<>B.Z a N@:@Z2V BJ< 01mop ¡ peC ?KVF)9=ACN>9 58<>:¢ a ?7 01m@p ?IBJ<I79D:_7>B6l3:F+ ~ #+DB.Z=:a7>:@?7INK5I+x:N@B6+D?ACZ=:T<>:@Z5cY a +DNT7ACB6+-Z=:T;=LC:T7A7+=W 5 ?>:<l a :F+DN@:VUxhS <>:T]GB:A7+=W 58L`L<+DBZ=:@?R79H587^Y 58A`L#79D: 7>:@?7:~HBJ<6'C:psm ¡ psC ?KV 79D:M?>:T]_5I+.7ACN@?B8Y 79D:,7>:@?7AC?45J?A7+79D: 6'C:pNm ¡ =p Z=:b1+=A`7ACB6+D?:£=Y BJ< 01m@p ¡ psC ?KV5+DBZ=:;H5J?>?\:@? A Y2A`79H5J? 5VX n_3 ;=<>BJ;:T<7S q :TLC:T]G:F+h7)5I+DZa5877<A7x a 7>:J+DB.Z=:@?9H5B3:Sv5I+DZG79D: 01mop ¡ peCAC?:TA`79D:T< BJ<)79D:M? 58]G: l a 58LÀcbH:@ZL+H58]G:E5J?)79H587B8Y679D:j+DB.Z=:~s <>:@ZbACNK587>:@? 58<>: 5ol.A7+DZB8YMY a <79D:T<+DBZ=: 7>:@?7>?KVN@B6+D?AC?7A7+=W B8YE5I+ YsP5879O:b;=<>:@?>?ACB6+ q 79D: Y a L`LL 5I+=W a 58W3:GNK5I+yx: a ?>:@Zv4:F+DNTLCB?>:@Z A7+ 5I+DZc5I+DZgY BJL`LCBKF)A7+=W 5O+DBZ=:I7>:@?7,BJ<,5a;=<>:@ZbACNK587>: ~MQ&9D::b;=<>:@?>?ACB6+D?RA7+-5c;=<>:@ZbACNK587>:9H5:3: 5JN@N@:@?>?R7>B 79D: Y a +DNT7ACB6+D?B \ [ [3 V .qp<r 5I+DZ X ):.qpr V F)9=ACN\958<>:?>B a <>N@:@? B8Y2] a N>9 N@B6+bY a ?ACB6+hg6Q&9D:TSI<>:T7 a </+a79D:);B?A`7ACB6+_B8Y5W+DBZ=:)A7+a5 79D:?\:<l a :F+DN@:79H587AC?x:TA7+=W;=<>:@ZbACNK587>:47>:@?7>:@Z2Vb5I+DZG79D:LC:F+=W79 B8Y279H587 ?>:<l a :F+DN@:V.<>:@?;k:@NT7A73:TL`SP~ Q&9H587&?>:<l a :F+DN@:AC?KVhA7+_7 a </+jV.79D:?>:<l a :F+DN@:IB8Y79D:+DBZ=:@?79H587 F#:T<>:fLC: Y 7 5 Y 7>:T<79D:+DBZ=:f7>:@?7 BJ<4;=<>:@ZbACNK587>:IA`]^]G:@ZbA 587>:TL`Sc;=<>:@N@:@ZbA7+=W79D:,;=<>:@ZbACNK587>:VI*! #79D:,B6+D:f5 Y 7>:T<)79D:f5ºbAC??7>:T;hg

m * `,1, a+1 2 )+*.* V p<r . 2 )1*._* V pr . e:F58L a 587>:@?7>B a ;7>BR7F BO+DBZ=:@?:g Q&9D: ]Â`W9.7Jx: 5I+.S+ a ]x:T<B8Y N>9=A`LCZL+DBZ=:@?<+H58]G:@Z7a 1£b79D:ibD<>?7¤ ¿® >D©uª!:ÄºÂºü«/¶S³ÁÀ·D©u«·²hÀ/D®jµ¯±²4¸µÂºÂ«/D¨r³±®i²4¸µÃ<«®I¸µ®*)Â6`©uªk«#"SÂSü«·²4²4³±¸®I² 'º»)«'»h³±¯±¯N®º¸µ©h®I«¬«/¶k©u¸À·¸µ®I²4³Á¶º«¨r©uªID©/¾¤$% ¼µ© 'S³±²'&)('*,+7¼µü«·D©u«¬¨h©uª6D®-«·²4À·µÂ«/¶PÄ6D®6¶ % ¯© 'º³Á².&0/'*,+7¯Á«¬²4²h©uªIµ®-¾

1

;=<>:@ZbACNK587>: <>:T]GB:3:@?I79D:bD<>?7KV 5I+DZX]_5Il3:@?R5L+D:TF tuxH5J?>:@Z ?>:<l a :F+DN@:_B8Y79D: BJ79D:T<>?:~ Q&9D: ?>:@N@B6+DZ;=<>:@ZbACNK587>:f<>:T7\58A7+D?79D:WbD<>?7JRB8Y679D:@?>:~

m * `,1, a+1 2 )+*.* V p<r . XV ` 2 )+*._* V p<r . :F58L a 587>:@?R7>B587E]GB?7^B6+D:+DB.Z=:£ 79D: ?>:@N@B6+DZ N>9=A`LCZ-+DBZ=:aB8Y79D: N@B6+.7>:7w+DBZ=:+H58]G:@Z a >~ [7N@B a LCZ9H5:3:fx:@:F+F)<A`77>:F+ 5J? 2 )1*.* ZV p<rY eHV=BJ<'¢ a ?7 eHVbF)9=ACN>9c]G:K5I+D?79D:,?\58]G:~[ a L`7Act?7>:T;U;H5879X:b;=<>:@?>?ACB6+D?M9H5B3:^79D:TA`<jbD<>?>7M?7>:T;U:FJ58L a 587>:@ZXLÀ7l3:G5 ?A7+=WLC:t?7>:T;X:b;=<>:@?>?ACB6+jV<>:t? a L`7A7+=WRA7+ 5E?>:<l a :F+DN@:~ Q&9D: ?>:@N@B6+DZ ?7>:T; AC?#79D:F+:FJ58L a 587>:@Z2VbF)A`79:K5JN>9L+DBZ=:4A7+ 79H587)?>:<l a :F+DN@: 5J?79D:MN@B6+.7>:7J+DB.Z=:VD5I+DZ79D: <>:@? a L`7A7+=W_?>:<l a :F+DN@:@?58<>: ]G:T<W3:@Z7>BJW3:T79D:T<A7+ 79D:,BJ<>Z=:T<WA73:F+LxhS 79D:?7>:T;h ? 5ºAC?S£b79D: <>:T]_58A7+=A7+=Wa?7>:T;D?);=<>BN@:@:@Z79D:M? 58]G: F#5@SP~

s65879^:;=<>:@?>?>ACB6+D?PNK5I+x:N@BJ]x=A7+D:@ZRA7+YsP5879 5J?p1intersectp2

V35I+DZp1exceptp2

V8A7+^5JZ=ZbA`7ACB6+7>B q 5I+DZx=A7+DZbA7+=W_?7<>B6+=W3:T<79H5I+nvYs65879 ?

p1 | p2~

a <b1+H58L F BJ<>Z 5IxkB a 7YsP5879 ] a ?>7x: B6+A`7>? ?A7K: 5I+DZN@BJ]^;=LC:bA`7S)gXQ&9D:!YsP5879 :T<>?ACB6+ 94:@N@BJ]^]G:F+DZD587ACB6+ q v 5I+DZ79D:]YW[!\ [+bY B?>:T794:@N@BJ]^]G:F+DZD587ACB6+ q vG7>BJW3:T79D:T<g58<>: -! u LÀ7+D:@?LCB6+=W F)9D:F+ ;H5J?7>:@Z A7+h7>B 5_7>:7 :@ZbA`7>BJ<:~MQ&9D:YsP58799:@N@BJ]^]G:F+DZD587ACB6+ q : v VY a :T<S ~ 5I+DZYsP5879d~ a +DNT7ACB6+D?45I+DZi4;:T<\587>BJ<>? q v#5I+DZ 79D:WYW[ 94:@N@BJ]^]G:F+DZD587ACB6+ q Æ v7>BJW3:T79D:T<58<>: - aLÀ7+D:@?:£D5IxkB a 7 I7A`]G:@?45J?)L 58<W3:~

Q&9D:3:T<>?ACB6+O~ 94:@N@BJ]^]G:F+DZD587ACB6+_B8YYf^N\.Q q N a <<>:F+.7L`SIA7+wUBJ</lA7+=W <\5 Y 7 ?7\587 a ?µvAC? 5 ?A`W+=AcbHNK5I+h7N\9H5I+=W3: Y <>BJ] 79D:4N a <<>:F+.7<Yj^N\Q ?7\587 a ?:~ [79H5J?#]GBJ<>: :;=<>:@?\?A73:;BKF#:T<KVb]_5Il.A7+=WR?7\587ACN 5I+H58L`S?>AC?]GBJ<>:N@BJ]^;=LÀCNK587>:@Z|~ k+ 79D: BJ79D:T<R9H5I+DZ2VA`7IAC?R?7<>B6+=WL`SX7S.;:@Z2V ]_5IlA7+=W ?\BJ]G: 5J?>;k:@NT7>?RB8Y7S.;:5I+H58L`Sb?AC?#B8Yj79D:L 5I+=W a 58W3: 5I+DZ_A`7>?#B a 7; a 7&:K5J?AC:T<79H5I+ A7+_79D: :T<>?ACB6+ 4W3:F+D:T<\587ACB6+hgU^.7\587ACN47S;=A7+=W9H5J?Wx:@:F+ 79DB a W9h7MA7+.7>B 79D:IZ=:@?>A`W+UB8YUY s65879bV$5I+DZ ?7\587ACNI7S.;:@N>9D:@NDl.A7+=WgB8Y#A`7>?,:;=<>:@?\?ACB6+D?,NK5I+x:,?\5 Y :TL`SaLC: Y 7)7>B_5R?7S.LC:@?9D:@:T7;=<>B.N@:@?>?\BJ<)79H587? a ;=;BJ<7>?)A`7:~

Q&9D:Yj^N\Q e&5I+DZbACZD587>:v9:@N@BJ]^]G:F+DZD587ACB6+;H5J?7>:@ZOA7+h7>B57>:b7R:@ZbA`7>BJ<EAC? : ÆÅ LÀ7+D:@?ELCB6+=W1£79D::T<>?ACB6+ 39:@N@BJ]^]G:F+DZD587ACB6+ B6+=L`S Å u ~U:F)A`L`LD7<Sl3:@:T;=A7+=WEA`7x:TLCBKF:TLC:F3:F+_79DB a ?\5I+DZGLÀ7+D:@?9D:T<>:V3A7+h7<>BZ a NTA7+=WRB6+=L`SI]_5º¢BJ<N\9H5I+=W3:@?Y <>BJ]:T<>?ACB6+ ,7>B :T<>?ACB6+]g

Yf^N\.Q/AC?^5 Z=:@NTL 58<\587A73:L 5I+=W a 58W3:Z=:@?>NT<A7x=A7+=W /- "S]%/D% %- /P£&;=<>BJW<\58]G?^79H587RF)A`L`L&7<\5I+D? Y BJ<] YW[!\7<>:@:@?7>B^BJ79D:T<Yi[!\U7<>:@:@?BJ<:F3:F++DB6+tuYW[]\UB a 7; a 7:~

! " # %$%&' (&$)

Q&9D:,]GB?>7A`]^;kBJ<7\5I+.74N@B6+D?7A`7 a :F+.7>?B8Y5^?7S.LC:@?9D:@:T758<>:g

• &%'(*S_ &%3'ZXST%EZ=:@NTL 58<\587ACB6+D?

•*[% Q &%'(*S_ &%fZ=:@NTL 58<\587ACB6+D?

•/' "ST%'/ D% % (D!s[%- &%-GZ=:@NTL 58<\587ACB6+D?

• 30 Z=:@NTL 58<\587ACB6+D?

• * V_Z \+`+3 *n+2 [ ._) Z=:@NTL 58<\587ACB6+D?

•X . .1[_* \ .3 o )Z3. Z=:@NTL 58<\587ACB6+D?

•q A7+LYj^N\QPvg *n+2 [ . o ) m 3:n X^Z=:@NTL 58<\587ACB6+D?

•q A7+LYj^N\QPvga \ V_ ._* VaZ=:@NTL 58<\587ACB6+D?

30 5I+DZ X . .1[_* \ .3 o )S3. 58<>:w+DBJ7MZ=:T7\58A`LC:@ZU9D:T<>:V|x a 7MA`7,AC?,Z=:@?\NT<A7xk:@Z9DB F 79D:TS58<>:R9H5I+DZbLC:@ZA7+B a <45I+H58L`Sb?AC?)A7+y^:@NT7ACB6+ :~

k "=k$2 ".$1

%'(*ST! &%'ZNS]%/X58<>: 79D:cN@BJ<>: N@BJ]^;B6+D:F+h7>? B8YYf^N\Qjg 5JN>9 9H5J?5 n X . m (D # &%' 5J?>?>BNTA 587>:@Z2VN@B6+D?7<\58A7+=A7+=W79D: ?>:T7 B8Y+DBZ=:@?_7>BOF)9=ACN>9 79D:c< a LC:58;=;=LÀC:@?KV5I+DZ :K5JN>9 9H5J?5( #' " a ?>:@ZA7+Z=:T7>:T<]Â7+=A7+=W F)9=ACN>9 < a LC:MF)A7+D?KV=A7+ NK5J?>:@?)F)9D:T<>:M]GBJ<>:,79H5I+gB6+D:f58;=;=LÀC:@?:~

\ # &%'/ 58<>:zYsP5879 ;H5879X:;=<>:@?\?ACB6+D?KV a ?\:@Zy+DBJ7,Y BJ<E?>:TLC:@NT7ACB6+XB8Y+DB.Z=:@?x a 7,Y BJ<MZ=:T7>:T<]Â7+=A7+=WF)9D:T79D:T< 55R &% f Q %fAC?5JN@N@:T;=7>:@ZLx.S3VHBJ<q! .R D%'/f79D: ;H5877>:T</+h~^BJ]G:,<>:@?>7<ACNT7ACB6+D?Y <>BJ] W3:F+D:T<\58LhYsP5879_:;=<>:@?>?>ACB6+D?58;=;=L`Sg

•k+=L`Sa79D:4m * ` BJ< X . .1[_* \ .3 5º=:@?58<>:,;:T<]Â`77>:@Z

•Q&9D:,?;k:@NTA 58L$BJ;k:T<\587>BJ< AC?);:T<]Â`77>:@Z|g

xk: Y BJ<>: 79D:WbD<>?7?>7>:T; B8Y 5R;H5877>:T</+jVDF)9D:T<>:,A`77<\5I+D?L 587>:@?7>BaSV ,/[ 1 .tp)Z3 Za , , V `3 p<r1r .1[3 X . X ) ` \Sn3 V . oV `3 prZ`3+) 3 V ` XZV . o [ o )Z3 Za , , V `3 p<r

xk:T7F :@:F+c7F B_?7>:T;D?KV=F)9D:T<>:,A`7)]G:K5I+D? Z`3+) 3 V ` XV . o [ o )Z3 Za ,1, V `+3-p<rQ&9D:4?>:T]_5I+h7ACN@?#B8Yk;H5877>:T</+D? 9H5J?x:@:F+_N\9H5I+=W3:@ZGA7+OYf^N\.QbVN@BJ]^;H58<>:@Za7>BM:K58<LÀC:T<U3:T<>?ACB6+D? V37>Bf58L`LCB FY BJ<,]_587>N>9=A7+=WgB6+YW[!\ Y <\58W]G:F+.7>?M79H587f58<>:w+DBJ7,<>BBJ7>:@ZcA7+X5 Z=BN a ]G:F+h7+DB.Z=:Vj5I+DZ Y BJ<,79D:w+D:TFYsP5879GA`7>:T] 7>:@?7>?:g

•sP5877>:T</+D?F)A`79 ` \Zn_3 V . oV `3 p,LNLML#r 5J?)79D:TA`<bD<>?7J+DB.Z=: 7>:@?7Z=: Y 5 a L`77>BR79D: )S3 Za 5ºAC?A7+79H587?7>:T;h~

•sP5877>:T</+D?I79H587x:TWA7+XF)A`795 m * ` 5ºAC?E?7>:T;o+DB F 5JN@N@BJ]^]GBZD587>:_Y BJ< (D!+%'* "ST%// N@B6+.7>:F+h7q :TLC:T]G:F+h7KV ?Umomop ; C V =>@ vx.Sf5 a 7>BJ]_587ACNK58L`L`SEN@B6+s3:T<7A7+=W 7>B79D:;D?>: a Z=B m * ` o: [ o . 2 5ºbAC?:gQ&9H587M5ºAC? 9H5J? m * ` ?>:T]_5I+h7ACN@? Y BJ< ;H58<>:F+h7>:@Zy+DBZ=:@?KVj5I+DZ )Z3 Sa?>:T]_5I+h7ACN@?,Y BJ< ;H58<>:F+h7LC:@?>?+DB.Z=:@?S~

•sP5877>:T</+D?g79H587Lxk:TWA7+ F)A`79 5I+ X . .1[_* \ .3 5ºAC??>7>:T; +DBKF 5JN@N@BJ]^]GBZD587>: Y BJ<;H58<>:F+h7LC:@?>?5877<A7x a 7>:@?KV=A7+ 79D:,? 58]G:,F#5KS q X . .1[_* \ .3 o: [ o . 2 v~

Q&9D:M?\:T]_5I+h7ACN@? B8Y 5I;H5877>:T</+ AC?+DBKFfg

QB Z=:T7>:T<]Â7+D:RF)9D:T79D:T<M5O+DBZ=:N]_587>N\9D:@? 79D:f;H5877>:T</+

pV:F58L a 587>:f79D:R:b;=<>:@?>?ACB6+

[ 1 .qp )Z3 Za ,1, V `+3-p<r1r-p p r F)A`79 N5J?P79D: N@B6+.7>:76A`7>:T]~6[ YD79D: <>:@? a L`76AC?65?>:<l a :F+DN@:

B8YU+DBZ=:@? 79H587,A7+DNTL a Z=:@? NV79D:F++DBZ=:

N]_587>N>9D:@?M79D:E;H5877>:T</+h£PBJ79D:T<F)AC?>:w+DBZ=:

NZ=B.:@?+DBJ7)]_587>N>9g79D:M;H5877>:T</+h~

[7 NK5I+x:c?\:@:F+%79H587/[% ! D%'* Q % AC? A7+e3BJL73:@Z A7+%79D: ;H5877>:T</+ :;=<>:@?>?>ACB6+h£ 79H587+DBZ=:cAC??>BJ]G:TF)9D:T<>:4A7+Ox:T7F#:@:F+a79D:)<>BBJ7B8Y

N ?UYi[!\ 7<>:@:45I+DZ

NA`7>?>:TL YVhBJ<:<l a 58LD7>Bf:TA`79D:T<:~ [+_5I+hSGNK5J?\:V

A`7] a ?7:bAC?7)A7+79D:M?\58]G:WYW[!\U7<>:@: Y <\58W]G:F+h7 5J? N~

s65877>:T</+D?NK5I+w+DBJ7 a ?>:#79D:Ys65879 * V .3[_)Z3 . 5I+DZ 3' 321. BJ;k:T<\587>BJ<>?:~U: F)A`L`L a ?>: XPathpattern7>BGZ=:F+DBJ7>:E5I+hS ;H5877>:T</+h~

z[% Q &%'(*ST! &%/X58<>:cLÀ7l3:cA7+ Yf^N\.Q ~ &BJ79 7>:T]^;=L 587>: < a LC:@? 5I+DZ +H58]G:@Z%7>:T]^;=L 587>:@?N@B6+h7\58A7+5 /%Z,%' R %JR !,/' "'ZDR . VY BJ<]G:T<L`S ls+DB F<+ 5J? 5U7>:T]^;=L 587>:]xB.ZbS)g ?>:<l a :F+DN@: B8Y,/' "'ZDR ""/ VZ=:b1+=A7+=W B a 7; a 745I+DZ B6+hF&58<>Z=?4N@B6+.7<>BJL HB F B8YP79D:M7>:T]^;=L 587>:~

#1 =P& = k$

Q&9D:I?>:T]_5I+h7ACN@? B8Y58<A 5Ix=LC:@? 5I+DZg;H58<\58]G:T7>:T<>? AC?B6+D:EA`]^;kBJ<7\5I+.7 N\9H5I+=W3:IA7+dYf^N\.QgYsP5879R !:F58L a 587>::;=<>:@?\?ACB6+D?IA7+O79D: N@B6+h7>:b7GB8YJ58<A 5Ix=LC:tuxkB a +DZZYW[]\ 7<>:@:@?S~]Yf^N\Q VF)A`79 A`7>?%/ZXS_ +% % P+[%' /TVDN@B a LCZL+DBJ7:~[7)AC?)79 a ?;kB?\?A7x=LC: 7>BGZ=B^Z=:b1+D:V=Y BJ<:D58]^;=LC:VH5I7F#BIt?7\58W3:M7<\5I+D? Y BJ<]_587ACB6+1eg

') ,L):. 0 3+) m 3 3Z. 3Z[)+* V Y O e L O'Zn V )U,/'_) Y O m . .12,# L :L [ d [ XV ) a [ZnIO

') ,J*n+2 [ . m [3 a Y O 2 mX )Z3 IL/'_) O ') ,J*n+2 [ . m [3 a Y O 2 mX )Z3 e L/'_) O ¤! ªI««#"ºµÃ<ÂI¯±«'À¬¸Ã<«·²|½ ü¸µÃ#"%$'&)(

Æ

') , X [_* X 3 VX n3ZYPO* V .3Z[Zn_3Z`* X .3O '_) , X 212 0 o .3n2 X .3) )S3 3 .+Y O O n `+3ZYPO 2 mX )S3 XO ') , X [* XZ 3 ') ,/.3n+2 X .3 n X . m Y O O '_) , X 212 0 o .3n2 X .3) )S3 3 .+Y O* V .3Z[Zn3S`* X .3*On `3ZY O<2 mX )Z3 e O ') , .3n2 1X .3 ') ,J). 0 3) m 313.

" 1 1#

[+Yf^N\QbV?>7SLC:@?9D:@:T7&5I+DZa7>:T]^;=L 587>: ;H58<\58]G:T7>:T<>?&]_5@SOx:Z=:@NTL 58<>:@Z [3;S\*[3Z` VhY BJ<>NTA7+=WR5fNK58L`LC:T<#B8YY a +DNT7ACB6+D?fBJ<M7>:T]^;=L 587>:@?E7>Bx=A7+DZX558L a :RY BJ<,79D:^;H58<\58]G:T7>:T<:~ [+Yf^N\.Q V a +exB a +DZU;H58<\58]G:T7>:T<>?Z=: Y 5 a L`7>:@Z 7>BG5^Z=:@NTL 58<>:@ZgZ=: Y 5 a L`758L a :VDBJ<)79D:M:T]^;=7S?7<A7+=WGA Y5IxD?>:F+h7:~

Yf^N\.Q ? a ;=;kBJ<7>?,5 a 7>BJ]_587ACNEY BJ<F&58<>ZbA7+=W B8YU58L a :x=A7+DZbA7+=W3? Y BJ< 5_7>:T]^;=L 587>:R;H58<\58]G:T7>:T< 79H587 9H5J?x:@:F+UZ=:@NTL 58<>:@ZU5J?M5 "ZNP%'S*(D+[%- &%'g 3:F+X5 Y 7>:T< HB F B8Y#N@B6+h7<>BJL79=<>B a W97>:T]^;=L 587>:@?,79H587MZ=B+DBJ7,Z=:@NTL 58<>:G5a7 a +>+D:TL6;H58<\58]G:T7>:T<KVjA`7 AC? ;=<>:@?>:T</3:@Z|~b 7 a +>+D:TL ;H58<\58]G:T7>:T<j+H58]G:@Z p

AC? NT<>:K587>:@ZyxhS5JZ=ZbA7+=W5 .1\ V V 3 Y O 03+)O VX n_3ZY O p O 5877<A7x a 7>:E7>Ba5 *. mo 2 X [ X n A7+D?7< a NT7ACB6+h£kA`7 NK5I+dx:MB:3:T<<ACZNtZ=:F+ q <>:tuxkB a +DZv,Y BJ<ML 587>:T<E7>:T]^;=L 587>:a<>:@N a <>?ACB6+ q a +h7A`L#79D:O+D:b7f<>:tux=A7+DZbA7+=WDV679H587EAC?µvWx.SX5I+DBJ79D:T<:b;=LÀCNTA`7 *. m o 2 X [ X n .1\ V1V 3 Y O<03+)O VX n_3ZYPO p O )Z3 3 .1Y O ~7~7~ O cA7+D?7< a NT7ACB6+jV BJ< ?>9H5JZ=BKF :@ZY BJ<45R?A7+=WLC:,7>:T]^;=L 587>:MA7+e3BNK587ACB6+gA7+ 79D:,?\58]G:MF#5@S3Vx a 7)F)A`79DB a 779D: .1\ V1V 3 Y O<03+)O 5877<A7x a 7>:~Q a +>+D:TL);H58<\58]G:T7>:T<>?G58<>: N@B6+DN@:T;=7 a 58L`L`S ?A`]Â`L 58<R7>BcZbSN+H58]ÂCNK58L`L`Sst?>N@BJ;k:@ZZ58<A 5Ix=LC:@?IA7+ ?\BJ]G:GY a +DNt7ACB6+H58L ;=<>BJW<\58]^]Â7+=WEL 5I+=W a 58W3:@?KVb5I+DZG79D:TSG58<>:5MN a <>?>:)7>BE5I+H58L`SNK:?7\587ACNK58L`L`SP~ Q&9D:TSR]_5Il3:;H58<\58]wt:T7>:T< 5I+H58L`S?AC?]GBJ<>:fN@B6+bY a ?A7+=WDV1x a 745JNT7 a 58L`L`S+DBJ74F BJ<>?>:~U:,F)A`L`LN\9D:TF 79=<>B a W9g79D:fF)9DBJLC:M?7>BJ<SB6+ 7>:T]^;=L 587>:f;H58<\58]G:T7>:T<>?A7+!^:@NT7ACB6+ :~

Pj! =3*k &6

Yf^N\.Q ? a ;=;BJ<7>? a ?>:T<·tZ=:b1+D:@ZY a +DNT7ACB6+D? VF)A`79%;H58<\58]G:T7>:T<>? 5I+DZ-<>:@? a L`7 7S.;:@?aZ=:b1+D:@Z 5J?a pV| Gp ; ?Pp ¡ =p ?:~ [+79D: Y a +DNT7ACB6+%Z=:b1+=A`7ACB6+jV 5I+ Ys65879O:b;=<>:@?>?ACB6+%BJ< 5I+ Yf^N\.Q ?>:<l a :F+DN@:N@B6+D?7< a NT7>BJ< N@BJ]^; a 7>:@? 79D:Y a +DNT7ACB6+h ?58L a :~ a +DNT7ACB6+D?5I+DZH+H58]G:@Z7>:T]^;=L 587>:@? 58<>:d+DBJ73:T<SZbA_^2:T<>:F+h7^:F+h7A`7AC:@?S£;H58<\58]G:T7>:T<>?RB8Y)Y a +DNT7ACB6+D?^58<>: 58L`F#5@Sb? [3S\_*[3S` V 5I+DZOB6+=L`S Y a +DNT7ACB6+D?RNK5I+ox:;=<>:@?>NT<A7x:@Z-5J?W¢ a ?7_5I+HYs65879 Y a +DNT7ACB6+h~ a +DNT7ACB6+D?KV#9DBKF#:F3:T<KV)B a 7; a 7G7>BX5I+.S.F)9D:T<>:F)9D:T<>:K5J?7>:T]^;=L 587>:@? B a 7; a 77>B_5I<>:@? a L`77<>:@:~¤ ½À·¸§Sü²4«Ä©uªI³±²D¯±²4¸k¼µ¸B«·²½çD¨ µµ¯±§I«·²À·¸®º²©4ü§IÀ¬©u«·¶f´B°WJ²4«B§º«·®IÀ·«UÀ·¸µ®I²©4ü§IÀ©u¸µ¨'³±®j©uªI«³±®I²©u«/µ¶j¸µ½

©uªI«! #"$"&%«#"SÂºü«¬²4²4³Á¸µ®

u

!#"$ & = 1

Q$:T]^;=L 587>:@?KV.?>7SLC:@?9D:@:T7PY a +DNT7ACB6+D?5I+DZ^?>7SLC:@?9D:@:T75I+DZR7>:T]^;=L 587>:<J58<A 5Ix=LC:@?6]_5KSx:#7S;k:t5I+>+DBJ7\587>:@ZA7+Yf^N\QbVDF)A`79g5I+X ):Y O p&| Grp ; ?ep ¡ =p O 5877<A7x a 7>:VD79 a ??7<>B6+=WL`S 7S;=A7+=WG79D:T] ~

&" &H =

Yf^N\.QgY :K587 a <>:@?EZbSN+H58]ÂCN_?\N>9D:T]_5dJ58LÀCZD587ACB6+ B8YA`7>?EB a 7; a 7KVP]_5IlA7+=WcA`7E;kB?\?A7x=LC:G7>Bc?;k:@NTA Y SU5I+Yf^N\.Q7<\5I+D? Y BJ<] 79H587,:TA`79D:T<MB a 7; a 7>?j58LÀCZyYW[]\VBJ< Y 58A`LC?M587 < a +.7A`]G:~RQ&9=AC?,N@B a LCZ?>:@:T] LÀ7l3:]_5IlA7+=Wc?7\587ACNJ58LÀCZD587ACB6+ <>:@Z a +DZD5I+h7KV679D:F+jV 5J?EB a 7; a 758LÀCZbA`7SUNK5I+xk:^W a 58<\5I+.7>:@:@Z|~ BKF :F3:T<KV?7\587ACNJ58LÀCZD587ACB6+_NK5I+a?7A`L`LD]_5Il3:5 ?7<>B6+=W3:T<W a 58<\5I+h7>:@:£N+H58]G:TL`SR79H587+DB < a +t 7A`]G:)Y 58A`L a <>:<x:@NK5 a ?>:B8Y5I+gB a 7; a 758LÀCZD587ACB6+c:T<<>BJ<F)A`L`L29H58;=;:F+h~

Q&9D:)<>:@? a L`7N@B6+D?7< a NT7ACB6+a?\:T]_5I+h7ACN@? AC?xkBJ77>BJ]wt a ;aA7+zYj^N\QbVb5,N>9H5I+=W3:Y <>BJ] Yf^N\.Q ? 7>BJ;tZ=BKF<+h~Q&9=AC?f]_5Il3:@?EZbSN+H58]ÂCN^<>:@? a L`7J58LÀCZD587ACB6+ ZbA_N a L`7KVrx:@NK5 a ?>:z+DBZ=:@?E58<>:^7S.;:@Z2V65I+DZX5J?MF#:_?\5KF A7+^:@NT7ACB6+ ~ Æ V=79D:,7S;:MB8Y 5z+DB.Z=:,NK5I+x:MZ=:T<A73:@Z Y <>BJ] A`7>?5I+DN@:@?>7>BJ<4?7<A7+=W x a 7 58779D:,7A`]G:MB8YZbSN+H58]ÂCNf58LÀCZD587ACB6+jVD79D:T<>:,AC?+DB_5I+DN@:@?7>BJ<?7<A7+=WD' Q&9D:T<>: Y BJ<>:VD79D:T<>:E58<>:,;=<>BS.AC?ACB6+D?Y BJ<?>7<A`;=;=A7+=WB^-5I+DZU<>:@Z=BJA7+=Wc7S;k: 5I+>+DBJ7\587ACB6+jV 5I+DZY BJ<fJ58LÀCZD587A7+=W 58Wh58A7+D?7f7S.;:GZ=:b1+=A`7ACB6+D?b +DBJ7E58Wh58A7+D?>7Z=:@NTL 58<\587ACB6+D?KVk5J?)A`7AC? a ? a 58L`L`S Z=B6+D:~

k+GB6xD?>N a <>:5J?;:@NT7 B8Yn58LÀCZD587ACB6+GAC?ts^ [$5I+>+DBJ7\587ACB6+hg 58LÀCZD587A7+=WM7<>:@:@? ]_5KSR5JZ=Z+DBZ=:@? 7>B 79D:T]~[Y$5M7<>:@:4AC? <>:@NTSNTLC:@ZaA7+ 5M7F#BIt?7\58W3: 7<\5I+D? Y BJ<]_587ACB6+jVs58LÀCZD587A7+=W^BJ<+DBJ7#]_5@SaN>9H5I+=W3: ?>:T]_5I+h7ACN@?&B8Y79D:I+DZ ;H5J?>?KV=:F3:F+ F)A`79DB a 758LÀCZD587ACB6+c:T<<>BJ<>?D~

16 &"

k+D: B8Y 7>:F+O<>:@N a <<A7+=W ;=<>B6x=LC:T] A7+Yj^N\Q a?>7SLC:@?9D:@:T7R5 a 79DBJ<A7+=W F#5J? V5J?MF : ?\5KF A7+ 79D:[7 ?>:F+D:T7]Â7+=Act? a </3:TS3VH79H587B8YPW<>B a ;=A7+=W 5R?>:T7)B8YPA7+=; a 7+DBZ=:@?xhS ?>BJ]G:,NT<A`7>:T<ACB6+jVk5I+DZ ;=<>B.N@:@?>?&79D:MW<>B a ;D??>:<l a :F+h7A 58L`L`SP~ Q&9D: a+ [ o 3 Xm o [ \12 A7+D?>7< a NT7ACB6+ A7+]Yj^N\QaF#5J? Z=:@?A`W+D:@Zc7>B_]Â`7A`Wh587>:E79H587:~[7>?Y BJ<]_587AC?:g

a+ [ o 3 Xm o [ \12 )Z3 3 .1Y O XPath O g Y O XPath O body a [ o 3 Xmo S[ \ 2

Q&9D:T<>:M58<>: ?>BJ]G: ZbA_^:T<>:F+.7&W<>B a ;=A7+=W^]G:T79DB.Z=? g5B58A`L 5Ix=LC:VbF)A`79ZbA_^:T<>:F+.7?>:T]_5I+h7ACN@?:~U:<>: Y :T<&7>B

1 ~ ?\:<l a :F+DN@: B8Yh+DB.Z=:@?#AC?#?>:TLC:@NT7>:@ZxhSG79D: )Z3 3 . :;=<>:@?\?ACB6+jV=5I+DZGY BJ<#:K5JN\9+DB.Z=:A7+a79D: ?>:<l a :F+DN@:V5 W<>B a ;=A7+=Wl3:TSEAC?W3:F+D:T<\587>:@ZOxhS^:F58L a 587A7+=Wf79D: g

:b;=<>:@?>?ACB6+_F)A`79G79D:<+DBZ=:5J? 79D:N@B6+.7>:7A`7>:T]~ W<>B a ; AC?79D:F+5^L 58<W3:@?>7 ? a xt?\:<l a :F+DN@:IB8Y+DB.Z=:@?479H587,58L`LW3:F+D:T<\587>:@Z 79D:f?\58]G:l3:TS q xhSg79D: 3;N@BJ]^;H58<AC?>B6+c?>:T]_5I+h7ACN@?µv V 5I+DZ 79D: ?\:<l a :F+DN@:,N@B6+D?7< a NT7>BJ< body

AC?&A7+e3B6l3:@Z Y BJ<):K5JN>9 W<>B a ;jVD5JZ=ZbA7+=W7>B_5b1+H58L$?>:<l a :F+DN@:M79H587AC?)79D: <>:@? a L`7B8Y679D:ba [ o 3 Xmo S[ \ 2 A7+D?7< a NT7ACB6+h~¤ #S«¬«S¾ !)D²4³ÁÀ²© °º¯±«·²4ªº«·«¬©rÂºü¸BÀ¬«·²4²4¸µü²¶º¸®I¸µ©r§º®6¶º«ü²©µ®6¶©°SÂ«·²·Äºµ®I¶k³±®I²©u«·¶W`ü«²4Â«·À·³ 6«/¶J©u¸½7D³Á¯7¾¤ #S¸µÃ<«·¸®º«<¸§º¼ªB©©u¸j²4Â«¬À·³½ °zj²4¸µÃ<«¬©uªI³±®I¼k©uª6D©²4«·ÂID¨D©u«¬² µµ¯±³Á¶ID©u³±¸µ®Oµ®6¶ µµ¯±³Á¶I`©u³±¸®*)8ü«·¯Á`©u«/¶w©4¨µ®I²½ ¸µüÃ`©u³Á¸µ®

©µ²4¹:²·¾«#":©hÂSü¸«·À¬©/¾±¾±¾

1!

[+D?ACZ=:body

VD79D: Y a +DNT7ACB6+ \1[ [3 V . o S[ \12_* V o 30tp<r <>:T7 a </+D?79D:MN a <<>:F+.7Jl3:TS A Y g Z=:b1+D:@?B6+D:VBJ< 79D::T]^;=7SG?\:<l a :F+DN@:4BJ79D:T<F)AC?>:~ \1[ [3 V . o S[ \12qp<r <>:T7 a </+D?79D:4N a <<>:F+h7#W<>B a ; 5J?#5M?>:<l a :F+DN@:~

X 2 2 0 o *<n+2 [1.) # V 3' . o n X . m

Q&9D: X 212 0 o *n+2 [ ._) A7+D?7< a NT7ACB6+ F BJ</lb?#LÀ7l3: X 2 2 0 o .3:n+2 X .3+) )Z3 3 .1YPOL-O Vh:=N@:T;=779H587#A`7B6+=L`Sc;=<>BJ;H58Wh587>:@?HBKF 7>B 7>:T]^;=L 587>:R< a LC:@? A7+U?7S.LC:@?9D:@:T7 ]GBZ a LC:@? 79H587M58<>:RA`]^;kBJ<7>:@Z2V2ZbA`<>:@NT7L`S BJ<A7+DZbA`<>:@NT7L`S Y <>BJ] 79D: ?7S.LC:@?>9D:@:T7ILC:F3:TL)79H587GN@B6+.7\58A7+D?^79D: A7+D?7< a NT7ACB6+h~ [7>?R?>:T]_5I+.7ACN@?^<>:@?>:T]x=LC:@?B8Y5 NK58L`L7>Bg5I+OB:3:T<<ACZ=Z=:F+X]G:T79DBZUA7+X5I+OB6x¢ :@NT7·tBJ<AC:F+.7>:@ZXL 5I+=W a 58W3:VY <>BJ] F)A`79=A7+U79D:GB:3:T<<ACZNtA7+=WU]G:T79DBZ|g ):\ 23Z[fL a+ p<r A7+79D:LxkBZbSOB8Y a p<r V#5I+DZ79D: ; a <;B?>:AC?^79D:?\58]G:ggQBX58L`LCB F;=<>BJW<\58]^]G:T<>?R7>B ?;:@NTA 58LÀ7K:a?>BJ]G:xk:T9H5:.ACBJ<RF)A`79DB a 7I9H5BA7+=W 7>B <>:T;:K587E79D:a;=<>:@?>NT<A`;=7ACB6+B8Y79D:W3:F+D:T<\58L$;H58<7:~

Q&9D:V 3'1. o n X . mEA7+D?7< a NT7ACB6+_F#BJ</l?79D:?\58]G:)F&5@S_5J?X 2 2 0 o *<n+2 [1.) V.:bN@:T;=779H587N@B6+h7<>BJLk]_5@SW3BcB6+=L`S 7>B 7>:T]^;=L 587>:_< a LC:@?fF)A`79O5LCB F :T<fA`]^;BJ<7f;=<>:@N@:@Z=:F+DN@:a79H5I+U79H587IB8Y&79D:_N@B6+h7\58A7+=A7+=W < a LC:q F)9=ACN\9 AC?EZbA_^:T<>:F+.7fY <>BJ] X 2 2 0 o *<n2 [1.) 5g?7SLC:@?9D:@:T7ELC:F3:TL ]_5KS9H5B3: 5LCBKF#:T<E;=<>:@N@:@Z=:F+DN@:79H5I+U5I+DBJ79D:T<KVF)A`79DB a 7,9H5BA7+=W 7>Bx:EA`]^;kBJ<7>:@ZcY <>BJ] A`7K'Áv V)_7>Ba7>:T]^;=L 587>:I< a LC:@? F)A`79 79D:R?\58]G:A`]^;BJ<7;=<>:@N@:@Z=:F+DN@:E5I+DZc5ILCBKF :T<4;=<ACBJ<A`7S79H5I+ 79H5874B8YP79D:,N@B6+.7\58A7+=A7+=Wa< a LC:~

& K / " =%1 = &

Q&9D:dx a A`L`7·t A7+-7>:T]^;=L 587>:c< a LC:@?GA7+ Yf^N\QX58<>: <\5879D:T< ?A`]Â`L 58<_7>BU79DB?>:A7+ Yf^N\Q g a 7; a 7 79D:X \3 oZaE5I+.SR7>:75I+DZ_5877<A7x a 7>:J+DB.Z=:@? V<>:@N a <>?>:)7>B 7>:T]^;=L 587>:@? ]_587>N>9=A7+=WR58L`LDN>9=A`LCZb<>:F+aB8Y2:TLC:T]G:F+h75I+DZ BUUC +DB.Z=:@? V5I+DZZ=B+DBJ79=A7+=W Y BJ< ?MUnmomop ; C 5I+DZ =>@ +DB.Z=:@?S~MQ&9D:x a A`L`7·t A7+< a LC:@? A7+!Yf^N\Q+DB F 9H5B3: 5 n `+3SY O X 1 O 5JZ=Z=:@Z2V+DBLCB6+=W3:T<+D:@N@:@?>?A`7\587A7+=WXN@B6+DN@:T;=7 a 58L B6+t 79D:t DSNT<>:K587ACB6+B8YZ=: Y 5 a L`7&< a LC:@?Y BJ<&:K5JN>9 ]GB.Z=: a ?>:@Z|~ Q&9D:4< a LC:4Y BJ<&:TLC:T]G:F+h7+DBZ=:@?&58LC?\BMY BJ<F#58<>Z=?&79D: N a <<>:F+h7)]GBZ=:5J? ?NGIBBºp ; C 5I+DZ5I+hS_7>:T]^;=L 587>: ;H58<\58]G:T7>:T<>?KV=5J?#BJ;=;B?>:@Za7>BI79D:4B6+D: A7+Yj^N\Q F)9=ACN>9 ?9D:@Za79D:;H58<\58]G:T7>:T<>?:~

Q&9=AC?x:T9H5BACBJ<)5JNT7 a 58L`L`S_]_5Il3:@?x a A`L`7·t A7+ < a LC:@? l a A`7>:4:K5J?S^7>BE9H5I+DZbLC:£=B6+=L`S^79D: A`]^;=LÀCNTA`7 ;H58<\58]G:T7>:T<Y BJ<F#58<>ZbA7+=W+D:@:@Z=?N@B6+D?ACZ=:T<\587ACB6+h~Wh58A7+jV=79D:M7<>:K587]G:F+h74B8Y679=AC?)W3B:@?)A7+h7>B^:@NT7ACB6+ :~

)$ ' $ " $ '

Q&9D:)!-!*R% ;H58<7B8Yb79D:Yf^N\.Q9:@N@BJ]^]G:F+DZD587ACB6+E?>;k:@NTAcbH:@?27F B4ZbA_^:T<>:F+.7LC:F3:TLC?jB8Y=?7SLC:@?9D:@:T7;=<>BN@:@?>?>BJ<>? q ;=<>BJW<\58]G?479H587:=:@N a 7>:jYf^N\.Q 7<\5I+D?Y BJ<]G?µv)N@B6+bY BJ<]_5I+DN@:g

0>@? Yf^N\Q ;=<>BN@:@?>?>BJ<>?RZ=B!+DBJ7 a +DZ=:T<>?7\5I+DZ ?>N>9D:T]_5J? V5I+DZ :F+bY BJ<>N@: 7S;:a?\5 Y :T7SxhSY 58A`LÀ7+=WU5875I+hS *n+2 [ . o ) m 3:n X ) A7+D?7< a NT7ACB6+cBJ<X ) 7S;k:MZ=:@NTL 58<\587ACB6+cF)A`79cBJ79D:T<79H5I+dx a A`L`7·t A7+g7S;:@?A7+g5^?7S.LC:@?9D:@:T7:~

?:psmK0XV W<0,BIp Yf^N\Q-;=<>BN@:@?>?>BJ<>?#NK5I+aA`]^;BJ<7 ?\N>9D:T]_5J?:£79D:TS_:F+bY BJ<>N@:7S.;=A7+=W^B8Y27S;k:tZ=:@NTL 58<>:@Z

1

J58<A 5Ix=LC:@?a5I+DZ ;H58<\58]G:T7>:T<>?KV)5I+DZ 79D:TS NK5I+ ZbSN+H58]ÂCNK58L`L`S-J58LÀCZD587>: 79D:TA`<_B a 7; a 7 58Wh58A7+D?7_5?>N>9D:T]_5~

tvw :t t tvDn

Q&9D:jYf^N\QGN>9H5I+=W3:@?79H58745Y^2:@NT779D:,?7\587ACNf5I+H58L`Sb?AC??A`7 a 587ACB6+jVHN@BJ]^;H58<>:@Z 7>B:T<>?ACB6+ VD58<>:g

G ; ?!C@U ; [+f5JZ=ZbA`7ACB6+f7>B?7SLC:@?9D:@:T7·tZ=:@NTL 58<>:@Z a ?>:T<Y a +DNT7ACB6+D? V 79D: LÀ7x=<\58<S,B8Yb;=<>:@Z=:b1+D:@ZfYsP5879Y a +DNT7ACB6+D?69H5J?6:b;H5I+DZ=:@ZR?A`W+=AcbHNK5I+h7L`SEY <>BJ] 79H587 B8YYsP5879 V3]G:T<A`7A7+=Wf5F)9DBJLC: 94:@N@BJ]^]G:F+tZD587ACB6+gB8Y6A`7>?BKF<+ q v~

0,B@F0,Eqp!V EH@ ; AH@ ; U ; CBG1?!C: ?2F : 9H5:3:?>:@:F+jV s65879)NK5I+M;:T< Y BJ<] :FJ58L a 587ACB6+IB6+jJ58<A 5Ix=LC:txkB a +DZ W[!\U7<>:@:@?:~

BYU GI=H@ ; a [ o 3 Xmo S[ \ 2 AC?&9H5I+DZbLC:@Z A7+]^:@NT7ACB6+ :~ 0"GrpV U Q&9D:7>:7·tu+DBZ=:XN@B6+D?>7< a NT7>BJ<gA7+D?7< a NT7ACB6+ X \3 o:Za +DBKF 5JN@N@:T;=7>?c5I+DZ B a 7; a 7>?c?>:tl a :F+DN@:@? VU+DBJ7_B6+=L`S A`7>:T]G? ~[7^9H5J? 58LC?>Bx:@:F+ :7>:F+DZ=:@Z xhS 5 )S32 X [ X . [ 5877<A7x a 7>:Y BJ<?;:@NTA Y SA7+=WE?>:T;H58<\587>BJ<&?7<A7+=W3?:£79=AC?+D:@:@Z=?#7>Bx:N@B6+D?ACZ=:T<>:@Z|~ X \3 oZaR9H5J?+DBfA`]^;=LÀCNK587ACB6+D?Y BJ< HB Ff£=A`7>?)9H5I+DZbLÀ7+=WaA7+LJ58LÀCZD587ACB6+cAC?:;=L 58A7+D:@Z A7+!^:@NT7ACB6+ -1~ 1~ UAps f^N\.Q ?,;BJL`SNJ58<A 5I+.7 ]GBZ=:@? N@BJ]^;=LÀCNK587>: HBKF 5I+H58L`Sb?AC? ?>BJ]G:TF)9H587:~MQ&9=AC? AC? Z=:@?>NT<A7x:@Z

A7+]^:@NT7ACB6+ Å ~ 1~X 2 2 0 o *<n+2 [1.) V 3Z' . o n X . m Q&9D:GF#5KSF :_]GB.Z=:TL 79D:@?>:Â7+D?7< a NT7ACB6+D?EAC?fZ=:@?>NT<A7x:@ZUA7+-^:@NT7ACB6+ Å ~ 1~6 ; @ C@0?U ; C:pC: [+ f^N\.QbV=5I+GA7+=A`7A 58LN@B6+h7>:b7U+DBZ=:45I+DZ 5I+GA7+=A`7A 58Ln+H58]G:@Z_7>:T]^;=L 587>:J+H58]G:4BJ<

5I+gA7+=A`7A 58L6]GBZ=:fNK5I+!xk:E? a ;=;=LÀC:@ZcY <>BJ]i79D:E:F+s.A`<>B6+=]G:F+.7MB8Y79D:E?7S.LC:@?>9D:@:T74;=<>BN@:@?>?>BJ< q ?>:@: 1 V^:@NT7ACB6+y~ Å v~J^.A7+DN@:f+DB6+D:fB8Y 79D:@?>:f;kB?\:@?5I+hS79=<>:K587KVkBJ<N>9H58L`LC:F+=W3:Vk7>B_79D: Y :K5J?>A7x=A`LÀ`7SB8Y$B a <?7\587ACN,5I+H58L`Sb?AC?KV=5I+DZ F : Y B a +DZ+DBR:D58]^;=LC:@?B8Y7<\5I+D? Y BJ<]G? a ?A7+=W^79D:4Y :K587 a <>:Vb79D:@?>:9H5B3:dxk:@:F+-b>=:@Z7>BUZ=: Y 5 a L`758L a :@?:g Y BJ<^79D: A7+=A`7A 58L4N@B6+h7>:b7+DBZ=:V Ap 0G-FC Y BJ<G79D:]GB.Z=:VD5I+DZ+DBÂ7+=A`7A 58Lh+H58]G:@Z7>:T]^;=L 587>:+H58]G:~Q&9=AC?)<>:H:@NT7>? f^N\Q f?>:T]_5I+.7ACN@?:~

G-FC@=q p@ ; =HG C A>U?MGm@p ; C:3 s65879 ?,?7\587ACNEN@B6+.7>:7,Z=:b1+=A`7ACB6+ ]_5Il3:@? A`7;B?>?A7x=LC:E7>B ?7\587·tACNK58L`L`S <>:T7<AC:F3:c5I+hS?>N\9D:T]_5J?a5J?>?\B.NTA 587>:@ZF)A`79Z=B.N a ]G:F+.7>?_LCB35JZ=:@Z-F)A`79 79D: sP5879 ` Y a +DNT7ACB6+jVk5I+DZ 79D: j^N\Q ` \Zn3 V . A7+D?7< a NT7ACB6+h~)Q&9D:@?>:xkBJ79 :FJ58L a 587>:f7>BG79D:,<>BBJ7J+DBZ=:B8Y79D:^Z=BN a ]G:F+h7,LCB35JZ=:@Z|~z^:T]_5I+h7ACN@?MB8Y s65879U:;=<>:@?\?ACB6+D?M58<>:RZ=:b1+D:@ZU? a N>9 79H587,A7+bY BJ<·t]_587ACB6+ 5IxB a 7F)9=ACN>9 ?>N>9D:T]_5GA`7458;=;=LÀCNK5Ix=LC:fNK5I+dxk:,<>:K5JN\9D:@ZY <>BJ] :F3:T<SL+DBZ=:VD?>BR] a L`7A`;=LC:Z=B.N a ]G:F+.7>?^58<>:O+DBg?>;k:@NTA 58L#N>9H58L`LC:F+=W3:aA7+O?7\587ACN 5I+H58L`S?AC?S~QB ?\5B3:_79D:_N@BJ]^;=LÀCNK587ACB6+D?KV6F#:F)A`L`L|+DBJ7; a <>? a :,] a L`7A`;=LC:MA7+=; a 7Z=BN a ]G:F+h7>? 5I+hSaY a <79D:T<:~

G-FC@=q p U*GIC=>GICA>U?MGmop ; C: f^N\.Q NK5I+cNT<>:K587>:R5I+DZgB a 7; a 7,5I+hSL+ a ]x:T<,B8Y W[!\X7<>:@:@?4A7+:K5JN>9c7<\5I+D? Y BJ<]~<^.A7+DN@:MA7+D?>7< a NT7ACB6+ Y BJ<B a 7; a 74B8YBJ79D:T<79H5I+g79D:M;=<A`]_58<S<>:@? a L`77<>:@:ENK5I+

¤ ¿® >`©uª$Ä $! "#"#$J»h³±¯±¯¶:ü¸ÂWD®B°k´º§º©|©uªº« Iü²©r³©u«·ÃWÄS³½>³©u²`ü¼§ºÃ<«·®B©h³Á²r®º¸:¶º«)²4«¬©

1

?7\587ACNK58L`L`SI5J?\?>B.NTA 587>: 79D:#7<>:@:#F)A`79^54?>N\9D:T]_5bV3?7\587ACNK58L`L`S58LÀCZD587A7+=W Y BJ<6]GBJ<>:#79H5I+^B6+D:#<>:@? a L`77<>:@:,AC?B6+=L`S 5R]_5877>:T< B8Y <>:T7<AC:F.A7+=Wa79D:,<>:TLC:FJ5I+.74?>N\9D:T]_5bV 5I+DZg;=<>B.N@:@?>?45J?)Y BJ<79D:,;=<A`]_58<S<>:@? a L`7)7<>:@:~Q&9=AC?AC?<+DBJ7); a <>? a :@Zg5I+.SaY a <79D:T<9D:T<>:~

0DCC:pMB ; :psmK0 ; C@F?e Q&9D:7<>B a x=LC:@?>BJ]G:c;D?>: a Z=BIt5º=:@?GA7+ f^N\.QU;H5877>:T</+D?_F)A`L`LJ+DBJ7a5Y^:@NT7 a ?KV5J? 79D:TS-9H5B3: :'^2:@NT7B6+=L`S Y BJ< ;H58<>:F+.7LC:@?>?+DBZ=:@? A7+%BJ79D:T<;H5877>:T</+D? 79H5I+ V79H587AC?KV&Y BJ<J58<A 5Ix=LC:tuxB a +DZZ+DB.Z=:@?S~dU: 7<>:K587J58<A 5Ix=LC:tuxB a +DZ-+DB.Z=:@?xhS 5JZ=ZbA7+=WU5 ;D?>: a Z=BIt ;H58<>:F+.7^7>B79D:T] V=]_5IlA7+=WG79D: ;D?>: a Z=BIt5º=:@?<>:@Z a +DZD5I+h7:~

479D:T< N>9H5I+=W3:@?F)A`L`Lr+DBJ7+D:@:@Z 5I+hSN@B6+D?ACZ=:T<\587ACB6+cA7+ 79=AC?)F BJ</lV=A7+DNTL a ZbA7+=W1g

0"Grp?UmJ=HG C0DC@U ; BJ79D:T<f79H5I+ X \3 o:Zang L 58<W3:z+ a ]xk:T<RB8Y&A`]^;=<>B:3:T]G:F+h7>?R9H5:3:Ox:@:F+]_5JZ=:_A7+ :b;=<>:@?>?ACB6+ :FJ58L a 587ACB6+h~@^:T]_5I+h7ACN@?^B8Y<>:TL 587ACB6+H58LBJ;:T<\587ACB6+D?^58<>:aZ=:b1+D:@Z A7+ 79D: i[!\_?\N>9D:T]_5JJ58L a : ?;H5JN@:@?A7+ j^N\QbVJ]_5IlA7+=W4ZbA_^2:T<>:F+h7P<>:T;=<>:@?>:F+h7\587ACB6+D? B8YD79D: ?\58]G:7S.;:@ZJ58L a :GACZ=:F+h7ACNK58L V 5J?fBJ;=;B?>:@Z7>B s65879 ? a ?>:^B8Y)A`7>?MB F<+X7S.;:GN@B6+e3:T<>?>ACB6+XY BJ<MBJ;k:T<\587>BJ<>?S~ s6587958LC?>B Y :K587 a <>:@?L+D:TF l a 5I+h7AcbH:T<g:b;=<>:@?>?ACB6+D? q Y BJ< 5I+hS 5I+DZ Y BJ< 58L`L ¬v ~ [+ 79D:;=<>:@?>:F+h7k3:T<>?ACB6+cB8YB a < 5I+H58L`S?>AC?KV=F)9=ACN>9 ]_5Il3:@?k+DBa5877>:T]^;=7 587 58L`L7>Ba?7\587ACNK58L`L`SLxkB a +DZg79D:<>:@? a L`7>?MB8Y&BJ79D:T<M79H5I+X5aY :TF ?>7<A7+=W :;=<>:@?>?>ACB6+D?KV279D:w+D:TF BJ;:T<\587>BJ<>?E58<>:V2LÀ7l3:^79D: f^N\Q B6+D:@?KVbA`W+DBJ<>:@Z|~

pMB@0@0DC@U ; D:K587 a <>:@?MY BJ<ib1+D:T<,W<\58A7+D:@Z<>:@? a L`7,7<>:@:^?>:T<A 58LÀ7 587ACB6+U9H5B3:Oxk:@:F+X5JZ=Z=:@Z2V2F)9=A`7>:@?/t;H5JN@:c?\:T]_5I+h7ACN@? F#5J? <>:b1+D:@Z2V45I+DZ `* ) XZ 3 o: \ . 21\ . o 3+) X 2_* V 9H5J?x:@N@BJ]G:cZ=:T;=<>:@NK587>:@Z5I+DZ <>:T;=L 5JN@:@ZLxhS N>9H58<\5JNT7>:T<4]_58;D?:~'U: 9H5B3:MA`W+DBJ<>:@Z79=AC?KVD5J?)B a <5I+H58L`Sb?AC?BJ;:T<\587>:@?587)79D:7<>:@:,LC:F3:TLjB8Y i[!\V>+DBJ7N@B6+D?ACZ=:T<A7+=W ?>:T<A 58LÀ7 587ACB6+h~

I; 01mK@?LpMBBUBI [ 5I+hS^;=<>:FACB a ?L`SÂ`W+DBJ<>:@Za:T<<>B6+D:@B a ?#?>A`7 a 587ACB6+D?9H5:3:x:@N@BJ]G:Z=:b1+D:@Z ?7\587ACNBJ<^ZbSs+H58]ÂCN:T<<>BJ<>?:~^.A7+DN@:g5]+DB6+t <>:@N@B:3:T<\5Ix=LC:cZbSs+H58]ÂCNg:T<<>BJ<^<\58AC?>:@Z W a 58<\5I+h7>:@:@?a58Wh58A7+D?>7A7+e58LÀCZ^B a 7; a 7B8Yk547<\5I+D? Y BJ<]_587ACB6+ q ?7>BJ;=;=A7+=W,A`7µv VF :&9H5:3:&A`W+DBJ<>:@ZR79=AC?5J?;:@NT7:~qY N@B a <>?\:VA`74AC?,58LC?>B A7+.7>:T<>:@?7A7+=W7>B ]_5Il3:EW a 58<\5I+.7>:@:@?,79H587 79=AC?,NK5I+>+DBJ7 9H58;=;k:F+h£j?>7\587ACNE7S.;:@N>9D:@NDl.A7+=WAC??;:@NTAcbH:@Z 5J?5I+gBJ;=7ACB6+Y BJ< sP5879bVk5I+DZg5J?)A`]^;=LC:T]G:F+h7\587ACB6+tZ=:b1+D:@ZcY BJ< f^N\.Q~

! #"

i - -| tvw mq zm <|

U:R5J?>? a ]G:,A7+c79D:MY BJL`LCBKF)A7+=W 79H587 5_?>N>9D:T]_5GY BJ< 5I+hS %$'&U79H587 AC? a ?>:@Z Y BJ<4A7+=; a 7Y BJ< 5I+ f^&Q7<\5I+D? Y BJ<]_587ACB6+ AC?f5B58A`L 5Ix=LC:G7>B B a <I5I+H58L`S?AC? V$5I+DZ2V$F)9D:F+O5?>N\9D:T]_5ºt5@F#58<>: ?7S.LC:@?>9D:@:T7M;=<>B.N@:@?\?>BJ<)(+* ²rÀ·§Sü³±¸²4³©°BÄ6©uªº«À·¯Áµ³±Ã<²³±®i©uªº«Iü²©r½ç§S¨§º²4«À/µ²4«·²³±® #S«·À¬©u³±¸µ® $¾ ,<¸µ½>©uªI« >D©uª!ü« :§º³ü«·Ã<«·®B©r¶º¸BÀ·§ºÃ<«·®B©

+ &#-/.0.1 3241 "#053.76789.7:###<;>=&"7?3. -µ´¸§S©hÀ·¸Ã<ÂIDü³±²4¸®º²|©uª6D© >D©uª$À/µ®i®I¸µ©r«#"SÂSü«·²4²A@ `ü«µ¯±¯e»|ü¸µ®I¼9B

1 Å

AC?D?\:@Z2Vj79H587E5I+.S ?\N>9D:T]_5J?fZ=:@NTL 58<>:@ZUF)A`79 *<n2 [1. o ) m 3n X 58<>:^79DB?>:R79H587fF)A`L`Lxk:D?\:@Z A7+XB=<5I+H58L`Sb?AC?:~zDBJ<xH5J?ACNG?7S.LC:@?9D:@:T7f;=<>B.N@:@?>?\BJ<>?KV2F :O+D:@:@Z7>B 5J?>?=]G:GB6+=L`S 79H587M79D:TS58<>:GN@BJ]^;=LÀ 5I+h7KVAC:~+D:F3:T<EB=7;=7R5I+hS79=A7+=WgY <>BJ] ?7S.LC:@?>9D:@:T7>?M79H587D?\:G?>N>9D:T]_5g7S;=A7+=W Y :K587=<>:@?,Y BJ<fBJ79D:T<E79H5I+;=<A`]Â`7A73:EZD587\587S;k:@?:~

DBJ< &QbVH?\BJ]G:ML 5I+=WH58W3:fN@B6+D?>7<DNT7>? q 79H587 58<>:f+DBJ7<>:K58L`L`SN@BJ<>: Y :K587=<>:@?KV 5I+DZg58<>:+DBJ745^N\9H58LctLC:F+=W3:,7>BG79D:jxH5J?ACN Y :K5J?A7x=A`LÀ`7SB8Y B=<458L`W3BJ<A`79=]v&9H5:3:jxk:@:F+gA`W+DBJ<>:@Z N@BJ]^;=LC:T7>:TL`SP~Q&9D:TS 58<>:g

•Q&9D: 3' Z \+`+3 o [3)\ . o 2 [3 a *'3+) ?7\5I+DZD58<>Zg5877<A7x=7>:

•XVX1 0 3 o ).1[_* V V n X . m * V o )\ ).1[_* V V+VVo n X . m * V o ):\ ). [* V

•e#B6+DZbA`7ACB6+H58L$:TLC:T]G:F+h74A7+DNTLD?ACB6+h£ \_)Z3 o 1m 3 V

•&5JNDl.F&58<>Z=?45I+DZ Y BJ<F#58<>Z=?4N@BJ]^;H587A7x=LC:M;=<>BN@:@?>?A7+=W

• 7>:F+D?>ACB6+Y>+DNT7ACB6+D? VD:7>:F+D?>ACB6+A7+D?7<DNT7ACB6+D? 5I+DZ 79D: a+X 1XaA7+D?7<DNT7ACB6+

•e#BJL`L 587ACB6+D?KVH5I+DZ79D:TA`<]G:K5I+=A7+=W

• s65879 ??7\587ACNK58L`L`S 5:J58A`L 5Ix=LC:EN@BJL`LC:@NT7ACB6+D?45I+DZ N@BJL`L 587ACB6+D?KV 5I+DZ79D:TA`<Z=: Y 5=L`7>?

•e 9H58<\5JNT7>:T<]_58;D?

•9:@?=L`7)7<>:@:M?\:T<A 58LÀ7 587ACB6+jV `* ) X 3 o: \1. 21\ . o 3+) X 2* V 5I+DZL+DB6+t %$ &OB=7;=7

•74?>:T<·tZ=:b1+D:@ZgZD587\5^:TLC:T]G:F+h7>?

•a+ [Sn X . oV \Zn 3[ Y BJ<]_587>? V )0):.3:n o 21[ 23[1. 0 V 3 3:n3 V . oX X * 1X 3 ~7~7~

&:TLCBKFt %$ ]GB.Z=:TLjZ=:T7\58A`LC?LÀ7l3:M:b;H5I+D?ACB6+gB8Y :F+h7A`7AC:@?:T7>N~ 58<>:f5IxD?7<\5JNT7>:@Zg5KF#5@Sg587)79=AC?LC:F3:TLu~U:f5J?\?=]G: 79H58779D:,7<\5I+D? Y BJ<] B=7;=7>? $'&V+DBJ7 Q $ &XBJ<7>:7:~ 4Q $'&7<\5I+D? Y BJ<]G?NK5I+Lx:5I+H58L`SNK:@Zc5 Y 7>:T< Q $'&UN@B6+e3:T<>?ACB6+jVH79DB=W9h~=7;=7G5I+DZXB6+.F#58<>Z=?^N@B6+.7<>BJLHB F Y <>BJ] 7>:T]^;=L 587>:@?E79H587I]_587>N>9 ?Umom@p ; C 5I+DZ =>@ +DB.Z=:@?R58<>:* N@B6+D?ACZ=:T<>:@Z2Vx:@NK5D?>: 79D:@?>:i+DB.Z=:klA7+DZ=?&58<>:i+DBJ7)Z=:@NTL 58<>:@Z2VD5I+DZ58<>:,58L`LCBKF :@Zc58L`]GB?75I+hSF)9D:T<>:A7+5I+ %$ & Z=BN =]G:F+h7:~[+cNK5J?>:@?4F)9D:T<>: =>@ +DBZ=:@? 58<>:f]_587>N>9D:@ZcY BJ<4B=7;=7KV F :INK5I+cB6+=L`Sg5JZAC?>:D?>:T<>?7>BEF)<\58;g79D:T] A7+g5MY <>:@?9=L`S Z=:@NTL 58<>:@Z :TLC:T]G:F+h7KVk5I+DZN@BJ;hS 79D: ]_587>N>9=A7+=WG7>:T]^;=L 587>: ?4N@B6+h7>:F+h77>BGB6+D:M]_587>N>9=A7+=W_79D:f+D:TF :TLC:T]G:F+h7:~

U:^5J?>?=]G:I?SN+h7\5JNT7ACN^5I+DZ <>: Y :T<>:F+.7A 58LJ58LÀCZbA`7ScB8YA7+=;=7,?7S.LC:@?9D:@:T7>?M5I+DZ ?>N\9D:T]_5J?KV2:F3:F+ 79DB=W979D:,A`]^;=LC:T]G:F+.7\587ACB6+D?\:@??>N>9D:T]_5OJ58LÀCZD587ACB6+cB6+ 79D:@?>:~

Q&9D:58L`W3BJ<A`79=] Z=:@?>NT<A7x:@ZZxH5J?>:@?IL 58<W3:TL`SOB6+ 58;=;=<>BBbA`]_587ACB6+h£#W3B.BZ 58;=;=<>B:A`]_587ACB6+D? 58Wh58A7+-xH5J?>:B6+ W3BB.Zc:@?7A`]_587>:@?,B6+cF)9D:T<>:I7>B_Y BN D?4;H58<7ACN =L 58<f5877>:F+h7ACB6+h~ Å 5I+DZ ! xBJ79 9H5:3:R:bN@:TL`LC:F+.7:T]^;=A`<ACNK58LxH5JN`lA7+=WcB8Y&79D:TA`<fxH5J?ACNGZ=:@NTAC?ACB6+D? 5I+DZF)9D:T<>:^F#:^9H5B3:a:7>:F+DZ=:@Z=;kB6+U79D:TA`<fF BJ</lZbA`<>:@NT7L`S3VHF :M?>:@:W+DBG<>:K5J?>B6+ 7>BR<>:T;:K58779D:TA`<B6xD?>:T</587ACB6+D?:~U: <>: Y :T<7>BR79D:,7F Ba58<7ACNTLC:@?S~

1

PA7+H58L`L`S3V 58Wh58A7+jVH7<\5I+D? Y BJ<]58LÀCZbA`7S AC?Z=:b1+D:@ZgA7+ 7>:T<]G?B8Y5^?7S.LC:@?>9D:@:T7TVH5I+ A7+=;=7 ?>N>9D:T]_5a5I+DZ

5I+B=7;=7,?>N>9D:T]_5~fQ&9D:EB=7;=7M?>N\9D:T]_5aAC?k+DBJ7 D?>:@Z >+h7A`L6L 587>:T< A7+ 79D:f;=<>BN@:@?>?KVx=7 79D:EA7+=;=7?>N\9D:T]_5

Din

AC? D?>:@Z ?>B B8Y 7>:F+79H587,F :RF)A`L`L¢ D?>7 NK58L`L A`7dV$5I+DZ D?>:I79H587f5J? 5Bl H58LÀcbH:T< Y BJ< ]GB?>7

Y >+DNT7ACB6++H58]G:@?<>:TL 587>:@Zg7>BRA`7:~

( 3nl:3y - <t|

.7S.LC:@?9D:@:T7 ?A`]^;=LÀcbHNK587ACB6+-AC?G79D: ;=<>B.N@:@?>?_B8Y <>:@Z DNTA7+=WU79D:gN@BJ]^;=LC: 5I+DZ-?>BJ]G:TF)9H587G<>:@Z >+DZD5I+h7 &.Q^L 5I+=WH58W3:,7>BG5I?]_58L`LC:T<<R % cL 5I+=WH58W3:V=<>:@Z DNTA7+=WG79D:W+ =]x:T<B8YPN@B6+D?7<DNT7>?79H587+D:@:@Z7>BOxk:,N@B6+D?ACZ=:T<>:@Z A7+ L 587>:T<45I+H58L`Sb?AC?:~ [7)AC?ZbA7.ACZ=:@Z A7+h7>B^7F B_BS3:T<\58L`L$?7\58W3:@?

~P%' "#R'/T(* %/%-N?>A`]^;=LÀHNK587ACB6+g7<\5I+D?L 587>:@? 5I+ &QG?>7SLC:@?9D:@:T77>B_5^N@BJ<>:ML 5I+=WH58W3:?7SLC:@?9D:@:T7F)A`79g58L`L$?>:T]_5I+h7ACN@?;=<>:@?>:T</3:@Z

~f(( sK!F! &% ?A`]^;=LÀHNK587ACB6+H+DB LCB6+=W3:T<^;=<>:@?>:T</3:@?^?>:T]_5I+.7ACN@?KVx=7R;=<>:@?>:T</3:@?G5I+.So58LÀCZbA`7S:T<<>BJ<79D:T<>:,]_5KS 9H5:3:jx:@:F+A7+ 79D:MBJ<A`WA7+H58L?7S.LC:@?>9D:@:T7

.7S.LC:@?9D:@:T7G?>A`]^;=LÀHNK587ACB6+ F#5J?D?>:@Z A7+ ;=<>:FACBD?RF BJ< q Å v£#B=<^N@B6+.7<A7x=7ACB6+ AC?G5 Z=:1+=A`7ACB6+B8Y,5gW3:F+D:T<\58Lct ;=<;B?>: A`]^;=LC:T]G:F+.7\587ACB6+B8Y 5 ?A7+=WLC:t ;H5J?\?R;=<>B.N@:@?>? V]GB.Z=:TLÀ7+=WU?7S.LC:@?>9D:@:T7>?R]GBJ<>:N@BJ9D:T<>:F+.7L`S F)A`7979D: &.Q|94:@N@BJ]^]G:F+DZD587ACB6+ q A`]^;BJ<7&7<>:@:,?7<DNT7=<>: A7+ ;H58<7ACN =L 58<µv)5I+DZ ]GBJ<>:W3:F+D:T<\58L`L`SP~

R (M(*FXEB8YHZ=:@? =Wh58<>:@ZIN@B6+D?>7<DNT7>?6F#5J? 5JZ=Z=:@ZIA7+I79D:#:@ZbA`7>BJ<·tBJ<AC:F+h7>:@ZGA`]^;=LC:T]G:F+h7\587ACB6+ 5JN\9:TLC:T]G:F+.7AC?&Z=:@N@BJ<\587>:@Z F)A`795[/ZN+R %fV5I+DZ5vR %fV=58LCB6+=WRF)A`79 ;H58<>?\:4LCBNK587ACB6+A7+bY BJ<]_587ACB6+h~ =<A7+=WO58L`L?7\58W3:@?_B8Y ?A`]^;=LÀHNK587ACB6+jV#F)9D:F+D:F3:T<a5I+:TLC:T]G:F+h7GA7+-5 ?>B=<>N@:g?7SLC:@?9D:@:T7^]GBZ =LC: BJ<?>N\9D:T]_5_Z=BN =]G:F+h74AC?N@B6+s3:T<7>:@Zg7>B_5GZbA_^:T<>:F+.7 N@B6+D?7<DNT7KVH79D:fBJ<A`WA7+H58LP:TLC:T]G:F+h7: ? ?>B=<>N@:f[ 5I+DZ;H58<>?>: LCBNK587ACB6+g58<>:,N@BJ;=AC:@Z 7>BR79D: <>:T;=L 5JN@:T]G:F+h7 N@B6+D?7<DNT7:~[+?>xD?>:<l D:F+h75I+H58L`SNK:@?KVxkBJ79NK5I+Lx:xH5JNet ]_58;=;:@ZR7>B?>B=<>N@:#Z=BN =]G:F+h7>?KV9D:TL`;=A7+=W 7\58<W3:T7 5I+hSM]G:@?\?\58W3:#5IxB=7P79H587$;H58<7ACN =L 58< :TLC:T]G:F+h7:~

Q&9D:,;=<A`]_58<S 7\5J?b?B8Y ?>:T]_5I+h7ACN@?/t ;=<>:@?>:T</.A7+=W ?7SLC:@?9D:@:T7?>A`]^;=LÀHNK587ACB6+ 58<>:

•QB <>:@Z DN@: ]GB?7IN@B6+.7<>BJLct HBKF <>:TL 587>:@Z A7+D?7<DNT7ACB6+D?R7>B X 212 0 o .3n2 X .3) V6;=<>:@?>:T</A7+=W ?\:t]_5I+h7ACN@?JxhS 5JZ=ZbA7+=WG]GBZ=:@Z7>:T]^;=L 587>:,<=LC:@?

•QB^<>:@?>BJL73:V 5J?&Y 58<5J?;kB?>?>A7x=LC:V=?7SLC:@?9D:@:T745I+DZ7>:T]^;=L 587>:fJ58<A 5Ix=LC:@? 5I+DZ;H58<\58]G:T7>:T<>?

•QB >+=A Y S 58L`L|x=<\5I+DN\9=A7+=WaA7+D?>7<DNT7ACB6+D?A7+h7>B7m1 )S3 A7+D?7<DNT7ACB6+D?F)A`79 . m 3[ * )Z3 x=<\5I+DN\9D:@?

•QB^<>:@Z DN@:f58L`L7>:7B=7;=77>B X \3 o:Zaa:;=<>:@?\?ACB6+D?

PA`<>?7KVF :^F)A`L`LA7+.7<>B.Z DN@: 5+D:TF Z=:@?A`W+UB8Y)B=<>?KV2Y BJ<,<>:T;=L 5JNTA7+=W &Q A7+D?7<DNT7ACB6+D?MF)9DB?\: %%+R R * "sS BJ<<%%+R ZD (*ZD )Z=:T;k:F+DZ B6+g5^7S;k:@Z58LD:~¬¥ ¿ ©u²|³±Ã<Âº¯Á«¬Ã<«·®B©D©u³±¸®J³±²rÃ§IÀªJ½cµ²©u«¬¨r©uª6D®k©uªID©h¸µ½ " ! , (8ÄI´º§º©hÀ·¸µ®I²4³Á¶º«¬¨DÍ¯±«©u³±Ã<«»|D²D¯±²4¸<²4Â«·®B©r¶º«·²4³±¼®º³±®I¼<³©+B

11

$)!' $(&'

Y :TF :7<\5EY >+DNT7ACB6+gZ=:1+=A`7ACB6+D? 58<>: D?>:@Z

• ') , \ V 1V1VXa+ 1 X .* ZV p<r AC?5R;D?>: DZ=BItN@BJL`L 587ACB6+cF)A`79c5I+ >+ N+DBKF<+gBJ<>Z=:T<A7+=W1~

• ') , \ V 1V1V 13; \3 V 3-p<r AC?5RY>+DNT7ACB6+g:F58LH587A7+=WG7>B_5I+.S.79=A7+=W_A7+ *.3nTpr; ~• ') , \ V 1V1V 1 3 XZV pr AC?5IY >+DNT7ACB6+g:F58LH587A7+=WG7>B_5I+ >+ N+DBKF<+dxBBJLC:K5I+LJ58LD:~

• ') , \ V 1V1VMd 3'1.qp<r AC?5IY >+DNT7ACB6+g:FJ58LH587A7+=W_7>B_5I+hS ?7<A7+=WGA7+ char∗~

QS.;:&<>:@N@B6+D?7<DNT7ACB6+_AC?5 ?>A`]^;=LC:)ACZ=:K5 / V9D:TL`;=A7+=WM7>B <>:@Z DN@:&79D:)7F B,7S.;:)?Sb?7>:T]G? B8Y s658790 pV| Gp ; ?Pp ¡ =p ?5I+DZ_79D: N@B6+.7>:F+h7)]GBZ=:TLC?#B8YP?>N>9D:T]_5IZ=:@NTL 58<\587ACB6+D?&7>BJ¢ D?7&B6+D:! p| Gp ; ?Pp ¡ =p ?58<>:,7<\5I+D?>L 587>:@Z 7>B^N@B6+h7>:F+.7]GBZ=:TLC?F)9D:T<>:,;B?>?A7x=LC:~

?>?=]G:I79H587iAC?,5 Z 210 o:SaHV X \3 oZa BJ< X 212 0 o .3n2 X .3) A7+D?7<DNT7ACB6+jV2F)A`79U5 )Z3 3 . :Nt;=<>:@?>?>ACB6+

i )S3 3 .+Y O $pr O BJ< i )S3 3 .+Y O a V , a+ O F)9D:T<>:

•79D:58<A 5Ix=LC:f<>: Y :T<>:F+DN@:

pBJ< 79D:fY>+DNT7ACB6+ aSV , a+1aAC?4Z=:@NTL 58<>:@Z 7>Ba9H5B3:^5a?>:<l D:F+DN@:E7S;:fB8Y7S;k:

tF)A`79 ??MG1Bºp ; ?PpN6 ; AH@?0DCUB

o

•79D: ;H5879g:;=<>:@?\?ACB6+

rAC?:T]^;=7S3V BJ<xk:TWA7+D?F)A`79 BJ79D:T<F)AC?>:

Z 2 0 o:SaHV X1 \3 o:SaB=7;=7c79=A7+=W3?KVMZ=:T;:F+DZbA7+=WB6+ 5-J58LD:X7S;k:@Z 5J?c5?>:<l D:F+DN@:XB8Y tVM5I+DZ

X 2 2 0 o .3n2 1X .3) N@B6+.7<>BJLC? HBKFMV)F)A`7979D:g?\58]G: Z=:T;:F+DZ=:F+DNTSP~ Q&9D:gA7+D?7<DNT7ACB6+D?aNK5I+ xk: 58;t;=<>B:A`]_587>:@Z

@ t@ 3 3:n3 V .qpLMLNL^r U*B ) m 3n Xo 3 3n_3 V .qp,LNLML#r J+ :TLC:T]G:F+h7Z=:@NTL 58<\587ACB6+ x

AC? 5JZ=Z=:@Z 7>B 5Y <>:@?>9 ?>N>9D:T]_5bV=F)A`79d+DB_5877<A7x=7>:@?BJ<ZD587\5RN@B6+.7>:F+h7

Cm(x) =

yA Y

oAC?45IxD?>:F+h7

c %:d ; (0, eS$SfeS$ ;S9<; , y)A Y

o = ∗c %:d ; (1, eS$SfeS$ ;S9<; , y)A Y

o = +c %:d ; (0, 1, y)A Y

o =?J+DBJ79D:T<&:TLC:T]G:F+h7)Z=:@NTL 58<\587ACB6+yAC?#5JZ=Z=:@Z 7>Bf79D:Y <>:@?9a?\N>9D:T]_5bVbF)A`79+DBE5877<A7x=7>:@?)BJ< ZD587\5

N@B6+h7>:F+.7 Cm(y) =

cqg " h<9 (T )F)9D:T<>:

TAC?45I+ =;=;:T<·t58;=;=<>BBbA`]_587>:@Z?>:T7B8Y:TLC:T]G:F+.7W Q?479H5874;H5J?\?79D:MA`7>:T] 7>:@?7

t£ 79D:

N@BJ]^;=7\587ACB6+cB8Y679=AC?)AC?Z=:@?>NT<A7x:@ZA7+:@NT7ACB6+ Å ~ Æ ~u¤ >¨u¸Â¸²4«·¶i´B°k§º² 'IÀ¬§º¨4¨u«·®B©u¯°®I¸D©³±Ã<Âº¯Á«¬Ã<«·®B©u«/¶½c§I¯±¯°B¾

1

J+ *n+2 [ . o ) m 3:n X Z=:@NTL 58<\587ACB6+jV.<>: Y :T<<A7+=Wf7>B479D:#Y <>:@?9G?>N\9D:T]_5bV3AC?5JZ=Z=:@Z^7>B 79D:?>7SLC:@?9D:@:T7]GB.Z =LC:fxk:TA7+=WG?A`]^;=LÀH:@Z|~Q&9D: Y BJL`LCB F)A7+=W_7>:T]^;=L 587>:f<=LC:,AC?58LC?>BG5JZ=Z=:@Z7>BG79D: ]GB.Z =LC: .3n+2 X .3 n X . m Y O '_) , , µ(x) Oi )Z3 3 .1Y O m * `, , µ(y) m * `,1, r O Z.3n2 1X .35I+DZ 79D:MBJ<A`WA7+H58LA7+D?>7<DNT7ACB6+

iAC?)<>:T;=L 5JN@:@ZLx.S

X 2 2 0 o .3n2 1X .3) )S3 3 .+Y O<') ,1, µ(x) OQ&9D: 5ºbAC? ') RAC?#5f;D?>: DZ=BIt5ºbAC?A7+.7<>B.Z DN@:@Z2V=Z=:1+D:@Z 7>BE]_58;a7>BEB6+=L`SG79D:4:TLC:T]G:F+.7)Z=:@NTL 58<\5ºt7ACB6+D?,5JZ=Z=:@Z 9D:T<>:~ .A7+DN@:I79D:@?>:RZ=:@NTL 58<\587ACB6+D?f58<>:+DBJ7 <>:K5JN\9H5Ix=LC:RY <>BJ]i79D:RZ=:1+D:@Z?>N\9D:T]_5Z=B.N =]G:F+.7f:TLC:T]G:F+h7KV79D:TS Z=B+DBJ7,A7+.7>:T< Y :T<>:^F)A`7979D:^?\N>9D:T]_5ºtuxH5J?>:@ZX5I+H58L`Sb?AC? 79H587,F#:^F)A`L`L?>BB6+A7+h7<>BZ DN@:~

@ t@ X . .1[_* \ .3 pLMLML#r U*B ) m 3:n XoX .1. [_* \1.3 pLMLNL^r k+c:TLC:T]G:F+.7 Z=:@NTL 58<\587ACB6+ x

AC?45JZ=Z=:@Zc5J?A7+79D: ;=<>:F.ACBD?4NK5J?>:~tk+DBJ79D:T<:TLC:T]G:F+h7Z=:@NTL 58<\587ACB6+

yAC?5JZ=Z=:@Z2VDF)A`79L+DBG:TLC:T]G:F+h7BJ<ZD587\5

N@B6+h7>:F+.7 Ad(y) = A

F)9D:T<>:AAC?79D:M?>:T7B8Y5877<A7x=7>: W4Q$?)A7+79D:,A7+=;=7?\N>9D:T]_5^79H587);H5J?\?)79D:,A`7>:T] 7>:@?7

t~

Q&9D: Y BJL`LCB F)A7+=W_7>:T]^;=L 587>:f<=LC:,AC?5JZ=Z=:@Z7>BR79D:M?>7SLC:@?9D:@:T7]GBZ =LC:jxk:TA7+=WG?>A`]^;=LÀH:@Z .3n+2 X .3 n X . m Y O ' ) , , µ(x) Oi )Z3 3 .1Y O m * `, , µ(y) X . . [* \ .3T, ,F r O Z.3n2 1X .35I+DZ 79D:MBJ<A`WA7+H58LA7+D?>7<DNT7ACB6+


X 2 2 0 o .3n2 1X .3) )S3 3 .+Y O<') ,1, µ(x) O@

t@ .3'1.qpr Q&9D:4BJ<A`WA7+H58LkA7+D?7<DNT7ACB6+ AC? <>:T;=L 5JN@:@Zx.S i )S3 3 .+Y O '_) ,/\ V 1V+VMd 3' .tp<rDO A Y

iF&5J? '_) , X1 \3 o:Sa_BJ< ') , 210 oZaHV=BJ79D:T<F)AC?\:jxhS X 2 2 0 o .3n2 1X .3) )S3 3 .+Y O Z`+3) 3 V ` XV . o:Sa_o )Z3 Sa ,1, V `+3-p<rZ.3Z' .qprXO

@ t@ [0 ; CUnm @? ¡ =pD [Y i

AC? X 212 0 o .3n+2 X .3+) V279D:T<>:ÂC?f5 ?>7\587ACN^:T<<>BJ<MA7+U79D:^?7S.LC:@?9D:@:T7:£<>:T;kBJ<7)A`7 5I+DZ7>:T<]Â7+H587>:~ 479D:T<F)AC?>:VJ+ :TLC:T]G:F+.7_Z=:@NTL 58<\587ACB6+

xAC?_5JZ=Z=:@Z7>BU5cY <>:@?9 ?>N>9D:T]_5bV)5J?Â7+79D: D<>?>7GNK5J?>:~ J+DBJ79D:T<

:TLC:T]G:F+h7 Z=:@NTL 58<\587ACB6+yAC?45JZ=Z=:@Z2V=F)A`79+DB^:TLC:T]G:F+h7 N@B6+h7>:F+.7 BJ<5877<A7x=7>:@?

Dd(y) = L(t)79H587AC?KV

yAC?5R?A`]^;=LC:t 7S;:@Z :TLC:T]G:F+h7 Z=:@NTL 58<\587ACB6+gF)A`79 79D: CUmK@? ¡ =p ~

Q&9D: Y BJL`LCB F)A7+=W_7>:T]^;=L 587>:f<=LC:,AC?5JZ=Z=:@Z7>BR79D:M?>7SLC:@?9D:@:T7]GBZ =LC: .3n+2 X .3 n X . m Y O '_) , , µ(x) Oi )Z3 3 .1Y O m * `, , µ(y) m * `,1,/.3Z' .tp<r r O Z.3n2 1X .35I+DZ 79D:MBJ<A`WA7+H58LA7+D?>7<DNT7ACB6+


X 2 2 0 o .3n2 1X .3) )S3 3 .+Y O<') ,1, µ(x) O ; UCpMB?0>:pH A7+DNTLDZbA7+=W t *.3nTpr 5I+DZ t

V `3 p<r Q&9D:T<>:&AC?67>BBLÀ`77LC:&7S.;:#A7+bY BJ<]_587ACB6+5B58A`L 5Ix=LC:_7>Bg]_5 3:a5 ;=<>BJ;k:T<E]GB.Z=:TLu~ 210 oZa )Z3 3 .1YPO ') ,/\ V1 V1V 3S\3 V_ 3 p<rDO 1

AC??>xD?7A`7=7>:@ZY BJ<i

X 2 2 0 o .3:n+2 1X .3+) BJ< Z 210 o:SaHV=BJ< X1 \3 o:Sa )S3 3 .+YO '_) ,/\ V V+VMd 3Z' .tp<rXO Y BJ< i

X \3 oZaHV5I+DZ 5RF#58</+=A7+=WaAC?)AC?>?D:@Z2VD5J? .A7+=W^79D:D?\:T<)7>BG?9H58<;:F+79D:MZ=:@NTL 58<>:@Z 7S.;: A YP;B?>?A7x=LC:~

Q&9=AC?,:b7<\5ºtZ=:@NTL 58<\587ACB6+9H5JN >+bY BJ<7>+H587>:TL`S]+D:@:@Z=? 5a;D?>: DZ=B ') g5ºbAC?KVnx=7 79D:F+U58Wh58A7+jVkA`7,NK5I+?Jl D:@:FK:479D:4]GB?>7#B8Yj7F BI7S;k: ?Sb?7>:T]G? A7+h7>BRB6+D: q 5I+DZ 79D: NK5J?>:@?Y BJ<#F)9=ACN>9 A`7&NK5I++DBJ7)58<>:,58L`]GB?79DBJ;:TLC:@?>?)7>B_5I+H58L`SNK:M?7\587ACNK58L`L`S 5I+.S.F&5@S1v~

'

Q&9D:A`]^;=LC:T]G:F+h7>:@Z ?>:T]_5I+h7ACN@?/t ;=<>:@?>:T</.A7+=WR?A`]^;=LÀH:T<#AC?]GBZ =L 58<KV5I+DZ_?>:T;H58<\5Ix=LC:Y <>BJ] 79D: 58;=;=<>BBNtA`]_587>:,?A`]^;=LÀH:T<5I+DZ 79D: ?7\587ACN,5I+H58L`Sb?AC?&;H58<7B8Y79D:,N@BZ=:~ Q&9D: ?>:T]_5I+h7ACN@?·t ;=<>:@?\:T</.A7+=W_?>A`]^;=LÀH:T<NK5I+!xk:IN@B6+D?ACZ=:T<>:@Z5^W3:F+D:T<\58Lct ;=<;B?>:R?A`]^;=LÀH:T< Y BJ< &.Q,V25J?4A`7 ?A`W+=AHNK5I+.7L`Sg<>:@Z DN@:@? 79D:EL 5I+tWH58W3:VHF)A`79DB=7Z=BJA7+=Wa5I+hS 9H58<]~

Pk # T"121 & " =H6k$

+ =]xk:T< B8Y6?>:<l D:F+h7A 58LP?7\58W3:@?&Y BJ<?A`]^;=LÀHNK587ACB6+gF#:T<>:,ACZ=:F+h7AH:@Z

U0,AH@ ; .7S.LC:@?>9D:@:T7G]GB.Z =LC:@?GA7+ 79D:?A`]^;=LÀH:@Z &.QX?SN+h7\5º 58<>: F)<\58;=;k:@ZA7+%5 7>:T]^;=L 587>:<=LC: F)A`79g5 ]_587>N>9;H5877>:T</+jV=<>:T7=</+=A7+=W_79D:T] 7>BfY =L`L2?SN+h7\5º|~ .7SLC:@?9D:@:T7]GBZ =LC:@?+H58]G:@Z. [ XV ) a+ [Zn 58<>: <>:F+H58]G:@Zg7>BR79D:M:<l =A7J58LC:F+.7 ).10 3+) m 3 3Z. ~L`L * V \1`+3 5I+DZ *n+2 [ . A7+D?>7<DNT7ACB6+D? A7+ 79D:I;=<A`]_58<S ?7SLC:@?9D:@:T7 ]GB.Z =LC:^58<>:R:b;H5I+DZ=:@Z2V5I+DZ5I+ F(D- "+% %@V45J?_B8Y 1bV &QbV:@NT7ACB6+ Å ~ ~ Å AC?x=A`L`7KV&;=L`LÀ7+=WOA7+79D:c:F+.7A`<>:?7SLC:@?9D:@:T7:~ 5JN\9 ?7SLC:@?9D:@:T7&]GBZ =LC: AC?58LÀCZD587>:@Z 58Wh58A7+D?75I+ $'&N>9D:T]_5EY BJ< &QxhS79D:f;H58<>?\:T<KV ;=<>:F3:F+.7A7+=W 7<\5I+D?AC:F+.7 ?>Ss+.7\5JNT7ACNI:T<<>BJ<>?,BN@N =<<A7+=WZ =<A7+=WB6+t LÀ7+D:I:@ZbA`7A7+=W Y <>BJ]?>:T77A7+=WgB^-5N@B6+bY D?A7+=W ;=LC:T79DBJ<\5gB8Y):T<<>BJ<f]G:@?>?\58W3:@?,Y <>BJ] xH5JNet:[email protected]=:~&5JN.]_58;=;=A7+=WA7+bY BJ<]_587ACB6+cB8Y6:TLC:T]G:F+.74[ ?45I+DZ;H58<>?>: LCBNK587ACB6+D?AC?5JZ=Z=:@Z|~

U ; CC-V B!@J=q"@>?0DC@U ; 5JN>9I?7SLC:@?9D:@:T7$]GB.Z =LC: AC?j;=<>B.N@:@?>?\:@Zf5&7>BJ;Z=BKF<+jV6+DB6+EN@BJ;hSA7+=W]_5I+>+D:T< -4L`L=5877<A7x=7>:58LD:@?P79H58758<>:#?>;k:@NTAH:@ZE7>B N@B6+h7\58A7+ sP5879^:b;=<>:@?>?ACB6+D? 58<>:;H58<>?\:@Z2V5I+DZ^79D:;H58<>?\:@ZG:;=<>:@?\?ACB6+D? 58<>:NK5JN\9D:@Z|~ b;=<>:@?>?ACB6+D?#5877>BJ; LC:F3:TL VbB=7>?ACZ=:5I+hS^7>:T]^;=L 587>:@? V58<>:,?A`]=L 587>:@Z 5J?<x:TA7+=W_:FJ58LH587>:@Z A7+ 79D: A7+=A`7A 58LN@B6+h7>:b7KVD<>:TF)<A`7A7+=W

• \ [1[3 V .qpr 7>BG79D:EA7+=A`7A 58LPN@B6+.7>:7 A`7>:T]i<>:<l D:@?7>:@ZgY <>BJ] 79D:f58LÀCZD587ACB6+:F+eA`<>B6+=]G:F+h7 F)9=ACN>9gZ=: Y 5=L`7>?7>B

• 2 )+*.* V p<r 5I+DZ X ):.qpr 7>B •VX n_3 pr VS X oVX n3-p<r 5I+DZ VX n_3+):2 X 3 o \ [_*(p<r 7>B479D:<>:@?=L`7>?6B8YH:F58LH587A7+=W 79D:Y >+DN7ACB6+D?B6+ 79D:W58LD:M?>xD?7A`7=7>:@ZY BJ< \ [ [3 V .qp<r

®I¯°<©uªº«¶º«¬½cµ§I¯©r³±²hÀ·§º¨4ü«·®B©u¯°J³±Ã<ÂI¯±«·Ã<«·®B©u«/¶<³±®i©uªI«'¶º«·Ã<¸µ®I²©4¨D©u¸D¨hÂºü¸µ¼µ¨µÃ

1 Æ

DBJ<&?>BJ]G:A7+D?>7<DNT7ACB6+D?KVbA Y$5I+ s658795877<A7x=7>: AC?&5IxD?>:F+.7 ;H58<>?\:T<#Z=: Y 5=L`7>?#A7+D?>:T<7ACB6+ 7=</+D:@ZB^ VD5RZ=: Y 5=L`7AC?5JZ=Z=:@Z

•m * `, , V `3 p<r Y BJ< )S3 3 . 5877<A7x=7>:@?A7+X 2 2 0 o .3:n+2 1X .3+) A7+D?7<DNT7ACB6+D?S~

• `+3 a+X \ . Y BJ< n `3 5877<A7x=7>:@?,B6+ X 212 0 o .3n+2 X .3+) A7+D?>7<DNT7ACB6+D?f5I+DZ58L`LP7>:T]^;=L 587>:<=LC:@?:~DBJ<?>BJ]G: :TLC:T]G:F+h7>? V=A Y65I+ X ) 5877<A7x=7>:,AC?5IxD?>:F+.7 ;H58<>?>:T<)Z=: Y 5=L`7>?A7+D?>:T<7ACB6+7=</+D:@Z B^ V=5Z=: Y 5=L`7AC?5JZ=Z=:@Z

• *.3:nTpr; Y BJ< X ) 5877<A7x=7>:@?A7+ X [* X 3 A7+D?7<DNT7ACB6+D?:~• *.3:nTpr; Y BJ< X ) 5877<A7x=7>:@?A7+ 2 X [ X n A7+D?>7<DNT7ACB6+D?:~• *.3:nTpr; Y BJ< X ) 5877<A7x=7>:@?A7+ *. mo 2 X [ X n A7+D?>7<DNT7ACB6+D?:~• *.3:nTpr; Y BJ< X ) 5877<A7x=7>:@?A7+ a \ V ._* Va7>BJ; LC:F3:TL:TLC:T]G:F+h7>?:~

4 eCBG1?!CGIB@ ; @J=q@H?0DC@U ; 5JN>9 ?7S.LC:@?9D:@:T7&]GBZ =LC: AC?&;=<>B.N@:@?>?\:@Z 5xBJ77>BJ] =;jV=N@BJ;hSA7+=W]_5I+>+D:T<

• .3Z' . s .3'1. :TLC:T]G:F+h7>?^58<>:aN@B6+s3:T<7>:@Z 7>B X \3 oZa )Z3 3 .1YPO s O V;=<>:@?>:T< .A7+=W^F)9=A`7>:@?>;H5JN@:~

•L`Lh5JZI¢>5JN@:F+h7$7>:7|+DBZ=:@?58<>:)¢BJA7+D:@Z A7+h7>B 5&?7<A7+=W

sV 5I+DZMZ=:T;:F+DZbA7+=WB6+M79D:58;=;=LÀCNK5Ix=LC:

J58LD:IB8Y79D: )2 X 3 ;=<>BJ;:T<7S I5I+DZ B6+ F)9D:T79D:T< sAC?,58L`LPF)9=A`7>:@?;H5JN@:VA`7 AC?4ZbAC?>NK58<>Z=:@Z

BJ<N@B6+e3:T<7>:@Zg7>B X \3 oZa )Z3 3 .1YPO s O ~• * a .3+).+Y O e O seq * a :b;=<>:@?>?ACB6+D?58<>:,N@B6+s3:T<7>:@Zg7>B m )Z3 +m 3 V .3+).+Y O e O seq 1m 3 V m )S3

•m1 )S3 :b;=<>:@?>?ACB6+D? F)A`79DB=75I+i . m 3[ *S)S3 x=<\5I+DN\9 9H5B3: B6+D: 5JZ=Z=:@Z2VF)A`795I+ :T]^;=7S?>:<l D:F+DN@:,N@B6+D?7<DNT7>BJ<:~

•L`L&7>BJ; LC:F3:TL<58<A 5Ix=LC:@?G5I+DZ ;H58<\58]G:T7>:T<>?_58<>:xkB>+DZ A7+79D: ?>N@BJ;: B8Y479D:TA`<^N@B6+h7\58A7+A7+=WO?7S.LC:@?>9D:@:T7aLC:F3:TLu~ 58<A 5Ix=LC:@?aF)A`L`L L 587>:T<x: <>:@?\BJL73:@Z-F)9D:T<>:c79D:TS58<>: D?\:@Z2V5I+DZ;H58<\58]G:T7>:T<>?F)A`L`Lj7<A`WW3:T< 5I<>:<l D:@?7Y BJ<558LD: Y <>BJ] 79D:jJ58LÀCZD587ACB6+c:F+eA`<>B6+=]G:F+h7:~

•L`L 7>BJ; LC:F3:TL&5877<A7x=7>:_?>:T7>?M58<>:zxB>+DZA7+U79D:_?>N@BJ;k:^B8Y&79D:TA`<fN@B6+.7\58A7+=A7+=Wc?7S.LC:@?9D:@:T7LC:F3:TLu~

•L`L 3:TS Z=:1+=A`7ACB6+D? 58<>:WxB>+DZA7+79D:M?\N@BJ;k:,B8Y679D:TA`<N@B6+h7\58A7+=A7+=W ?7S.LC:@?9D:@:T7)LC:F3:TLu~

•9: Y :T<>:F+DN@:@? 7>BM58L`L(X1 o .3:n+2 1X .3 A7+D?7<DNT7ACB6+D?#58<>:)N@BJL`LC:@NT7>:@Za5I+DZwxB>+DZÂ7+^79D:)?>N@BJ;:B8YP79D:TA`<4N@B6+h7\58A7+=A7+=Wa?>7SLC:@?9D:@:T7LC:F3:TLu~

•L`L2LÀ`7>:T<\58L:TLC:T]G:F+.7>?

elename att1 = ”avt1” · · · attk = ”avtk” body

elename A7+g5w+H58]G:@?;H5JN@:MZbA_^2:T<>:F+h7Y <>BJ] 79D: &Q +H58]G:@?;H5JN@:I58<>:,N@B6+e3:T<7>:@Zc7>B

$ ¸D©rµ¯±¯ i²h¶º¸©uªº³Á²rD§º©u¸Ã`©u³±À/µ¯±¯° µ²r¶S«¬ü³ F«/¶J½ ü¸Ã-©uªº«²4À·¸Â«/¶ &%#"<`©4©4ü³±Í§º©u«¬²r¸D½1µ®ºÀ·«·²©u¸Dü²·Ä6²4«·« " #! !( #:«·À¬©u³±¸®º¾ ! ¸D©h³±Ã<ÂI¯±«·Ã<«·®B©u«/¶<³±®i©uªI«À·§º¨4ü«·®B©r¶S«·Ã<¸®º²©4¨D©u¸µ¨hÂSü¸¼D¨µÃ

1 u

3 3n_3 V . VX n3SY O elename O X .1. [* \1.3 VX n3ZYPO att1 O X1 \3 o:Sa )S3 3 .+Y O avt11 O ~7~7~ X1 \3 o:Sa )S3 3 .+Y O avtl11 O X . .1[_* \ .3~7~7~

X .1. [* \1.3 VX n3ZYPO attk O X1 \3 o:Sa )S3 3 .+Y O avt1k O ~7~7~ X1 \3 o:Sa )S3 3 .+Y O avtlkk O X . .1[_* \ .3 79D:MN@B6+e3:T<7>:@Z

body

13 3:n3 V .F)9D:T<>:

avtjiAC?479D:

j79 sP5879:b;=<>:@?>?ACB6+ ;H58<>?>:@ZgY <>BJ] 79D:

i795877<A7x=7>: ?M5877<A7x=7>:

J58LD: 7>:T]^;=L 587>: Q&9D:f5877<A7x=7>:f58LD: 7>:T]^;=L 587>: Q a+1 ):\ ). [* V o:XSa .3[qp# Z X [ r AC?KVY BJ<:=58]^;=LC:V=;H58<>?\:@Z7>B

a+1

, )\ ).1[_* V oXZa .3[tp Z X [ r &77<A=7>:@? F79D: &Q +H58]G:@?;H5JN@:+DBJ7i+H58]G:@Z )2 X 3 58<>:+DBJ7 N@B6+3:T<7>:@Z2V79DB=W9jV=758<>:MN@BJ;=AC:@Z7>B^79D:M<>:@?=L`7A7+=W 3 3n_3 V . :TLC:T]G:F+h7 N@B6+D?7<DNT7>BJ< 0,B@F0,Eq BeU"G C@U ; 5JN\9G?7SLC:@?9D:@:T7 ]GBZ =LC: AC?6;=<>BN@:@?>?>:@ZEA7+G5kBJ77>BJ] =;jV.N@BJ;hSA7+=W,]_5I+>+D:T<

•58<A 5=LC:<>: Y :T<>:F+DN@:@?KVA7+DNTLDZbA7+=WE79DB?\:A7+kB>+DZ 5877<A=7>: ?>:T7>?KV.58<>:4<>:@?>BJL3:@Z2Vb5J?Y 58<#5J?;kB?\?A=LC: LCBH58L$5I+DZ LCBNK58L58<A 5=LC:,<>: Y :T<>:F+DN@:@? 58<>: <>:T;=L 5JN@:@Z.S 79D:TA`<4Z=:1+=A`7ACB6+D?KVD:=N@:T;=7 9: Y :T<>:F+DN@:@?A7+D?ACZ=:I54a+ [ o 3 XmaA7+D?>7<DNT7ACB6+c79H5874<>: Y :T<47>B^LCB.NK58L`L`S B>+DZ58<A 5=LC: A7+ 79D:I? 58]G:f7>:T]^;=L 587>: 79H587 7<\5I+D?>N@:F+DZ 79D: a+ [ o 3 XmA7+D?7<DNT7ACB6+jV58<>:+DBJ7 <>:?>BJL3:@Z Q&9=AC?_AC?_7>B]_58A7+h7\58A7+ ?>B>+DZ+D:@?>? B8Yf5 L 587>:T<_]GB3:gB8Y,79D: A7+D?7<DNT7ACB6+h ?kBZbSX7>BU5gY <>:@?97>:T]^;=L 587>:<=LC:VY BJ<F&58<>ZbA7+=WU79D:+H58]G:@Z=A7+DZbA7+=W3?_5J?G7>:T]^;=L 587>:;H58<\58]G:T7>:T<>?

9: Y :T<>:F+DN@:@?_7>B58<A 5=LC:@?B>+DZ.S sP5879 ?Ba+ [ NTL 5D?>:@?KV5l H5I+h7AH:@Z :b;=<>:@? ?ACB6+D?:T7>N 79H5874Z=:@NTL 58<>:,A7+h7<\5 :b;=<>:@?>?ACB6+J58<A 5=LC:@? Q&9D:@?>:f58<>:,;=A7+=;BJA7+h7>:@Z D?A7+=W?7\5I+DZD58<>Z ?>N@BJ;=A7+=W 5I+H58L`S?AC? Å DBJ< X [_* X 3 Z=:@NTL 58<\587ACB6+D?aN@B6+h7\58A7+=A7+=W5 ?>:<l D:F+DN@: N@B6+D?7<DNT7>BJ<KV#<>: Y :T<>:F+DN@:@?_7>B79D:@?>: 58<>: S <>:@?>BJL3:@Z%A7+ B6+D: NK5J?\: 2 0 o:Za )S3 3 .+Y O e A7+D?7<DNT7ACB6+D?KVF)9D:T<>:eAC?558<A 5=LC:,<>: Y :T<>:F+DN@:V 58<>:,B=7<A`W9h7<>:T;=L 5JN@:@ZhS 79D:,N@B6+h7>:F+h7 ?>:<l D:F+DN@:

N@B6+D?7<DNT7>BJ< "ºÂSü«·²4²4³±¸®º²hü«½c«¬¨4ü³±®I¼©u¸©uªI«'À·§S¨4ü«·®B©hÀ·¸®B©u«#":©h³©u«·ÃªI «'´«·«·®Jü«·ÂI¯ÁµÀ¬«/¶i´B°©uªI«'³±®I³©u³Áµ¯sÀ·¸®B©u«#":©h³©u«·ÃHD¯±ü«·¶S°B¾* ©©uªI³±²²©µ¼«µÄ©uªI«¬ü«U³±²'µ¯±²4¸iÂ¸µ²4²4³±Í³±¯±³±© °f¸µ½1ü«·Ã<¸ :³±®I¼ % " !" $i³±®I²©4ü§ºÀ¬©u³±¸®º²©uª6`©'ªI «<²© °º¯±«·²4ªº«·«¬©½c§I®ºÀ¬©u³±¸®f³±®©uªI«·³¨ #" $"&%i«#"SÂºü«¬²4²4³Á¸µ®I²·Äü«·Âº¯ÁµÀ·³±®I¼©uªI«¬Ã ´B°k©uªI«²4«B§I«·®ºÀ·«UÀ·¸®º²©4ü§IÀ¬©u¸D¨'¸µ½1©uªº«½ §I®ºÀ¬©u³±¸®¶º«·À¬¯ `¨D©u³±¸®e¾ ¸`»« F«¬¨/Ä©uªI«¸µ®I¯°i²4³©u§ID©u³±¸®W»hªº«¬ü«©uª6D©|»¸§º¯ ¶W´«'»¸µ¨4©uªB»hªI³±¯±«³±²r»hªº«·®i©uªI«'½ §I®ºÀ¬©u³±¸®W« µµ¯±§ID©u«·²|©u¸²4«B§º«·®IÀ·«¸D½1®I¸:¶S«·² @»)«¶º¸®I¸D©)«#"SÂ«·À©²© °º¯±«·²4ªº«·«¬©)µ§º©uªº¸µü²1©u¸U¶º¸©uªI« % "! #" $U½c§I®ºÀ¬©u³±¸®º²·ÄB©uªI«·®('B®6DÃ<«/¶©u«·Ã<ÂI¯Á`©u«·²`ü«r©uªº«|©uªI³±®I¼©u¸§I²4«¾

•L`LA7+D?7\5I+DN@:@?4B8Y \_)Z3 o:X .1. [* \1.3 o )Z3Z.) V.A7+DNTLDZbA7+=Wa79DB?>: A7+ B>+DZ J58<A 5=LC:@?KVD58<>:M<>:?>BJL3:@Z2V7\5 A7+=WMNK58<>:)79H5875877<A=7>:@? 58L`<>:K5JZbSI;=<>:@?>:F+.7B3:T<<ACZ=:4?>:T75877<A=7>:@?;=<>BJ;:T<L`S3V5I+DZ 79H587?>:T7>?B3:T<<ACZ=:f:K5JN\9cBJ79D:T<A7+79D:M?>;k:@NTAH:@Z F&5@S

• 5JN>9 bodyB8Y

a [ o 3 Xm )Z3 3 .1Y O e Osortsbody a+ [ o 3 Xm AC?N@BJ;=AC:@Z7>BG5R7>:T]^;=L 587>:M<=LC:

.3n+2 X .3 n `3ZYPO m O n X . m Y O m * `,1, V `+3-p<r X .1. [_* \1.3t,1, O 2 X [ X n VX n3SY O v1 O X ):Y O as1 O 2 X [ X n VX n3SY O vk O X )Y O ask O 79D:,N@B6+3:T<7>:@Z

body Z.3n2 1X .3F)9D:T<>:

mAC?M5_Y <>:@?9 ]GB.Z=:V

vi · · · vk

58<>:E79D:4a [ o 3 Xm 7<\5I+D?>N@:F+DZbA7+=W58<A 5=LC:@? ]G:F+7ACB6+D:@Z 5B3:Vj5I+DZas1 · · · ask

58<>:f79D:TA`< Z=:@NTL 58<>:@Z 7S;k:@? Q&9D: a+ [ o 3 XmA7+D?>7<DNT7ACB6+AC?)<>:T;=L 5JN@:@Z .S X 2 2 0 o .3n2 1X .3) n `3ZY O m O )S3 3 .+Y O e O *. m o 2 X [ X n VX n3SY O v1 O )S3 3 .+Y O $v1 O X )Y O as1 O *. m o 2 X [ X n VX n3SY O vk O )Z3 3 .1YPO $vk O X ):Y O ask O sorts X 2 2 0 o .3:n+2 X .3+)

¡ K=U0DCy@J=q"@ MB. 5JN>9^?7SLC:@?9D:@:T7P]GB.Z =LC: AC?j;=<>BN@:@?>?>:@ZEA7+I57>BJ;Z=BKF<+jV+DB6+RN@BJ;hSA7+=W ]_5I++D:T<KV=<>:T;=L 5JNTA7+=WO+H58]G:@Z7>:T]^;=L 587>:@? V 5I+DZ ?;=L`A`77A7+=W >+=ACB6+ n X . ma;H5877>:T</+D? Q:T]^;=L 587>:@?#F)A`79 kBJ79 5 VX n3 5I+DZa5 n X . mG5877<A=7>: 58<>:]GBZbAH:@ZG7>Bf7F#BE7>:T]^;=L 587>:@?S£5I<=LC:,F)A`79DB=779D: VX n_3 5I+DZg5+H58]G:@Z7>:T]^;=L 587>:fF)A`79DB=779D: n X . m 58]G:@Z 7>:T]^;=L 587>:@?49H5!3:E5 n `+3ZYPO m O 5877<A=7>:MY BJ<?>BJ]G:,Y <>:@?9]GBZ=: m

VD5I+DZg5n X . m Y O m * `, , V `3 p<r X .1. [_* \1.3t,1, O5877<A=7>:f5JZ=Z=:@Z L`L ZX o .3n+2 X .3 *. m o 2 X [ X n VX n3SY O p1 O *. m o 2 X [ X n VX n3SY O pn O X 1o .3n2 1X .3

A7+D?7<DNT7ACB6+D?A7+3B .A7+=Wa79D:W+H58]G:@Z7>:T]^;=L 587>:E58<>:E58L`7>:T<>:@Z7>B

X 2 2 0 o .3n2 1X .3) )S3 3 .+Y O)Z3 Sa ,1, V `+3-p<rXO n `+3SY O m O *. m o 2 X [ X n VX n3SY O<2 )+*.* V O )Z3 3 .1Y O<2 )1*.* ZV p<rDO X ):YPO '_)U,J* V .3+3Z[PO *. m o 2 X [ X n VX n3SY O X ):.PO )Z3 3 .1YPO 1X ).tp<rDO X ):YPO ')q,J* V .3+3Z[PO *. m o 2 X [ X n VX n3SY O p1 O *. m o 2 X [ X n VX n3SY O pn O X 2 2 0 o .3:n+2 X .3+) Q&9D:VX n3 ?B8YP79D:,7>:T]^;=L 587>:@? 58<>:,79D:F+ <>:T]GB3:@Z

Å L`L27>:T]^;=L 587>:M<=LC:@?9H5!3: 2 X [ X n VX n3SY O<2 )+*.* V O )Z3 3 .1Y O<2 )1*.* ZV p<rDO X ):YPO '_)U,J* V .3+3Z[PO 2 X [ X n VX n3SY O X ):.PO )Z3 3 .1YPO 1X ).tp<rDO X ):YPO ')q,J* V .3+3Z[PO

;=<>:T;k:F+DZ=:@Z 7>Bc79D:TA`<R;H58<\58]G:T7>:T<ILÀC?>7 4L`L&NK58L`LC?E7>Bc79D:_Y>+DNT7ACB6+D? 2 )1*._* V pr 5I+DZ X ).qpr 58<>: 58L`7>:T<>:@Z 7>B k:@N@BJ]G: <>: Y :T<>:F+DN@:@?R7>B J58<A 5=LC:@?^B8Y 79D: ?\58]G:+H58]G:V:=N@:T;=779H587 2 )+*._* V p<r A7+D?ACZ=: a+ [ o 3 Xmo [ \ 2 AC?ELC: Y 7 >+DN>9H5I+=W3:@Z Q&9=AC?^?>:T<3:@?E7>Bc9=ACZ=:79H587 ZX o .3n+2 X .3 <>:T7\58A7+D?f79D:<R-ZN/ 79D:J58LD:@?EB8Y79D:_7F BgY>+DNT7ACB6+D?KV 5I+DZO79D:N@B6+h7>:b7A`7>:T] F)9=A`LC:,79D: X 2 2 0 o .3:n+2 X .3+) 79H587F)A`L`L2<>:T;=L 5JN@:MA`7 =;ZD587>:@?A`7 L`L1X 2 2 0 o *<n2 [1.) 5I+DZV 3'1. o n X . m4A7+D?7<DNT7ACB6+D?j9H53:79D:TA`<2Y B.N D?kY BJ<F#58<>Z=:@Zf79=<>B=W9;H58<\58]G:T7>:T<>?fA7+O79D:_?\58]G:GF#5@S 5J? X1 o .3:n+2 X .3 Q&9=AC?f?>:T<3:@?E7>Bg58L`LCB F 79D:GY BN D? 58L`7>:T<A7+=WX 2 2 0 o .3n2 1X .3) 5I+DZ,79D: Y BN D? <>:T7\58A7+=A7+=WX 2 2 0 o *<n2 [1.) 5I+DZ V 3Z' . o n X . mA7+D?7<DNT7ACB6+D?7>B : 7<>:K587>:@Z >+=A Y BJ<]^L`S L 587>:T< 79D: L 5877>:T<7F B_58<>:*! #<>:T;=L 5JN@:@Z

Q$:T]^;=L 587>:_<=LC:@?fF)A`79 5 >+=ACB6+ n X . m ;H5877>:T</+ 58<>:a?;=LÀ`7MA7+.7>Bc5?>:T7EB8Y&7>:T]^;=L 587>:a<=LC:@?M79H587R58<>:ACZ=:F+h7ACNK58L V$:bN@:T;=7 79H587 79D:TA`< n X . mg;H5877>:T</+D?,:K5JN>9O58<>:^5+DB6+ >+=ACB6+U? :;=<>:@?>?>ACB6+ B8Y#79D:>+=ACB6+

Q$:T]^;=L 587>: <=LC:@?&79H587Z=B+DBJ7#9H53:,5I+ :b;=LÀCNTA`7 2 [* [_*.10 5877<A=7>: 9H5!3:,B6+D:,5JZ=Z=:@Z2V=N@B6+h7\58A7+=A7+=W79D:^Z=: Y 5=L`7f;=<ACBJ<A`7SN@BJ]^;=7>:@ZY <>BJ] 79D: n X . mc;H5877>:T</+XB8Y&79D:R<=LC:V$5J? .S 1 V :@NT7ACB6+

94:T]_58A7+=A7+=WO+H58]G:@Z7>:T]^;=L 587>:@? 58<>: >+ D?>:@Z2Vk5I+DZ NK5I+ : <>:T]GB3:@Z

g""$16P0# "= 6

V @G>"@ ; L`LY >+DNT7ACB6+GNK58L`LC? 7>B 79D: 3Z0 Y>+DNT7ACB6+^F)A`79 3:TS+H58]G: k58<>: <>:T;=L 5JN@:@Z hSI79D: ;H5879

:;=<>:@?\?ACB6+ Z`3+) 3 V ` XZV . o [ o )Z3 Za , , V `3 p<r k(k)VhF)9D:T<>:

k(k)AC?79D: n X . m^5877<A=7>:Y BJ<79D: 3:TS) ?Z=:1+=A`7ACB6+D?KV B>+DZGA7+a79D:4:F+.A`<>B6+=]G:F+.7&B8Y279D:4?7SLC:@?9D:@:T7#]GB.Z =LC:4B6+D:?7>:T;H5JN

4B F : 3:T<KVHA Yk(k)

AC?5D?>BJL=7>:V1+DB Z`3+) 3 V ` XV . o [ o )Z3 Za ,1, V `+3-p<r AC?);=<>:T;:F+DZ=:@Z : ³±²h´¸§º®6¶J©u¸U©uªI« "!$#SÀªI«¬Ã®6DÃ<«·²4Â6DÀ·«Ä & -/.0.1 32 1"#053.>;>=0= . % " ¿ ½6²4¸Ã<«)¸D½©uªI«·²4«|®IµÃ<«·²1`ü«|³Á®§I²4«hµ²Â6`¨µÃ<«¬©u«¨1®6µÃ<«¬²1µ¯ü«/¶:°BÄ©uªº«|¸µ©uªI«¨n®IµÃ<«·²1`ü«hÀ·¸®º²4³Á²©u«¬®:©u¯°À·¸®& F«¨4©u«/¶e¾

U*BV N0,?: V BU*G1= 5JN>9 a [ o 3 Xm o S[ \12 A7+D?7<DNT7ACB6+ a [ o 3 Xmo S[ \ 2 )Z3 3 .1YPO p1 O g Y O p2 O body a+ [ o 3 Xmo S[ \ 2

AC?)7<\5I+D?L 587>:@Z7>B X 2 2 0 o .3n2 1X .3) )S3 3 .+Y O p1 O n `3ZY O m O *. m o 2 X [ X n VX n3SY O \ [1[3 V . o S[ \ 2O )Z3 3 .1Y O p1 O X ):YPO V `+3-p<rE O *. m o 2 X [ X n VX n3SY O \ [1[3 V . o S[ \ 2* V o 30O )S3 3 .+Y O p1 p2 O X )Y O V `3 p<rO ) [ . )Z3 3 .1YPO '_) ,/\ V V+VXa11 1X ._* V p<rXO X 2 2 0 o .3:n+2 X .3+) A Y

gAC? S[ \ 2 o 0 BJ< S[ \12 o:X ` X 3 V . £ BJ79D:T<F)AC?>:V p1 p2

AC?<>:T;=L 5JN@:@Z .S O3n2 .10 o )S3; \3 V 3-p<rXO Q&9D: ) [ . ?>:T<3:@?)7>BRA7+DZbACNK587>:M79H5874?>:<l D:F+DN@:@?458<>:,<>:@BJ<>Z=:T<>:@ZA7+g?>BJ]G: >+ N+DBKF<+cF#5KS +D:TF 7>:T]^;=L 587>:fAC?5JZ=Z=:@Z .3n+2 X .3 n X . m Y O m * `,1, V `+3-p<r X .1. [_* \1.3t,1, O n `+3SY O m O 2 X [ X n VX n3SY O \ [1[3 V . o S[ \ 2O X ):YPO V `+3-p<rE O [3S\_*[3S` Y O<03),O 2 X [ X n VX n3SY O \ [1[3 V . o S[ \ 2* V o 30O X ):YPO V `+3-p<rA*O [3; \_*[3Z`1Y O<03+)O body Z.3n2 1X .3[+D?>ACZ=:

bodyV8Y >+DNT7ACB6+GNK58L`LC?P7>B \ [1[3 V . o S[ \ 2* V o 30tp<r 58<>:#<>:T;=L 5JN@:@Z hSR5 58<A 5=LC:&<>: Y :T< :F+DN@:,7>B \ [1[3 V . o S[ \ 2* V o 30 VD5I+DZ Y>+DNT7ACB6+ NK58L`LC?7>Bi \ [1[3 V . o S[ \ 2tp<r 58<>:M<>:T;=L 5JN@:@ZhS J58<A 5=LC:M<>: Y :T<>:F+DN@:@?7>B \ [ [3 V . o [ \ 2

¡ K=U0DC=10,B0 MCMBI PA`<>?7KV=LC:T7 D?)<>:@NK58;=A`7=L 587>:EF)9H587AC?)LC: Y 7B8Y 58<A 5=LC:@?5I+DZ;H58<\58]G:T7>:T<>?

•9: Y :T<>:F+DN@:@?7>BJ58<A 5=LC:@? B>+DZhSg?>:<l D:F+DN@:IN@B6+D?7<DNT7>BJ<>?M5I+DZg<>: Y :T<<>:@Z 7>BGY <>BJ] 79D:)Z3 3 . :b;=<>:@?>?ACB6+ B8Y X \3 oZaa5I+DZ X 2 2 0 o .3:n+2 1X .3+) 58<>:f?7A`L`L2;=<>:@?>:F+h7

•.7SLC:@?9D:@:T745I+DZ7>:T]^;=L 587>:f;H58<\58]G:T7>:T<>?458<>:M?7A`L`L2;=<>:@?\:F+h7

Q&9D:T<>: 58<>: ZbA_^2:T<>:F+h7 F#5KS? 7>BO;=<>B.N@:@:@ZF)A`797>:T]^;=L 587>: ;H58<\58]G:T7>:T<>?KVA7+%BJ<>Z=:T< B8YMW<>BKF)A7+=W58] =A`7ACB6+D?

N03 Y BJ<4L 587>:T< J4BJ74Y :K5J?>A=LC: Q&9D:IL 587>:T< HBKF 5I+DZJ58L`ACZD587ACB6+U5I+H58L`SK:@?,58<>:E7>BB ZbA_N =L`77>BR]GB.Z=:TL$N@B6+D?>:T<J587A3:TL`S F)A`7958<A 5=LC:@?45I+DZ ;H58<\58]G:T7>:T<>? G1A D L`L7>:T]^;=L 587>:;H58<\58]G:T7>:T<<>: Y :T<>:F+DN@:@?$58<>:6<>:T;=L 5JN@:@Z hS ') ,/\ V1 V1V 3S\3 V_ 3 p<rQ&9=AC?)AC? >+H5JN@N@:T;=7\5=LC:V WA3:F+ 79H587)7>:T]^;=L 587>:M;H58<\58]G:T7>:T<>? B8Y 7>:F+ :F+DZ =; A7+ B=7;=7 UNW|V@ ; ; @FC@ lBeU"G C@U ; 4L`L *. mo 2 X [ X n A7+D?7<DNT7ACB6+D? 58<>:&;H58<7A`7ACB6+D:@Z hSE;H58<\58] :T7>:T<r+H58]G:V5I+DZf58L`LJ58<A 5=LC:=A7+DZbA7+=W :;=<>:@?\?ACB6+D?jY BJ<:K5JN\9f;H58<7A`7ACB6+IAC?N@BJL`LC:@NT7>:@Z 79DB?>:

79H587IZ=:T;:F+DZXB6+5 N@B6+.7>:7w+DBZ=:GF)A`L`L#9H5!3:a7>B :a58;=;=<>B:A`]_587>:@Z|£ 79D:TSUNK5I+>+DBJ7I<>:TL`A 5=L`Sk:g]GB3:@Z 3:T<S <>: Y :T<>:F+DN@:g7>B 5U7>:T]^;=L 587>:c;H58<\58]G:T7>:T< F)A`79%?\BJ]G:+H58]G:cAC?+DBKF <>:T;=L 5JN@:@Z hS 5 m1 )S3 V<\5I+=WA7+=WGB3:T<58L`L =A7+DZbA7+=W3?)A7+ 79D:i+H58]G: ?&;H58<7A`7ACB6+jVbF)A`79') , \ V1 V1V 1 3 XVg7>:@?>7f:;=<>:@?\?ACB6+D? Q&9=AC?MAC?M79D:a58;=;=<>B35JN>9 ?=WW3:@?7>:@Z .S V5I+DZMA`7PF#5J?1+D: Y BJ< &Q VF)9D:T<>:79D:#B6+=L`Sj+H5J?7SMN@B6+D?7<DNT7KV!96Q<D?KVN@B=LCZk:<>:T;=L 5JN@:@ZhS ') ,/\ V1 V1VNd 3Z' .qpr

Å

M? 0,BMAIV C = E10> MA B sU"GIC@FU ; Q&9D: &Q X ) p<r 7S;k:gZ=:@NTL 58<\587ACB6+-Y BJ<^79D:58<A 5=LC:RB8Y ;H58<\58]G:T7>:T<,AC? D?>:@Z2V<>:T;=L 5JNTA7+=W58<A 5=LC:I<>: Y :T<>:F+DN@:@? hSc?\BJ]G:IBJ79D:T<MN@B6+D?>7<DNT7KVN@B6+D?7<\58A7+D:@Z .S 79D:fZ=:@NTL 58<>:@Z7S;k:

E>B@A C = !V E>0>MA 0 ; AHUXW|V@ ; ; @FC@ B sU"GIC@FU ; Q&9=AC?P9H5J?P79D:&5JZ 5I+h7\58W3:&B3:T<5 ;=<>: 7S.;:H5J?>:@Z ?>BJL=7ACB6+ 79H587IA`7IF)A`L`L&<>:T7\58A7+?>BJ]G:_;=<>:@NTAC?>ACB6+ 79D: NK5J?>: B8Y45g;=<>: &Q M?7S.LC:@?>9D:@:T7>?KV=F)9D:T<>: 58<A 5=LC:@?45I+DZ ;H58<\58]G:T7>:T<>? 58<>:>+h7S.;:@Z

UNW|VD ; @FC@ BeU "G C@U ; [ YP79D:,:'^:@NT7B8YP;H58<\58]G:T7>:T< =A7+DZbA7+=WGB6+ N@B6+h7<>BJL HBKF NK5I+ :<>:K5J?>B6+H5=L`S 58;=;=<>B:A`]_587>:@Z A`7^NK5I+jV A Y 79D:T<>:58<>:+DB ;H58<\58]G:T7>:T<^<>: Y :T<>:F+DN@:@?Â7+ 5I+hSX 212 0 o .3n+2 X .3+) A7+D?7<DNT7ACB6+ 79D:F+-<>:@?>BJL=7ACB6+%N@B=LCZ : ;k:T< Y BJ<]G:@Z +' &%'HB F5I+H58L`S?>AC?KV=?9H58<;:F+=A7+=WG79D:M?>:T7B8Y6;kB?\?A=LC: =A7+DZbA7+=W3?)Y BJ<:K5JN>9 <>: Y :T<>:F+DN@:

E>B@A IW[@FC$@ ;- NB ; ? H 4? 79D:^5kB3:V2A7+bY :T<<A7+=W]GBJ<>:I?>;k:@NTAHNI7S;:@? 79H5I+UZ=:@NTL 58<>:@Z2VF)9D:T<>:G;B?>?A=LC:V 5J?E5 L =<S Y BJ<M79D:a?7SLC:@?9D:@:T7^5=79DBJ< DBJ< &Q V6<>:@?>BJL=7ACB6+OB8Y7>:T]^;=L 587>:;H58<\58]G:T7>:T<>?&NK5I+ k:A`]^;=<>B3:@Z B3:T<#79H587 B3:T< 79H587&B8Y &.Q V :@NK5D?>:79D:TS]_5@Sk:&Z=:@NTL 58<>:@Z [3;S\*[3Z` V:TLÀ`]Â7+H587A7+=Wf79D:)Z=: Y 5=L`7 =A7+DZbA7+=WM7>B 79D:):T]^;=7SR?>:<l D:F+DN@:

e =<<>:F+h7L`S3V.B=<PA`]^;=LC:T]G:F+.7\587ACB6+ D?>:@?-HB F A7+D?>:F+D?A`7A3:)<>:@?>BJL=7ACB6+jV k:@NK5D?>:#A`7 5=7>BJ]_587ACNK58L`L`S:T]=L 587>:@? kBJ79f;H58<\58]G:T7>:T<$7>+>+D:TLÀ7+=W,5I+DZ,79D:;H58<\58]G:T7>:T< Y BJ<F#58<>ZbA7+=WM:'^2:@NT7B8Y &.Q =A`L`7 A7+ 7>:T]^;=L 587>:@? #[7)AC?4:K5J?S DBJ<45R<>:K58L &Q 7>BBJL V=;=7A7+.7>BG79D:,9H5I+DZ=?4B8Y D?>:T<>?F)9DBGZ=B+DBJ7s+DB F 79D:@?>:,Z=:T7\58A`LC?KV 5 HBKF ?>:F+D?>A`7A3:f58;=;=<>B35JN>9 ?>:@:T]G?:K5J?AC:T<)7>B_Z=: Y :F+DZ

G ; ?!C@U ; ?0G =1BeS@U ; 0 ; A$C K=U0DC=10,B0 MCMBI Y 7>:T< J58<A 5=LC: 5I+DZ,;H58<\58]G:T7>:T<<>:@? BJL=7ACB6+jVY >+DNT7ACB6+ NK58L`L :b;=<>:@?>?ACB6+D??>7A`L`L4<>:T]_58A7+ 5J?+DB6+ ;H5879 :;=<>:@?\?ACB6+D? 79H587 ]_5KS%5 Y Y :@NT7EN@B6+h7<>BJL HBKF BJ<EB=7;=7 Bg5877>:T]^;=7IAC?M]_5JZ=:a7>B ?7\587ACNK58L`L`SO5I+H58L`SK:^Y >+DNT7ACB6+D?KV 5I+DZ?7SLC:@?9D:@:T7 ;H58<\58]G:T7>:T<>?f58<>:+DBJ7 <>:@?>BJL3:@Z hS 5J?A7+=W_Y BJ<M558LD: [+D?7>:K5JZ2V BJ79 B8Y#79D:@?>:58<>:f58;=;=<>BBbA`]_587>:@ZgY BJ< X \3 oZa V( 2 0 oZa 5I+DZ X 212 0 o .3n2 X .3) D?A7+=W B=<7S;k:M<>:@N@B6+?7<DNT7ACB6+ 7>:@N\9>+=A l D:Vk5I+DZw¢ D?>7#LC: Y 745J? AC?)Y BJ<BJ79D:T<A7+D?>7<DNT7ACB6+D?

2 0 oZa )Z3 3 .1YPO e A7+D?7<DNT7ACB6+D? 58<>:MN@B6+3:T<7>:@Zg7>B X 2 2 0 o .3n2 1X .3) n `3ZY O m O )S3 3 .+Y O e O5I+DZ 5R7>:T]^;=L 587>:,<=LC:,AC?45JZ=Z=:@Z .3n+2 X .3 n `3ZYPO m O n X . m Y O m * `,1, V `+3-p<r X .1. [_* \1.3t,1, O 2 [* [*.101Y O*O 2 0 X 212 0 o .3n+2 X .3+) n `+3SY O m O )Z3 3 .1YPO m * `,1, V `+3-p<r X . .1[_* \ .3t, ,F,O Z 210 Z.3n2 1X .3 79=AC?)<=LC:,AC?)<>: D?\:@Z Y BJ<58L`L 210 oZaÂ7+D?7<DNT7ACB6+D? N@B6+3:T<7>:@Z2VHF)A`79 79D:M?\58]G: ]GBZ=: m

V \Zn 3[ A7+D?7<DNT7ACB6+D?458<>:fN@B6+3:T<7>:@Z 7>B X \3 o:Za

N@BJ;: 2 0 oZa X \3 oZa X 2 2 0 o .3n2 1X .3) BJ79D:T<WLCBH58L V :; <>:@?>BJL3: <>:@?\BJL3: <>:@?>BJL3: <>:@?>BJL3:WLCBH58L V ?>:<l <>:T;=L 5JN@: 7 7 LC:K5!3:I5J? AC?LCBNK58L VD:b; <>:@?>BJL3: <>:@?\BJL3: <>:@?>BJL3: <>:@?>BJL3:LCBNK58L VD?>:<l <>:T;=L 5JN@: 7 7 LC:K5!3:I5J? AC?C)2fj5vuv)2e)2f3s*)2<f&!;)z"yuw"6' o_AG^]636365<;c ;*=)6v)2e)2f3s)6wE=<)$4)E3g$365J,l_Q=<*=Fc ;*=)6v)2)f3`*)2<(5E;"6E'A"`6e)*F <&3%"6*F"65<3 Fhr=<i"54"'= f$1)*=5$5h"'\36A=<&*F>Ef;" )6w'&)2+;=o"5;)uw"6'hr5`52"6'=y<3g"6* "5E<3 uqj36E3g"oK$&j*=5<3g"6*F"65<J, <i;8;Ci> 36A<*F=c fV5<v)2e)2f3u 6oCw3>J)2< *F5Ee<5"ifV6=hr=67"65khr5 @"!$#" %E@"!/<3g"6* "5E<3=,& <0!8;C';>;"'=$)(+* ,,N@BJ;: Z 210 o:Sa X \3 oZa X 2 2 0 o .3n2 1X .3) BJ79D:T<WLCBH58L 7 7 7 LC:K5!3:I5J? AC?LCBNK58L <>:@?\BJL3:- m1 )S3 F)<\58; <>:@?>BJL3:- m1 )Z3 F)<\58; <>:@?>BJL3:- m1 )Z3 F)<\58; LC:K5!3:I5J? AC?C)2fB .j5vu &)2+)2F"=+3*)2< f&B;)2"uw"6' ./!5f)w)2+)2="6=+3S*=)2< >`52h!*F536>`)2"1f&3%"1fVk"%$VFc)5$01)v"^><363\5<)*=*==;"+3j)(36B3g"%$3g'F"j"')v"5<$.=36=<A"+3w5<)26"6e*Fe)2wf<< <0"6')2"j*=)36>"'p))S="6q*)2<0f&i"6)v"6k)E3w)S5f)1v)6e)2f,s8 5*)2Q))S="63q<k63g5E;"5E<)<06)E*FS<A"q5hL"'p6=hr==<*=<<3g"6* "5E<0f$.)z"=<)v"2E3,

43 ;k:T<AC:F+DN@:MF)A`79 A`]^;=LC:T]G:F+h7\587ACB6+ B8Y6?>7SLC:@?9D:@:T7?A`]^;=LÀHNK587ACB6+ 5 58]G:@?;H5JN@: =A7+DZbA7+=WE?>N@BJ;=A7+=WM]_5 3:@? ?7SLC:@?9D:@:T7#Z=B.N =]G:F+.7<>:@?7<DNT7=<A7+=WI;H58A7+bY=L '6Q$B:#N@:T<7\58A7+IB8Y N@BJ<<>:@NT7/+D:@?\?KVJA`7$AC?+D:@N@:@?>? 58<SM7>B;H58<>?\:#58L`L s65879^: 3 ;=<>:@?\?ACB6+R5I+DZ4 5 58]G:5877<A=7>:@? V5I+DZ <>:@?>BJL3:d+H58]G:@?;H5JN@:c;=<>: 3 :@?_7>BK79[ ? Y 7>:T<G<>:@?7<DNT7=<A7+=WDVA`7_AC?58Wh58A7++D:@N@:@?>?\58<S 7>B 3:T<A Y S 79H587E58L`LU+H58]G:@?;H5JN@:=A7+DZbA7+=W3?I58<>:_?7A`L`LA7+h7\5JNT7 &.Q 6 ?'12 X . mo `+3 a+X \ . oVX n3)2 X 3 Y :K587=<>: 79H587G58L`LCBKF? =A7+DZbA7+=W B8Y >+=;=<>: 3 :@Z 5 58]G:@?A7+ sP5879: 3 ;=<>:@?>?ACB6+D? 7>B+H58]G:@?;H5JN@:@? AC? LÀ 3:TF)AC?>:R?>N@BJ;:@Z2Vj5I+DZ87 D?7 ]_5 3:@? A`7 : 3:F+F#BJ<>?>: W3BB.Z=<=7>: Y BJ<>N@: 7>:@N>9>+=A l D: ]Â`W9h7 k: 7>B N@BJ;hS+H58]G:@?;H5JN@: =A7+DZbA7+=W3?R7>B: 3:T<S+DBZ=:,A7+79D:TA`<?>N@BJ;:V : Y BJ<>:M5I+.S <>:@?>7<DNT7=<A7+=WGAC?Z=B6+D:

7 ?A7+=WG;H58<\58]G:T7>:T<>? Y BJ<)Y BJ<F#58<>ZbA7+=W 58<A 5=LC:@? 5I+DZ Y BN D?AC?J+DBJ7 5R;=<>B=LC:T] A7+c?\:T]_5I+7ACN@?R;=<>:@?\:T<.A7+=WU?A`]^;=LÀHNK587ACB6+jV =7G5 Y 7>:T<_58;=;=<>B 3 A`]_587>: ?A`]^;=LÀHNK587ACB6+jV#79D:T<>: AC?G5I+>+>+D:@N@:@?\?\58<S LCB?>?fB8Y&;=<>:@NTAC?ACB6+ F)9=ACN\9ON@B=LCZ k:G53BJACZ=:@Z .S D?>A7+=WY <>:@?>9@+H58]G:@?,Y BJ<79D:M;H58<\58]G:T7>:T<>?

Å [7AC?Y :TL`7KVk5 Y 7>:T<479D:E: 3 ;:T<AC:F+DN@:fB8YA`]^;=LC:T]G:F+h7A7+=W ?>7SLC:@?9D:@:T74?A`]^;=LÀHNK587ACB6+jV25I+DZ=;W<\5JZ=:4A`7F)A`79 H5JN ]_58;=;=A7+=WDVb79H587A`7#AC? 5 1+D:7>:@N\9>+=A l D:Y BJ<<>:@?>:K58<>N\9 ;=<>B%7:@NT7>? F)9D:T<>::T]^;=A`<ACNK58L ZD587\5 58<>: D?>:@Z2V29D:TL`;=A7+=Wg<>:@Z DN@:^79D:z+ =]k:T<IB8Y#:F+.7A`7AC:@?+D:@N@:@?>? 58<Sc7>B: 3 ;=L 58A7+ BKF#: 3:T<KVhA7+_5 ;=<>BZ DNT7ACB6+_?>:T77A7+=W,F)9D:T<>: :T77>:T< H5JN ]_58;=;=A7+=WI5I+DZ^:@?>;k:@NTA 58L`L`S:T77>:T<)?>NK58L 5=A`LÀ`7S +D:@?7>:@Zia [ o 3 XmG: 3 ;=<>:@?>?ACB6+D?)Z=:@?=Wh58<&A7+g5I+ 58L`L [email protected]=: : 3 ;=LCB?>ACB6+ 58<>:+D:@:@Z=:@Z2V :9/' "+R "#aF B=LCZR;=<>BH5=L`SIF BJ< k:T77>:T<679H5I+l "+,/ST! "# 3:T<SN@B6+D?>7<DNT779H587: 58LH587>:@?45I+ sP5879c;H5879 : 3 ;=<>:@?>?>ACB6+jV=WA3:F+c5RN@B6+h7>: 3 7 Y BN D? V=5I+DZ;H5J?\?>:@?,N@B6+h7<>BJL7>B?\BJ]G:^BJ79D:T<fN@B6+D?7<DNT7KVN@B=LCZ :^5D?7<\5JNT7>:@Z79D:^B7:@NT7 BJ<AC:F+h7>:@ZF&5@S3V25I+DZc79D:M;H58<7ACN =L 58<>? X 2 2 0 o .3:n+2 1X .3+) Va+ [ o 3 Xm :T7>N N@B=LCZk:f]_5JZ=:5J? ?;:@NTA 58LÀ 587ACB6+D?,B8Y79H587 &2A 3:TF)AC?>:V2?>:<l D:F+DN@:EN@B6+D?>7<DNT7>BJ<>?,N@B=LCZg9H53:E79D:TA`<,B F<+5D?>7<\5JNT7ACB6+jV3F)A`79GA`7>? B F<+_N@B6+h7>: 3 7?>:T7 ?>:@:&79D: HB F5I+H58L`Sb?AC??>:@NT7ACB6+ V5I+DZG5 W3:F+D:T<\58L5D?>7<\5JNT7ACB6+cN@B=LCZ : ]_5JZ=:MB8Y N@B6+h7\58A7+D:T<>? B8Y6?>:<l D:F+DN@:,N@B6+D?7<DNT7>BJ<>?

.A`]^;=LÀHNK587ACB6+U9H5J? 79D:G5JZ 5I+h7\58W3:^B8Y&?7\5@SA7+=WF)A`79=A7+X5aF :TL`L N+DBKF<+XL 5I+=WH58W3: &Q 5LCB6+=W ;H58<7 B8Y79D:EF#5KS3V =74A7+ 79D:f;=<>:@?\:F+h7 ;=<>B%7 :@NT7KVkA`]^;=LC:T]G:F+h7\587ACB6+OB8Y79D:E?A`]^;=LÀH:T< F#5J?ZbAC?;=<>BJ;BJ<7ACB6+H58L`L`S ZbA_N =L`7KVDN@BJ]^;H58<>:@Z 7>BG79D:M?A`]^;=LÀCNTA`7S B8Y679D:MN@B6+D?7<DNT7>?79H587 :F+D:D7>:@ZY <>BJ] A`7 .;=LÀ`77A7+=W 7>:T]^;=L 587>:#<=LC:@?$F)A`79 >+=ACB6+R;H5877>:T</+D?6A7+h7>B ?A7+=WLC: ;H5879^;H5877>:T</+I<=LC:@?fF/&5W<>:K5875JZ

1

' )$ &

U:I9H5!3:^?\:TLC:@NT7>:@Z ! 7>B_Y BJ<]_58L`L`S ?;:@NTA Y Sg5aW<\58]^]_58< Y BJ<479D:RN@BJ<>: &Q L 5I+=WH58W3:V :@NK5D?>:5 NK58<A7+=W B=7,B8Y : 3:T<S :TLC:T]G:F+h7f5I+DZ : 3:T<Sc5877<A=7>:R<>:T]GB3:@ZBJ< <>:T7\58A7+D:@Z F#B=LCZ ]_5 3:G5 3:T<SLCB6+=W^5I+DZG<\5879D:T< D?>:TLC:@?>? LÀC?7 5I+.S.F&5@S [+D?7>:K5JZ2V.F :'7 D?7&5J?>?>:T<779H587#79D:N@BJ<>: L 5I+=WH58W3: ?7S.LC:@?>9D:@:T7

•[?)?SN+h7\5JNT7ACNK58L`L`SN@BJ<<>:@NT7KVHLC:@?>?)79D: ') 5 3 AC?

•s <>:@?>:T<3:@?45I+.Sa7<\5I+D?Y BJ<] A7+J58LÀCZbA`7S B8YP79D:fBJ<A`WA7+H58L 5I+DZ;B?>?A=L`S5JZ=Z=?)]GBJ<>:

• 5J?9H5JZf58L`L_X 1o .3n2 1X .3 A7+D?7<DNT7ACB6+D?A7+3B .A7+=WJ+H58]G:@Z,7>:T]^;=L 587>:@?<>:T;=L 5JN@:@Z hS X 212 0 o .3n2 X .3)A7+D?7<DNT7ACB6+D?KVD?\:T]_5I+h7ACN@?;=<>:@?\:T<3:@Z

• 5J?9H5JZf58L`L1a+ [ o 3 Xm4A7+D?7<DNT7ACB6+D?j<>:T;=L 5JN@:@Z hSM5&?>:T]_5I+h7ACNK58L`L`SM:<l =A58LC:F+h7UX 2 2 0 o .3n2 1X .3)5I+DZ 7>:T]^;=L 587>:M<=LC:MN@B6+D?>7<DNT7 +H58]G:@?;H5JN@:f+DBZ=:@?58<>:,A`W+DBJ<>:@Z

•k+=L`Sa9H5J?)7>:T]^;=L 587>:f<=LC:@?>+DBw+H58]G:@Z7>:T]^;=L 587>:@?

• 5J?+DB >+=ACB6+g7>:T]^;=L 587>:M<=LC:,;H5877>:T</+D?

• 5J?#A7+D?7<=]G:F+.7\587ACB6+gZD587\5EACZ=:F+h7A Y S.A7+=WGNK5J?>:@?&B8Y7>:T]^;=L 587>: ;=<ACBJ<A`7S N@B6+DACNT7>?A7+h7<>BZ DN@:@Z hS>+=ACB6+ ;H5877>:T</+g?;=LÀ`77A7+=W

• 5J?I5I+ : 3 ;=LÀCNTA`7f;=<ACBJ<A`7SOB6+ 58L`L#7>:T]^;=L 587>:@? [+U79D:a7>:T]^;=L 587>:@?I79H587EF#:T<>:aNT<>:K587>:@ZOF)A`795Y <>:@?>9]GB.Z=:Vb79D:,;=<ACBJ<A`7SAC?&A`<<>:TLC: J5I+.7KVD79DB=W9

• 5J?&9H5JZg58L`LLÀ`7>:T<\58Lj7>: 3 7)<>:T;=L 5JN@:@Z hSX \3 oZaGA7+D?>7<DNT7ACB6+D?

• 5J?&9H5JZg58L`LLÀ`7>:T<\58Lj<>:@?=L`7:TLC:T]G:F+.7>?<>:T;=L 5JN@:@Z.S :<l =A58LC:F+h7 3 3:n3 V . A7+D?7<DNT7ACB6+D?

• 5J?&9H5JZg58L`LLÀ`7>:T<\58Lj<>:@?=L`745877<A=7>:@?<>:T;=L 5JN@:@ZhS :<l =AJ58LC:F+.7X .1. [* \1.3 A7+D?7<DNT7ACB6+D?

• 5J?+DBiZ 210 o:SaGA7+D?7<DNT7ACB6+D?

•$ 5KS49H53:6Y>+DNT7ACB6+EZ=:@NTL 58<\587ACB6+D?KV=7j79D:@?>:58<>:+DBJ7 D?\:@Z Y <>BJ] X \3 oZa V BJ<-X 212 0 o .3n2 X .3)A7+D?7<DNT7ACB6+D? : 3 N@:T;=7 '_) ,/\ V V+V 3S\3 V_ 3 pr

•$ 5KS49H53: J58<A 5=LC:Z=:@NTL 58<\587ACB6+D?KV=7j79D:@?>:58<>:+DBJ7 D?\:@Z Y <>BJ] X \3 oZaHV8BJ<-X 212 0 o .3n2 X .3)A7+D?7<DNT7ACB6+D?

•$ 5KS49H53: 7>:T]^;=L 587>:;H58<\58]G:T7>:T<>?KV=7279D:@?>: 58<>:'+DBJ7 D?>:@Z Y <>BJ] X1 \3 o:SaHV BJ<-X 2 2 0 o .3:n+2 1X .3+)A7+D?7<DNT7ACB6+D?

• 5J?+DB4V \Zn 3[ A7+D?7<DNT7ACB6+D? ?>B^B6+=L`S X \3 o:Za 5I+DZ 2 0 NK5I+gNT<>:K587>:,7>: 3 7<+DB.Z=:@?

9DBJLCZ5 Y 7>:T<4?A`]^;=LÀHNK587ACB6+ 4LC?>B=Vk58L`L sP5879 : 3 ;=<>:@?>?ACB6+D?4A7+c79D:I?7SLC:@?9D:@:T7i+DBJ74]G:F+.7ACB6+D:@Z 9D:T<>:58<>:,<>:T7\58A7+D:@Z Y=L`L`S3V=: 3 N@:T;=779H587A`]^;=LÀCNTA`7 5 3 :@?)9H53: :@:F+]_5JZ=:M: 3 ;=LÀCNTA`7

algorithm

schemainput

templaterules

built−in

stylesheetXSLT 2.0 template

rule setschema−less

schema−less flow

graph

flowdeathanal.

dead flowand code

report

compe−titionreport

validationreport

SGvalidate

transformSG

constructSGr−RNGconverter

datatypelibrary

constructfragment

repr.graph

schemaprocess

flowgraph

outputschema

schema

simplifiedstylesheet

schema

document

SGassembly

flowanal.

outputSG

data structure

Schematools

BRICS

stylesheetsimpl.

fragmentSG

set

extraction flow

b(C '75 E=+)2`)v"+)&5vu <a"6'7 0;5+)v"5$95E) ==<A"6ae3)2"6'<5^ <;c"Se35E<"6'0Fh "gcd')<X36;k52hw"'(E,4 X*+'=1)v"55e34e3)< 0"66<) *=5&5E<=<A"S3ghr5")<3%hr5E6 v)2e)v"5E<J,!C '1)%5E*=5&5E<=<A"+3)6"6' * ,1* >J;=V=<<05< ).36F"!52hy"=e)v"6\=36=<A")2"65<3`)2<()<1<;"w36*+'1)>)2<S"'i:/ 1)2$ /!)'`*F5<&3%"6*F"65<()<1)33gf$>E=<)2"6<S361)2$(+)2'3 hr54 7;*+')2"655e3 "65 v)2e)v", < "6'0'A"gcd')2<& 367)6k"6'B5;";"31"6')2"S"+)2="Shrz< 5h5E15A)2e3= ;)E &5vu )2<H*=5=V56"`*F5E<E"+)2<<p<hr5)2"65<S5<1S"%$Ec 36=* "<! 0;636365<3s)<;)E1*F5;;>A)p*F5ESVF"z"5E<16&5Eg"y5E<"=e)v"6p65z"%$1e33g3=>)<0) v)e)v"5E<k=V56" 5<k"6'p5 E=+)2 v)2e;z"%$.52h "'i"6+)2<&3%hr5E6 5E;"6"juwz"'36&* "w"5)<k5E;"6;"\36*+'=1),

\ t tvDn

[+79=AC?);H58<7KV=F#:,F)A`L`Lj;=<>:@?>:F+.779D:M58L`W3BJ<A`79=]iZ=: AC?>:@Z 5J?)79D: ]_58A7+g:F+=WA7+D:fB8Y6B=<);=<>BJ;B?>:@Z7S.;:?\5 Y : &Q/7>BBJL V 79D: H5JN W<>B>+DZZ=:1+=A`7ACB6+D?O+D:@N@:@?>? 58<SX7>B >+DZ=:T<>?7\5I+DZ A`7KV 5I+DZ 79D: <>:@?=L`7>?^B8Y?>BJ]G:f: 3 ;:T<A`]G:F+h7>?;k:T< Y BJ<]G:@Z7>B 3:T<A Y Sa79D:,Z=:@?>A`W+

& "

PLCBKF%5I+H58L`S?AC?AC?679D:N@BJ]^;=7\587ACB6+aB8Y25 +( Q&9D:5I+H58L`Sb?AC?6AC?Z=B6+D:)B6+ H5J?>AC?B8Y25 ?7S.LC:@?>9D:@:T75I+DZg5I+A7+=;=74?>N>9D:T]_5bVk5I+DZ 79D:,W<\58;=9 N@B6+h7\58A7+D?4A7+bY BJ<]_587ACB6+g79H587458;=;=LÀC:@?7>Bl 58;=;=LÀCNK587ACB6+gB8Y79D:M?>7SLC:@?9D:@:T77>BG5I+ A7+=;=7Z=BN =]G:F+h7479H587AC? 58LÀCZ F)A`79 <>:@?;:@NT7)7>B^79D:,A7+=;=7?\N>9D:T]_5 Q&9D:EA7+bY BJ<]_587ACB6+Z=:T<A5=LC:MY <>BJ] 79D:HBKF W<\58;=9 AC?4:@?\?>:F+h7A 58LPA7+ 58L`LP? D?>:<l D:F+h7,5I+H58L`SK:@? A7+ 79D: &.Q 7>B.BJL A`7 aQ&9D: 58LÀCZD587>BJ<_5J?>?>:T] =LC:@?GA`7>?^?=]^]_58<SXW<\58;=97>B <>:@?>:T]=LC:79D: N@B6+h7<>BJLHB FW<\58;=9 29DB F : 3:T<KV279D:R?=]^]_58<SgW<\58;=9 AC? ;BJL`S58<A 5I+h7KVF)9D:T<>:K5J? 79D:HBKF W<\58;=9 AC?4]GB6+DB58<A 5I+h7 :K5JZHBKF 5I+DZEN@BZ=: 5I+H58L`Sb?AC?KV5I+DZ.A`<7H58L`L`SI5I+hSfBJ79D:T<6?7\587ACN&5I+H58L`S?AC?PB8Y 54?7SLC:@?9D:@:T7PF)A`L`L.Z=:T;:F+DZB6+c5IW3BBZHBKF W<\58;=9 Q&9D:,]GB?7)A`]^;BJ<7\5I+h7A7+bY BJ<]_587ACB6+cZ=:T<A5=LC: Y <>BJ] 5HBKF W<\58;=9 AC?

• A3:F+I57>:T]^;=L 587>:VJ79D:R &%! /%- B8YHZ=:@NTL 58<>:@Z+DBZ=:7S.;:@?$79H587$]_5KS k:7S;k: B8YD79D: N@B6+.7>: 3 7+DB.Z=:,B8Y679D:,7>:T]^;=L 587>:f5874?>BJ]G: A7+D?7\5I+DN@:E587)<>+.7A`]G:

• A3:F+f5q &%'(*ST! &% F NF/' "'ZDR "# X 212 0 o .3n+2 X .3+) V:X 2 2 0 o *<n+2 [1.) BJ<(V 3'1. o n X . m V5GN@B6+.7>: 3 7 7S;k:R5I+DZ 5^7>:T]^;=L 587>:Vk79D:v% Q M% \ H/EB8YZ=:@NTL 58<>:@Z!+DBZ=:M7S.;:@? 79H587]_5@S k:E?>:LC:@NT7>:@Z hS 79D:EA7+D?7<DNT7ACB6+F)9D:F+ A`7>? N@B6+.7>: 3 7W+DBZ=:f9H5J? 79D:RN@B6+h7>: 3 7 7S;k:V25I+DZ HBKF 7>B 79D:7>:T]^;=L 587>:

Q&9D: 3:T<S H5J?ACN,58L`W3BJ<A`79=]/AC?#7\5 3:F+B3:T<#Y <>BJ] ;=<>: ACBD?&F BJ< V =7&]GB?7&B8YA`7>?&?=;:T<>?7<DN7=<>:,9H53: :@:F+<>:@Z=:@?A`W+D:@Z2VD7>B^? 587AC? Y S+D:TF NT<A`7>:T<A 5

• A`]Â7+=WY BJ<f5 7>BBJL79H587fNK5I+X:F+=9H5I+DN@: 5I+ &.Q Z=: 3:TLCBJ;=]G:F+h7I;=<>B.N@:@?>? Vj79D:GN@B6+.7<>BJLHBKF58L`W3BJ<A`79=]/]D?7KV :@?ACZ=:@? N@BJ]^;=7A7+=WHB FMVb58LC?\B :45=LC:47>Bf;=<>B.ACZ=: 79D: D?>:T< F)A`79 A7+bY BJ<]_5 7ACB6+aB6+aF)9H587F :4F)A`L`L NK58L`LH:9/%' \ H/ 7>:T]^;=L 587>:4<>:@N =<>?ACB6+D? 79H587 Z=B+DBJ7]_587>:T<A 58LÀ K:,587<>+ 7A`]G: :@NK5D?>:R79D:RA7+=;=7M?>N>9D:T]_5 Z=B.:@?W+DBJ7,;:T<]Â`7,79D:z+D:@N@:@?>?\58<S ?7<DNT7=<>:RY BJ< 79D:T]7>BR9H58;=;k:F+

• &Q 9H5J?4?>: 3:T<\58Lr+D:TF N@B6+h7<>BJLHBKF <>:TL 587>:@Z N@B6+D?7<DNT7>?479H587,58LC?>Bz+D:@:@Zc7>B :f5JN@N@B>+h7>:@ZY BJ< $ BZ=: J58LD:@?5I+DZ7V 3'1. o n X . m

•$LCB Fi5I+H58L`Sb?AC?ÂC?^L 58<W3:TL`S sP58795I+H58L`Sb?AC? Q&9D:+D:TF Y :K587=<>:@?_B8Y sP5879 +D:@:@Z=:@Z7>B :A7+DNTLDZ=:@Z

• $'& N\9D:T]_5 AC? 5_L 58<W3:T< L 5I+=WH58W3:RNTL 5J?>?79H587 Q RVk5I+DZ ?>BJ]G:fY :K587=<>:@? B8Y79D:IBJLCZ 58L`W3B<A`79=] +D:@:@Z=:@Z7>B :,: 3 7>:F+DZ=:@Z Y BJ<)79H587

•[7RF#5J?GY B>+DZ 79H587^79D:F BJ<>?7aBD?7\5JNTLC: Y BJ<G?DN@N@:@?>? Y =L58;=;=LÀCNK587ACB6+-A7+-5I+-B6+ LÀ7+D: :@ZbA`7A7+=WN@B6+h7>: 3 7EF&5J?f7A`]G: 5I+DZU]G:T]GBJ<SX;k:T< Y BJ<]_5I+DN@: Q&9D:_F BJ<U9H5JZXA`7>?MY B.N D?f7=</+D:@ZX7>B F#58<>Z=?79H587KVH5I+DZ <>:@?=L`7>:@ZA7+ 5+D:TF 58L`W3BJ<A`79=] 79H587F&5J?] DN>9g]GBJ<>:f?\587AC? Y 5JNT7>BJ<S

Q&9D:MB3:T<\58L`L$N@B6+.7<A=7ACB6+D?4B8Y679=AC?F#BJ< 7>B^?>7\587ACN &Q HB F 5I+H58L`Sb?AC?58<>:

+ : 3 7>:F+D?ACB6+gB8Y679D:M58L`W3BJ<A`79=] 7>BG<>:T;kBJ<75D?>:F+.77>:T]^;=L 587>:,<>:@N =<>?>ACB6+D? + : 3 7>:F+D?ACB6+gB8Y679D:M58L`W3BJ<A`79=] 7>BGF BJ< F)A`79 &Q 5I+DZ s65879 + : 3 7>:F+D?ACB6+gB8Y679D:M58L`W3BJ<A`79=] 7>BGF BJ< F)A`79 $'& N\9D:T]_5

+D:TF HBKF-58L`W3BJ<A`79=] VhF)A`79G?A`W+=AHNK5I+h7L`SRA`]^;=<>B3:@Z^7A`]G:)5I+DZR]G:T]GBJ<SE;:T< Y BJ<]_5I+DN@:VhN@BJ] ;H58<>:@ZM7>B79D:;=<>: ACBD?$58L`W3BJ<A`79=]G? L`Lh79D:: 3 7>:F+D?ACB6+D?$7>B79D: 58L`W3BJ<A`79=] F :T<>:A7+DN@BJ<;kBJ<\587>:@Z2V5I+DZ 79D:T<>:,F#5J?J+DB^LCB?>?B8Y6;=<>:@NTAC?ACB6+

Q&9D: Z=:@?>NT<A`;=7ACB6+B8Y79D:,58L`W3BJ<A`79=]/AC?#<\5879D:T<&Z=:T7\58A`LC:@Z2Vb]_5 A7+=WR79D:<>:@? =L`7&B8Y$79D:F#BJ<_;=<\5JNT7ACNK58L`L`SA`]^;=LC:T]G:F+.7\587ACB6+ <>:K5JZbS :@NT7ACB6+ ;=<>:@?>:F+h7>? 79D:;=<>B=LC:T] 7>B k:&?>BJL3:@ZGA7+G? _NTAC:F+h7Z=:T7\58A`Lk5I+DZ :@NT7ACB6+ Z=:@?>NT<A:@?5W3:F+D:T<\58L 3 :@Z ;kBJA7+.7?>BJL=7ACB6+jVD58L`LCBKF)A7+=WGY>+DNT7ACB6+D?&<>:T;=<>:@?>:F+.7A7+=WG79D: ZbA_^:T<>:F+.7<>:@?7<ACNT7ACB6+D?B6+HB F79H587 F)A`L`L : 3 AC?7 A7+G79D:N@BJ]=A7+H587ACB6+ B8Y279D:4?7SLC:@?9D:@:T7 5I+DZ_79D:)A7+=;=7 ?>N\9D:T]_5,7>B : ;=L=WW3:@Z A7+.7>BA`7 :@NT7ACB6+ ;=<>:@?>:F+.7>?$5)Y>+DNT7ACB6+E]GB.Z=:TLÀ7+=W49DBKFX7>:T]^;=L 587>: ]GBZ=:@?j<>:@?7<\58A7+HBKF?KV5I+DZ :@NT7ACB6+ 1;=<>:@?>:F+.7>? 5Y >+DNT7ACB6+^<>:T;=<>:@?>:F+h7A7+=WM79D:)?\:T]_5I+h7ACN@?B8Yk79D:)ZbA_^:T<>:F+.77>:T]^;=L 587>: A7+3B A7+=WfA7+D?7<DNT7ACB6+D? 5 B &.Q HB F 5I+H58L`Sb?AC?)F B=LCZ k:,N@BJ]^;=LC:T7>:fF)A`79DB=779D:@?>: Q&9D:&<>:@?76B8Y 79D: Y >+DNT7ACB6+D?58L`L=: 3 58]Â7+D: sP5879^;H5879^: 3 ;=<>:@?>?ACB6+D?67>B Z=:T7>:T<]Â7+D:&A Yk5 HBKF AC?PY :K5J?A=LC::@NT7ACB6+ Z=:@?\NT<Ak:@?f5 ?A`]^;=LC:V: _NTAC:F+h7 =7MB6+=L`Sc]GB.Z=:T<\587>:TL`S ;=<>:@NTAC?>:IY >+DNT7ACB6+jV279H587,F)A`L`L :;=74A7+h7>BG?>:T<ACN@:f5J?5I+c:K58<L`S :TLÀ`]Â7+H587>BJ< B8Y ]GB?7A7+bY :K5J?A=LC: HBKF? Q&9D:,<>:T]_58A7+=A7+=WaY>+DNT7ACB6+D? 58<>:]GBJ<>:f;=<>:@NTAC?>:V =7 58LC?>BGN@BJ]^;=7\587ACB6+H58L`L`S 9D:K5.AC:T< #Q&9D:E5D?7<\5JNT7 : J58LH587ACB6+gY>+DNT7ACB6+ B8Y :@NT7ACB6+ 5I+DZR79D:5I+DN@:@?7>BJ< L 5I+=WH58W3:#Y >+DNT7ACB6+GB8Y :@NT7ACB6+ u 58<>: BJ79GNK5I+DZbACZD587>:@?6Y BJ<679D: 1+H58LD?7\58W3:B8Y#79D:G5I+H58L`S?AC? VF)9D:T<>:R79D:IY :TFMV9H58<>Z=:@?7,7>B <=LC:^B=7 HB F?f58<>:EY B>+DZ [7 F)A`L`L :R?9DBKF<+F)9=ACN\9ZbA_^2:T<>:F+h7 5JZ J5I+.7\58W3:@? 5I+DZZbAC?\5JZ 5I+h7\58W3:@?479D:,7F B^9H53: :@NT7ACB6+ Z=:@?>NT<A:@? 9DBKF-79D:Y>+DNT7ACB6+D?#NK5I+:N@BJ]^;B?>:@ZGA7+.7>BE5M]GBJ<>:: _NTAC:F+h7 HBKF 5I+H58L`S?>AC?58L`W3BJ<A`79=] F)A`79DB=7ILCB?>?EB8Y;=<>:@NTAC?>ACB6+jV5I+DZO5I+ : 3 ;:T<A`]G:F+h7IAC?f;:T< Y BJ<]G:@Z2V 1+DZbA7+=W 5 ]DN>9 S_ &%']G:T79DBZY BJ< kBB?7A7+=WA`7>?^;:T< Y BJ<]_5I+DN@: 79H5I+ F)9H587GF&5J?G;=<>: ACBD?L`S D?>:@Z $ BJ<>:: 3 ;:T<A`]G:F+h7\58L<>:@?=L`7>?^58<>:a;=<>:@?>:F+h7>:@Z2VA7+DZbACNK587A7+=WU5g? D?>7\5I+h7A 58L&A`]^;=<>B3:T]G:F+.7_N@BJ]^;H58<>:@Z F)A`79O;=<>: ACBD?IF BJ<V=7?>7A`L`L2F)A`79g?>BJ]G:,79=A7+=W3?LC: Y 7)7>B :,Z=:@?A`<>:@Z :@NT7ACB6+ E5I+DZ :@NT7ACB6+ ;=<>:@?>:F+h7 7F#B+D:TF 58L`W3BJ<A`79=]G?4A7+3:F+h7>:@Z A7+g79=AC?F BJ<7>BaZ=:@NTACZ=:N@:T<7\58A7+ 5J?;:@NT7>?fB8YHB F Y :K5J?A=A`LÀ`7SXA7+ 5I+ 58;=;H58<>:F+.7L`SXLC:@?>?EW3:F+D:T<\58L V =7E?>7A`L`L ?A`]^;=LC:V5I+DZX]DN>9Y 5J?7>:T<MF&5@S 79H5I+ : Y BJ<>: U:^F)A`L`L79D:F+U;=<>B3:G79H587M79D:z+D:TF 58L`W3BJ<A`79=]G?f9H53:a587,LC:K5J?7E5J?MW3B.BZ;=<>:@NTAC?ACB6+ 5J?)79D:,N@BJ]^;B?A`7>:f58L`W3BJ<A`79=] 79D:TS <>:T;=L 5JN@:V 5I+DZ 79H58779D:T<>:,AC?+DB^LCB?>?B8YPW3:F+D:T<\58LÀ`7S

u

1+H58L V6N@BJ]^;kB?>A`7>:a58L`W3BJ<A`79=] F)A`L`L 79D:F+ :^;=<>:@?>:F+.7>:@ZXA7+ V 5I+DZX5g?>:T<AC:@?fB8Y&;=<\5JNT7ACNK58L#7>:@?7<>+D? F)A`L`L ?9DBKF 79H587 A`7>? ;=<>:@NTAC?ACB6+cAC? 79D:I?\58]G:R5J?KVBJ<:T77>:T<479H5I+ 79H587 B8Y;=<>: ACBD? 58L`W3BJ<A`79=]G? V=7A`7>?458;=;=LÀCNK587ACB6+ 58<>:K5RAC?)F)ACZ=:T<KV 5I+DZA`7<>+D?)] DN>9 Y 5J?7>:T<5I+DZA7+] DN>9cLC:@?>?)]G:T]GBJ<S PA7+H58L`L`S3V :@NT7ACB6+ 1^N@B6+DNTLDZ=:@?

7k+DZ=:T<a;:@ZD5I+h7ACN N@BJ<<>:@NT7/+D:@?>?KV&79D:d+H58]G:@?aB8Yf?\BJ]G:gB8Y,79D:Y >+DNT7ACB6+D? Z=:1+D:@Z :TLCBKF ?9DB=LCZ :;H58<\58]G:T7>:T<A K:@Z .S_79D: ?A`]^;=LÀH:@Z ?7S.LC:@?9D:@:T7

TVb?A7+DN@:479D:TS_]_5KSaN>9H5I+=W3: F)9D:F+

TAC?&N>9H5I+=W3:@Z U:BJ]Â`779H587KV 5I+DZ.7 D?>7)<>: Y :T<)7>B_5IWA3:F+

TF)9D:T<>:j+D:@N@:@?>?\58<S

&j:T7M

:f79D: &.Q ]GB.Z=:+H58]G:@?k79D:I?>:T7 B8Y 58LÀCZ 0 ?KV ;=LD? 79D:E?>;k:@NTA 58LP7>B 3:F+ A V 0G-FC H5RZ=: Y 5=L`7KV>+>+H58]G:@Z ]GBZ=: &j:T7R: 79D: 7>:T]^;=L 587>:M<=LC:@?)A7+

TVD5I+DZ

Ik: 79D:M7>:T]^;=L 587>: A7+3B A7+=WaA7+D?7<DNT7ACB6+D?A7+

T &j:T7

match : R→ XPathpattern

<>:T7=</+ 79D:,]_587>N>9g;H5877>:T</+cB8Y :K5JN>9 7>:T]^;=L 587>:Vk5I+DZselect : I → XPathpath

<>:T7=</+I79D: ?>:TLC:@NT7ACB6+R: 3 ;=<>:@?>?ACB6+EB8YH:K5JN\9E7>:T]^;=L 587>: A7+3B .A7+=W,A7+D?>7<DNT7ACB6+DBJ<P5I+ X 2120 o .3n+2 X .3+) A7+D?7<DNT7ACB6+jV 79H587jAC?2A`7>? )S3 3. : 3 ;=<>:@?>?>ACB6+ Y BJ<279D: <>:T]_58A7+=A7+=W7>:T]^;=L 587>:A7+3B .A7+=W A7+D?>7<DNT7ACB6+D?KV )Z3 a ,1, V `+3-p<r AC? D?>:@Z2V2:F+H5=LÀ7+=Wg5 >+=A Y BJ<] 7<>:K587]G:F+h7fB8Y&58L`L 7>:T]^;=L 587>:A7+3B .A7+=WaA7+D?7<DNT7ACB6+D?F)9=A`LC:,;=<>:@?\:T<.A7+=W_?\:T]_5I+h7ACN@?

ri : I → R<>:T7=</+D?)79D:,7>:T]^;=L 587>:f<=LC:MN@B6+h7\58A7+=A7+=W 5I7>:T]^;=L 587>: A7+3B A7+=W A7+D?7<DNT7ACB6+

U: H5J?>:)79D:5I+H58L`Sb?AC?B6+_79D:N@B6+h7>: 3 7]GBZ=:TL B8Y 1 V :@NT7ACB6+ 1 7 <>+h7A`]G:Vb587 5I+hS^WA3:F+_7A`]G:Z =<A7+=W 79D:E: 3 :@N =7ACB6+ B8Y5_?7SLC:@?9D:@:T7KV25GN@:T<7\58A7+ 7>:T]^;=L 587>:E<=LC:VH79D:R-ZN' %' &%'(*ST! &% 'ZXST%EAC?4A7+N@B6+.7<>BJL VH5fN@:T<7\58A7+ sP5879L+DBZ=:4AC? 79D: R ! &%! :* Q % 79D:4B _NTA 58L|+H58]G: AC?+DBKF N@B6+h7>: 3 7&A`7>:T] V =7A`7MAC? s+DB F<+Y BJ<E?=<>:R79H587fN@B6+h7>: 3 7fA`7>:T]G?EB8Y#7>:T]^;=L 587>:@?I58<>:z+DBZ=:@? V$5I+DZX5 N@:T<7\58A7+O]GB.Z=:GAC?,79D:R-ZX'+%'* Q % .7\587ACNK58L`L`S3VHF :I5D?7<\5JNT7<>+h7A`]G:fA7+D?7\5I+DN@:@?47>BR79D:TA`<7S;:@?KVD5I+DZgNK58L`Lj79D:fZ=:@NTL 58<>:@Z+DBZ=:,7S;: ?>:@: B8Y5^N@B6+h7>: 3 7+DBZ=:,A`7>?zR * &%! "(,% '_) ,/\ V V+V 3S\3 V Z3 pr )Z3 3. : 3 ;=<>:@?>?>ACB6+D? A7+ X 212Z0 o .3n2 X .3) A7+D?7<DNT7ACB6+D?#58<>:47 D?>7N@B6+?ACZ=:T<>:@Z A7+DN@BJ]^;H587A=LC:fF)A`79g: 3:T<S79=A7+=WGA7+ 79D:M5I+H58L`Sb?AC? Q&9D: Z=:@?\NT<Ak:@ZAC?f79D:^<>+ 7A`]G:G7<\5I+D?Y :T<fB8Y3R * "sS :T7F#:@:F+O7>:T]^;=L 587>:_<=LC:@?KVj79H587INK58<<AC:@?58LCB6+=WIF)A`79aA`7)5MN@B6+.7>: 3 7+DBZ=:45I+DZ 5,]GBZ=: Q&9D:7>:T<] R * &%! \ -F)A`L`L258LC?>B k: D?>:@Z h79=AC?#AC? 79D:]_58;=;=A7+=W B8YB6+D:MN@B6+h7>: 3 747S.;:,7>B_5G?>:T7B8YN@B6+h7>: 3 77S.;:@?KVDF)9D:F+ 5^;H5879g: 3 ;=<>:@?>?ACB6+cAC?5D?7<\5JNT7L`S: 58LH587>:@Z

+ % Q M% \ F)A`79c]GBZ=: m5I+DZgN@B6+h7>: 3 7 7S;k: q′

Y <>BJ] 5_7>:T]^;=L 587>: A7+3B A7+=WA7+D?7<DNT7ACB6+i7>B 5

7>:T]^;=L 587>:f<=LC:r′AC?5R?7\587ACNM5D?>7<\5JNT7ACB6+g79H587)AC?)]_5KS 9H58;=;:F+79H58745+DBZ=:,B8YP7S.;:

q′HB F?)Y <>BJ]

i7>B

r′Z =<A7+=W 5 58LÀCZ: 3 :@N =7ACB6+cB8Y T VbA7+3B A7+=W r′

>+DZ=:T<]GB.Z=:m

Q&9D:EW3B358LAC?7>B_N@B6+D?7<DNT7,5^W<\58;=9c79H587 5D?7<\5JNT7L`SgZ=:@?\NT<Ak:@?KVDY BJ< 5I+hS58LÀCZg: 3 :@N =7ACB6+cB8Y SVH79D:

5 Q?79H5874]_5@S :@N@BJ]G:MN@B6+h7>: 3 77S.;:@?)Y BJ<:K5JN\9g7>:T]^;=L 587>:M<=LC:Vk5I+DZA7+g7=</+gF)9=ACN>9 5 Q?]_5@S

U

phipre

phi

phi1

2

N

P

Fp

U ?=<<>B>+DZbA7+=W_79D:DW=<>: AC?5 >+=A3:T<>?>:MB8Y58L`L:@ZbW3: HB F?79H587NK5I+:,Z=:@?>NT<A:@ZA7+7>:T<]G?B8Y?>BJ]G: WA3:F+g?7S.LC:@?>9D:@:T745I+DZ ?>N\9D:T]_5

Fp

AC?)79D:M?\:T7B8Y6:@ZbW3: HB F?79H587]_5KS : 3 AC?7Z =<A7+=W : 3 :@N =7ACB6+gB8Y679D:M?7S.LC:@?>9D:@:T7KV=WA3:F+ 79H587A7+=;=7Z=BN =]G:F+h7>?458<>: J58L`ACZ F)A`79 <>:@?>;k:@NT77>BR79D:MA7+=;=7?>N>9D:T]_5bV 58LC?>B N+DBKF<+c5J?)79D:f: 3 5JNT7:@ZbW3: HBKF ?>:T7 φpre

φ1

0 ; Aφ258<>:M: 3 58]^;=LC:@?B8Y =;=;:T<458;=;=<>B 3 A`]_587ACB6+D? B8Y Fp

N@B6+h7\58A7+=A7+=W58L`LjB8Y6A`7KVH5I+DZ;kB?\?A=L`S_]GBJ<>:

NAC?5I+ : 3 58]^;=LC:MB8Y 5R?\:T7B8Y6Z=:@?>NT<AH5=LC:f:@ZbW3: HBKF?79H58745ILCBKF#:T< 58;=;=<>B 3 A`]_587A7+=WP%#! "%HBKF58L`W3BJ<A`79=]iNK5I+WH58<\5I+.7>:@:fF)A`L`L|+D: 3:T<: 3 AC?7Z =<A7+=W : 3 :@N =7ACB6+

PAC?45S_ f%-^58;=;=<>B 3 A`]_587ACB6+ B8Y Fp .7\587ACNI5I+H58L`S?AC?;=<>:@NTAC?ACB6+gNK5I+:,:F+=9H5I+DN@:@Z hS

•DBJ<45R?A7+=WLC: HB FMVD?A7+=Wa5J?45I+ =;=;k:T<458;=;=<>B 3 A`]_587ACB6+ φ1 ∩ φ2

VbA7+D?7>:K5JZ B8Y7 D?>7:TA`79D:T<

•[ YV.Y BJ<?>BJ]G:M<>:K5J?>B6+jV

φ2AC?<+DBJ7 D?>:@Z2V

φ1\NAC? :T77>:T<)79H5I+

φ158LCB6+D:

.7\587ACNI5I+H58L`S?AC?;k:T< Y BJ<]_5I+DN@:MNK5I+:,:F+=9H5I+DN@:@Z hS

•$A`<>?>7: 3 NTLDZbA7+=WG]GB?>7B8Y U hS <>+>+=A7+=W 5RN@BJ]^;=LC:T7>:I5I+H58L`S?AC? V D?A7+=Wa5EY 5J?7)7>:@?7)L`A 3:

φpre

•DBJ<45R?A7+=WLC: HB FMV=A Y679D:

φ17>:@?7<>+D??A`W+=AHNK5I+.7L`S Y 5J?>7>:T<)79H5I+ 79D:

φ27>:@?7KV=<>+ 79D:

φ17>:@?7 D<>?7KVD5I+DZ79D:F+g<>+ 79D:φ27>:@?7A Y679D:HBKF ;H5J?\?>:@Z

φ1 DL`7>:T<A7+=W

•DBJ<45R?A7+=WLC: HB FMV=A Y679D:

P7>:@?7)<>+D?4?A`W+=AHNK5I+h7L`S Y 5J?7>:T<)79H5I+ 79D:,]GB?7;=<>:@NTAC?>:

=;=;k:T< 58;=;=<>B 3 A`]_587>:E7>:@?7KVb<>+ 79H5877>:@?7B6+=L`SaA Y679D: P7>:@?7)F&5J?+D:TWh587A3: ?7 O+=W

U:D?\:@Z 58L`LB8YP79D:@?\:MBD?>:T<587ACB6+D?)A7+ 79D:MZ=:@?A`W+ B8Y679D: HB F 5I+H58L`S?>AC?58L`W3BJ<A`79=]

HB F Y <>BJ] F)9=ACN>9g7>:T]^;=L 587>: A7+3B .A7+=W A7+D?7<DNT7ACB6+D?7>B^F)9=ACN>9 7>:T]^;=L 587>:f<=LC:@?

G = (C,F )

F)9D:T<>:

Σd

AC?)79D:MZ=:@NTL 58<>:@Z+DB.Z=:,7S.;:@?B8Y679D:|F!(*ZX &?>N\9D:T]_5Din

C :M→ R → 2ΣdZ=:@?\NT<Ak:@?479D: R ! &%! /%- /MY BJ<79D:M7>:T]^;=L 587>:E<=LC:@? Q&9D:@?>:I58<>: =;=;:T<58;=;=<>B 3 A`]_587ACB6+D?4B8Y679D:M?>:T7B8Y67S;:@?B8YP;B?>?A=LC:,N@B6+.7>: 3 7J+DB.Z=:@?&Y BJ<45I7>:T]^;=L 587>: ∈ R

F :M→ Σd → I → R → 2Σd=;=;:T< 58;=;=<>B 3 A`]_587>:@?4?>:T7>?)B8YP:@ZbW3:HBKF?&Y <>BJ] 5I7>:T]^;=L 587>:A7+3B A7+=WGA7+D?7<DNT7ACB6+

∈ I7>BR5I7>:T]^;=L 587>:

∈ RVWA3:F+c5IN =<<>:F+.7]GB.Z=:

∈M5I+DZ 5RN@B6+h7>: 3 77S;k:

∈ Σd

e#B6+D?>:T<587AA`7SB8Y479D:F)9DBJLC: 58LÀCZbA`7S 5I+H58L`Sb?AC?R<>:<l =A`<>:@?^79D: W<\58;=9 7>B : B6+79D: L 58<W3:g?ACZ=: \VSAC:TLCZbA7+=WG79D:@?>:,<>:<l =A`<>:T]G:F+h7>?

U ; NB ,0DC@ I@FC U ?U ; CCOMC: [ Y79D:T<>:R: 3 AC?7>? 5_Z=BN =]G:F+h7 58LÀCZcF)<7 7>B dV?DN>9 79H587M587

?>BJ]G: 7A`]G: Z =<A7+=WM58;=;=LÀCNK587ACB6+^B8YT7>B479D:#Z=B.N =]G:F+.7KV

m ∈MAC?$79D: N =<<>:F+.7 ]GB.Z=:V

q ∈ ΣdAC?)79D:,N =<<>:F+h7 N@B6+h7>: 3 77S.;:M5I+DZ r ∈ RAC?)79D:,N =<<>:F+.77>:T]^;=L 587>:VD79D:F+

q ∈ C(m)(r) U ; NB ,0DC@ I@FC U MA >UXWO [Y79D:T<>: : 3 AC?>7>?R5 Z=BN =]G:F+h7 58LÀCZ F)<7 7>B d

V?DN\9 79H587_587?>BJ]G:M7A`]G:IZ =<A7+=W58;=;=LÀCNK587ACB6+ B8Y

T7>B_79D:EZ=B.N =]G:F+.7KV 79D:IN =<<>:F+h7 ]GBZ=:MAC?

m ∈ MVH79D:

N =<<>:F+h7 N@B6+h7>: 3 7+DBZ=:9H5J?G7S.;: q ∈ Σd

5I+DZ-79D:7>:T]^;=L 587>: A7+3B A7+=WOA7+D?>7<DNT7ACB6+i ∈ I7<\5I+D? Y :T<>? N@B6+.7<>BJLk7>Bf79D:7>:T]^;=L 587>: <=LC:

r′ ∈ RV3F)A`795fN@B6+.7>: 3 7+DB.Z=: B8Yj7S;: q′ ∈ Σd

Vh79D:F+q′ ∈ F (m)(q)(i)(r′)

6 ; C B@FC Q&9D:GN@B6+h7>: 3 7f?>:T7MB8Y): 3:T<Sc7>:T]^;=L 587>:_<=LC:R]D?7EN@B6+h7\58A7+X79D:^N@B6+.7>: 3 7E7S;k:@?fB8Y HBKF?79H587HBKF A7+h7>B^79D:,7>:T]^;=L 587>:f<=LC:

5 BJ79=A7+=WF#5J?^?\58ACZ5B=7G5I+hS79=A7+=W<>:<l =A`<>:@Z *! f7>B k:aA7+DNTLDZ=:@Z A7+ C5I+DZ

FV?>B 5I+B.ACBD?

?>BJL=7ACB6+X79H587M?\587AC? H:@? 79D:R<>:<l =A`<>:T]G:F+h7>?MAC? V2B8Y&N@B=<>?>:Vj7>B A7+DNTLDZ=:G58L`L 5 Q?MA7+58L`L 58LD:@?MB8Y C5I+DZF Q&9=AC? ?>BJL=7ACB6+ EF#B=LCZ 9H58<>ZbL`S LC:K5JZ 7>B 5I+.S.79=A7+=W79H587 AC?,5=LC:E7>Ba;=<>BACZ=:R79D: D?>:T<4F)A`79A7+.7>:T<>:@?7A7+=WUA7+bY BJ<]_587ACB6+ ?RF :?9H58L`L)?>:@: L 587>:T<KV#5L 58<W3:T< W<\58;=9 >+=A Y BJ<]^L`SX7<\5I+D? Y BJ<]G?^7>B5

L 58<W3:T<?\:T7&B8Y6?;=<ACBD?:T<<>BJ<>? ?>A`7H587ACB6+D?)79H587)F)A`L`L k: <>:T;BJ<7>:@Z 5J?)?7\587ACN,:T<<>BJ<>? =7)<>:K58L`L`S58<>:79D:M:'^2:@NT7>?B8Y58;=;=<>B 3 A`]_587ACB6+D? A7+79D:f5I+H58L`S?>AC? QF B_B8Y B=< =L`7A`]_587>:E?DN@N@:@?>?)NT<A`7>:T<A 5RY BJ<5I+c5I+H58L`Sb?AC?)7>BBJL2A7+g5RF)ACZ=:T<?>:T77A7+=W_<>:T7=</+ 9D:T<>:

•QBU]_58A7+.7\58A7+ 5;=LC:K5J?\5I+h7 D?>:T<_: 3 ;k:T<AC:F+DN@: 79D:c58L`W3BJ<A`79=] ]D?>7_9H5!3:gW3B.BZ7A`]G: 5I+DZ]G:T]GBJ<S ;k:T< Y BJ<]_5I+DN@:

•QB =A`LCZ D?\:T<N@B6+HZ=:F+DN@: ?;=<ACBD?:T<<>BJ<>??9DB=LCZ :3:T;=77>BG5I]Â7+=A`] =]

Q&9D:M:F+=WA7+D:@:T<A7+=W N>9H58L`LC:F+=W3:@? B8YP79=AC? 5I+H58L`S?>AC?58<>:

•$LCB F 5I+H58L`Sb?AC?$?9DB=LCZ :: _NTAC:F+.7P:F+DB=W9EY BJ<$B6+ LÀ7+D:#: J58LH587ACB6+IA7+R5I+I:@ZbA`7>BJ<PB6+R5?7\5I+DZD58<>ZZ=:@?7>BJ; N@BJ]^;=7>:T<

•Q&9D:MN@B6+D?7<DNT7>:@ZgN@B6+.7<>BJL HB F W<\58;=9 ?9DB=LCZ :f5JN@N =<\587>:f:F+DB=W9c7>B_5!3BJACZc]GB?7?;=<ACBD?:T<<>BJ<>?

B6+D:M;=<>: ACBD?L`S D?>:@Z ? DN@N@:@?>?NT<A`7>:T<ACB6+ F#5J?47>BG9H53:E5^W3:F+D:T<ACNfACZ=:F+h7A`7Sg7<\5I+D? Y BJ<]J58LÀCZD587>: F)A`79c58L`L?>N\9D:T]_5J?A7+c5^7>:@?7?>:T7KV=;=LD?: 58LH587ACB6+cB8Y5^N@BJ<;D?4B8YP;=<\5JNT7ACNK58L D?>:NK5J?>:@?

)$

Q<\5JZbA`7ACB6+H58L`L`S V5 3 :@Z-;kBJA7+.7 58L`W3BJ<A`79=] ?7\58<7>? B=7_F)A`79 5L 5877ACN@:V5XN@B6+h7<>BJL HBKF W<\58;=95I+DZ 5g?\:T7EB8YN@B6+D?7<\58A7+.7>?KV =7IA7+X79=AC?RNK5J?>:V 5gN@B6+.7<>BJL HBKF W<\58;=9OAC?E;H58<7^B8Y79D:G<>:@?=L`7KV'+DBJ7^5;=<>:T<>:<l =AC?A`7>: Q&9D: N@B6+h7<>BJL HB F W<\58;=9 D?>:@Z587M?7\58<7 =;AC?M5 ZbA`<>:@NT7>:@ZW<\58;=9F)A`79X5+DB.Z=:EY BJ<: 3:T<SG7>:T]^;=L 587>: <=LC: 5I+DZa: 3:T<S_7>:T]^;=L 587>: A7+3B A7+=WGA7+D?7<DNT7ACB6+ [7F)A`L`Lk9H5!3:,5I+ :@ZbW3:Y <>BJ] : 3:T<S7>:T]^;=L 587>:E<=LC:,7>BÂ`7>?4N@B6+h7\58A7+D:@Zc7>:T]^;=L 587>: A7+3B A7+=W A7+D?>7<DNT7ACB6+D?KV 5I+DZcB6+D: Y <>BJ]i: 3:T<S7>:T]^;=L 587>:A7+3B .A7+=W A7+D?7<DNT7ACB6+-7>BO: 3:T<S 7>:T]^;=L 587>:g<=LC: Q&9D:L 5877ACN@:@? D?>:@Z58<>: 587_L 58<W3:@?7 ? D?>:T7>?GB8YΣd ×M 7k+DZ=:T<79D: 3 :@Z ;kBJA7+.7458L`W3BJ<A`79=] VD79D:@?\:MN@B6+D?7<\58A7+h7>?F)A`L`L?\587AC? Y S_79D:M<>:<l =A`<>:T]G:F+.7>?

6 ; @ C@0"@0DC@U ; Q&9D:" ""!S#7>:T]^;=L 587>: <=LC:5J?IB8Y79D: 1 V :@NT7ACB6+ V679H587IAC?KV679D:a7>:T]^;=L 587>:<=LC:r79H587 AC?#A7+=A`7A 58L`L`SGA7+3B 3:@Z F)A`79 79D:4A7+=A`7A 58L2N@B6+h7>: 3 7&7S;k: q

>+DZ=:T<&79D:4A7+=A`7A 58Lk]GBZ=:mV

]D?79H5!3:q ∈ C(m)(r)

UXW =1BU=>0 0DC@U ; %9D:F+g?>BJ]G:j+DBZ=:M7S.;:qk:@N@BJ]G:@? 5w+D:TF N@B6+.7>: 3 747S;k:MB8Y67>:T]^;=L 587>:E<=LC:

r>+DZ=:T<_]GBZ=:

mV Y BJ< :K5JN>9%7>:T]^;=L 587>: A7+3B A7+=W A7+D?7<DNT7ACB6+

i : ri(i) = r5I+DZ Y BJ< :K5JN>9

7>:T]^;=L 587>:,<=LC:r′Vb79D:F+A Y679D:T<>:,: 3 AC?7>?5RZ=B.N =]G:F+.7 58LÀCZ F)<7 d

V=?DN\9 79H5875RN@B6+h7>: 3 7HBKF587r]_58;D?E5+DB.Z=:GB8Y)7S.;:

q7>Bc5L+DB.Z=:GB8Y)7S.;:

q′V$5I+DZX7>:T]^;=L 587>:

r′AC?MZbA`<>:@NT7L`SA7+3B 3:@Z

F)A`79q′5J?A`7>?N@B6+h7>: 3 7+DBZ=:V q′ ∈ F (m)(q)(i)(r′)

6 ; C B@FC Q&9=AC? 1+H58L2N@B6+D?7<\58A7+.7&?>A`]^;=L`SG:F+bY BJ<>N@:@?#79H587#A7+ HBKF)A7+=WR7S;k:@? :@N@BJ]G:4N@B6+.7>: 3 7#7S;:@? F (m)(q)(i)(r) ⊆ C(m)(r)

DBJ<J+DBKFMV=F#: F)A`L`L?>BJL3: 79D:,?>:@:T]Â7+=WL`S ZbA_N =L`7HBKF ;=<>BJ;H58Wh587ACB6+cN@B6+D?7<\58A7+.7?A`]^;=L`S hS Z=:1+=A7+=W5^NTL 5J?\?B8Y

ΦZX*R "#,/ Y =LDL`LÀ7+=WGA`7KVH5I+DZ 79D:F+ LCBB aY BJ<)<>:K58LÀ 587ACB6+D? B8Y6? DN>9Y >+DNT7ACB6+D?

ΦT&6$4

:1+D:5Φ Y>+DNT7ACB6+^7>B :)5I+hSEY>+DNT7ACB6+

φ :M×Σd×I×R→ 2ΣdVh?DN>9R79H5876Y BJ<P79D:&?7S.LC:@?>9D:@:T7

SVbY BJ<5I+hS A7+=;=7Z=BN =]G:F+h7 J58LÀCZF)<7 7>B d

VH5I+DZ Y BJ<5I+hSN@BJ]=A7+H587ACB6+cB8Y(m, q, i, r′)

B8Y

•5I]GB.Z=:

mV

•5 5 Q q

V

•5I7>:T]^;=L 587>: A7+3B A7+=WaA7+D?7<DNT7ACB6+

iA7+

T

•5I+DZ 5R7>:T]^;=L 587>:,<=LC:

r′A7+

TV

φ(m, q, i, r′)AC?G5 ? =;k:T<>?>:T7^B8Y 79D: 7S;k:@?^B8Y 79D:+DBZ=:@?^79H587R]_5@S : ?\:TLC:@NT7>:@Z hS

iF)9D:F+

mAC?

79D:IN =<<>:F+h7,]GBZ=:VqAC?79D:IN@B6+h7>: 3 7 7S;k:V5I+DZ ri(i)

AC?479D:EN =<<>:F+.7 7>:T]^;=L 587>:I<=LC:V25I+DZk:@N@BJ]G:N@B6+.7>: 3 7k+DB.Z=:@?B8Y5 HBKF Y <>BJ] i

ZbA`<>:@NT7L`Sa7>Br′

[YφAC?5

Φ Y >+DNT7ACB6+jV=79D:F+ 79D:fN@B6+D?7<\58A7+h7

q ∈ C(m)(r)⇒ φ(m, q, i, r′) ⊆ F (m)(q)(i)(r′)

F)9D:T<>:r = ri(i)

V F)A`L`L hSO79D:Z=:1+=A`7ACB6+-?\587AC? Y SON@B6+D?>:T<587AA`7S B8Y :@ZbW3: HB F?^LCB.NK58L`L`S3V#5I+DZ F :NK5I+ <>:TL`SUB6+O79D: 3 :@ZO;BJA7+h7^58L`W3BJ<A`79=] V6F)A`79 ?=A`7\5=LC:aA7+=A`7A 58LÀ 587ACB6+jV 7>B ?\587AC? Y S 79D:_7F B BJ79D:T<N@B6+D?>:T<587AA`7S NT<A`7>:T<A 5

5 BJ7ACN@:79H587 Φ Y >+DNT7ACB6+D? 9H53:79D:4;=<>BJ;:T<7S_79H587#79D:A7+.7>:T<>?>:@NT7ACB6+ ⋂

j φj

AC?&5Φ Y >+DNT7ACB6+ A Y$58L`L B8Y

φj

58<>: [+79D: Y BJL`LCBKF)A7+=WDVDF#:,F)A`L`Lj;=<>:@?>:F+.7?A 3 Φ

Y>+DNT7ACB6+D?

• Q % R (D! " 9'FS" " Y>+DNT7ACB6+ F#5J? Z=:@?A`W+D:@ZgY BJ< 79D:f: 3 7>:F+DZ=:@Zc]GB.Z=:I?Sb?7>:T]iB8Y &.Q V5I+DZ AC?5w+D:TF Z=:@?>A`W+ • + !%;=<ACBJ<A`7SUN@BJ]^;H587A=A`LÀ`7SY >+DNT7ACB6+XAC?E58LC?\Bg5+D:TF Z=:@?>A`W+jV5JN@N@BJ]^]GB.ZD587A7+=W Y BJ< 79D:R7>:T]^;=L 587>: A7+3B A7+=WgA7+D?7<DNT7ACB6+D?M79H587 <>:@?>7<ACNT7,79D:E<\5I+=W3:^B8Y 79D:TA`<7\58<W3:T747>:T]^;=L 587>:E<=LC:@? Q&9D: X"" # o$ n " [%'& A7+D?7<DNT7ACB6+ F#5J?,58;=;H58<>:F+h7L`ScA`W+DBJ<>:@ZgA7+ ;=<>:.ACBD?F BJ<B6+ ?7\587ACN &.Q J58LÀCZD587ACB6+

• /-R D%- !ST%//gY >+DNT7ACB6+ ,BJ<A`WA7+H58L`L`S 79D:cACZ=:K5XB8Y V5I+DZ?9H58<;:F+D:@Z%5I+DZ%: 3 7>:F+DZ=:@Z-Y BJ< &Q .S D? • +5:9/- "sR >%'Y!SZ,! "#^Y >+DNT7ACB6+jVF)9=ACN>9RAC? 5<>:=<\5I+DZbA7+=WMB8YD;=<>: ACBD?6F BJ<EB6+R?>7\587ACN &.Q5I+H58L`S?>AC? VD: 3 7>:F+DZ=:@ZY BJ< &Q &587>:T<4B6+jV=A`7AC?: 3 7>:F+DZ=:@Z 5I+DZ<>:1+D:@ZY =<79D:T<KV 5I+DZ A`7>?A7+h7>:T</+H58LC? 58<>:,;=77>Bw+D:TF D?>:@?

• + *R %'/' .vSTNZ,M%Y>+DNT7ACB6+79H587RF&5J?G58LC?>BcZ=:T<A3:@Z Y <>BJ] ;=<>: .ACBD?RF#BJ< V 5I+DZ: 3 7>:F+DZ=:@ZY BJ<?A7+=WLC: 7S.;:M?>N\9D:T]_5RL 5I+=WH58W3:@? • +D:TF$/- 'ZX*R "#HVkF)9=ACN>9AC?,5_;=<A`]_58<Sg<>:@?=L`7,B8Y79=AC? F BJ<V H5J?>:@Z B6+ N@BJ]^;kB?A7+=W79D:M5kB3:,Y >+DNT7ACB6+D?)A7+c5+D:TF F&5@S3Vk5I+DZ D?A7+=Wz+D:TF ? 58L`W3BJ<A`79=]G?

Y 7>:T<5RZ=:T7\58A`LC:@ZgZ=:@?>NT<A`;=7ACB6+gB8Y679D:@?>: Y>+DNT7ACB6+D? VbF :f58<>:M5=LC:,7>B^Z=:@?\NT<Ak: 79D:,?;:@NTA 58LjN>9H58<\5JNT7>:T< AC?7ACN@? B8Y:K5JN\9 B8Y 79D:T] V5I+DZ Z=:@?>NT<A:f79D:R: 3 ;k:T<A`]G:F+.7>?,5I+DZc<>:@? =L`7>? B8YN@BJ]^;B?A7+=W 79D:T] A7+h7>B5I+5I+H58L`Sb?AC?58L`W3BJ<A`79=]

' Φ & '

&.Q 7>:T]^;=L 587>:E]GB.Z=:@? 58L`LCBKF ?7S.LC:@?9D:@:T7,5=79DBJ<>?47>B_;=<>BZ DN@:fZbA_^2:T<>:F+h7 7<\5I+D? Y BJ<]_587ACB6+c<>:@? =L`7>?Y BJ<R]=L`7A`;=LC: 7<\5I+D? Y BJ<]G?^B8Y479D: ?\58]G: A7+=;=7w+DB.Z=: .SX<>:@?7<ACNT7A7+=W HB FMV?>B5 HBKF 5I+H58L`Sb?AC?^NK5I+:F+D:D7 Y <>BJ] A7+DN@BJ<;BJ<\587A7+=W ]GBZ=:@? 5JN>9U7>:T]^;=L 587>:^<=LC:I9H5J?f5 ?>:T7,B8Y#]GB.Z=:@?M5J?>?\B.NTA 587>:@Z Y <>BJ]79D: R5877<A=7>: B8Y79D: 7>:T]^;=L 587>: <=LC: B8YA7+DN@BJ]Â7+=WHBKF 79H587#79D:4<=LC: 58;=;=LÀC:@?&7>B=VbBJ< A7+D?>7>:K5JZ2V79D:M?>;k:@NTA 58L27>B 3:F+ 0 VbF)9=ACN\9 ]G:K5I+D?79H587)79D: <=LC:f58;=;=LÀC:@?7>BHBKF B8Y5I+hS ]GB.Z=: ]GBZ=: AC?5]G:T]k:T< B8Y

M %9D:F+G57>:T]^;=L 587>:&<=LC:#AC?$A7+3B 3:@Z2V.5]GBZ=: AC?$;H5J?>?>:@Z^58LCB6+=W F)A`79I79D: <>:@?>7PB8YH79D:&ZbSN+H58]ÂCN&N@B6+h7>: 3 7KV:@N@BJ]Â7+=WG79D: R-ZX %' f Q % Y BJ<&79D: 7>:T]^;=L 587>: A7+3BNK587ACB6+ 5JN\9 7>:T]^;=L 587>: A7+3B A7+=W_A7+D?>7<DNT7ACB6+A7+79D: 7>:T]^;=L 587>:<=LC: A7+ 7=</+ ?>:TLC:@NT7>?G5]+D:TF ]GBZ=:V 5I+DZ2VA Y479D: A7+D?7<DNT7ACB6+;H5J?>?>:@?^N@B6+.7<>BJL7>BBJ79D:T<)7>:T]^;=L 587>:,<=LC:@? V.A`7Z=B:@?&?>BRB6+=L`S_7>BI79DB?>: <=LC:@?&79H58758<>:,58;=;=LÀCNK5=LC:,7>BI79D:W+D:TF ]GB.Z=: HBJ< "" #% " % & V879D:]GBZ=:]_5KS k:WA3:F+fA7+E79D:?7S.LC:@?9D:@:T7KVBJ<P5?;:@NTA 58Lh7>B 3:F+ ?MG1BB ; C ]_5@S: D?>:@Zg7>BG;H5J?>?79D:EN =<<>:F+.74]GBZ=: Q&9D:EBJ79D:T<47>:T]^;=L 587>: A7+3B .A7+=W A7+D?7<DNT7ACB6+D?,58<>:M9H58<>Z F)A`<>:@Z7>B ?MG1BYB ; C =< D<>?7 Φ

Y>+DNT7ACB6+F)A`L`Lj]GBZ=:TLj79=AC? &:T7

moder : R→ 2M ∪ #any

<>:T7=</+c79D: ]GB.Z=:,LÀC?>7&Y BJ<:K5JN\9g7>:T]^;=L 587>:,<=LC:,A7+g79D:,?A`]^;=LÀH:@Zg?7S.LC:@?>9D:@:T7SVH5I+DZ LC:T7

modei : I →M∪ #current

<>:T7=</+c79D: ]GB.Z=:MB8Y :K5JN>9g7>:T]^;=L 587>: A7+3B A7+=W A7+D?>7<DNT7ACB6+ A7+S

modei(i) =

mA Y

i = "" #% " % & O O LMLNL#

#currentBJ79D:T<F)AC?\:

Q&9D: Y BJL`LCBKF)A7+=W_Y>+DNT7ACB6+D?<>: H:@NT779D:M?>:T]_5I+.7ACN@?B8Y67>:T]^;=L 587>:M]GBZ=:@?

app(M)<>:T7=</+D? 5R?>:T7B8Y6]GB.Z=:@?)7>BGF)9=ACN>9 5I7>:T]^;=L 587>:f<=LC: F)A`79 ]GBZ=:,LÀC?7

MAC?458;=;=LÀCNK5=LC:

app : 2M ∪ #all → 2M

app(M) =

MA Y

M = #all M

BJ79D:T<F)AC?>:

modeflow (m, c)<>:T7=</+D?&79D: ]GB.Z=: B8Y79D:HB F B=7&B8YP?>BJ]G: 7>:T]^;=L 587>: A7+3B A7+=W_A7+D?7<DNT7ACB6+F)A`79

]GBZ=:mVWA3:F+-5 N =<<>:F+h7_]GB.Z=:

c [7^?A`]^;=L`S ?7\587>:@?R79H587 ?NGIBB ; C ;H5J?>?>:@?^B6+79D: N =<<>:F+h7]GBZ=:VH5I+DZg5I+.S BJ79D:T< G5877<A=7>:M?>;k:@NTAH:@? 5+D:TF ]GB.Z=:

modeflow : (M∪ #current)×M → M

modeflow (m, c) =

cA Y

m = #current mBJ79D:T<F)AC?>:

Q&9D:,]GBZ=::F+bY BJ<>NTA7+=WΦ Y >+DNT7ACB6++DBKF :@N@BJ]G:@?

1

d:(2,2) e:(3,3)

builtin:(0,0) a:(5,1)

import href=b

import href=c

import import href=d href=e

c:(4,2)b:(1,1)

root:(6,0)

4 \<1V56"y"6=E,oC 'j)f&5h^)p3g"%$3g'=F" =le3 hr5E61)v"6"6k)E3=o<)Si5h

l : (P (l), Pm(l)),C 'pf"gcd<03w)E3w) E=^e3w5<$.*=5<*==;")2 ,

ωm(m, i, r) =

liveA Y

modeflow (mode i(i),m) ∈ app(moder(r))dead

BJ79D:T<F)AC?>:

φm(m, q, i, r′) =

Σd

A Yωm(m, i, r′) = live

∅BJ79D:T<F)AC?\:

[7 <=LC:@?B=7 79H5875I+hS HBKF:F+DZ=? =;_587 7>:T]^;=L 587>:)<=LC:@? 79H58758<>:<+DBJ758;=;=L`ACNK5=LC:7>B 79D:&]GB.Z=:)B8Y79D:HB F Q&9=AC?F)A`L`Lr+DBJ7 k: 79D:ML 5J?7)7A`]G:MF#:,F)A`L`L?>:@: ]GBZ=:@?KV=9DB F : 3:T< &587>:T<B6+jV=F)9D:F+ A7+.7<>B.Z DNTA7+=WN@B6+.7>: 3 7 ?>:F+D?>A`7A3: Φ

Y >+DNT7ACB6+D?KV=F :MF)A`L`Lj]_5 3:M:@ZbW3: HB F? 58<A 5I+h7A7+ ]GBZ=:@? 3 :@Z ;BJA7+h7_58L`W3BJ<A`79=] B3:T<^79=AC? Φ

Y>+DNT7ACB6+F)A`L`L)9H53: ? D?>:T7>?RB8YMF)A`79-5I+DZ 79D:? D?\:T7

<>:TL 587ACB6+5J?A`7>?L 5877ACN@:V NK5D?>A7+=W 5^]GBZ=:M;=<>BJ;H58Wh587ACB6+ 7>Bk: D: D:@ZY BJ<4:K5JN\9g7A`]G:R5R]GBZ=:HBKF?7>B_5I7>:T]^;=L 587>:f<=LC: Y BJ<)79D:D<>?7)7A`]G:

!#"Φ &'

Q&9=AC?Φ Y>+DNT7ACB6+ 79H587]GB.Z=:TLC?)79D:f?>:T]_5I+h7ACN@?4B8YP79D: "" # $ "%$ %'& '& %( % % *) A7+D?>7<DNT7ACB6+D?

7679D:#?7SLC:@?9D:@:T7PLCB35JZE7A`]G:VJ79D:,+.-0/1%233426575@Vh5J?6Z=:@?>NT<Ak:@ZEA7+ 1 VJ?>:@NT7ACB6+ VJAC?PN@B6+D?>7<DNT7>:@Z Q&9D:F+jVk79D:f?>7SLC:@?9D:@:T74LC: 3:TLC? 58<>:+ =] :T<>:@Z A7+g79D:EBJ<>Z=:T<4A7+cF)9=ACN>9U5^;B?7 BJ<>Z=:T< 7<\5!3:T<>?\58L6B8Y79D:7<>:@:,F)A`L`L .AC?A`7)79D:T]

P : L → N

LCBKF#:@?7;=<>:@N@:@Z=:F+DN@:EB8YPA`]^;BJ<7>:@ZLC: 3:TLC?)Y BJ<:K5JN>9gLC: 3:TLjAC?5J?>?A`W+D:@Z

Pm : L → N

Pm(l) = minP (l) ∪ Pm(l′)|l′AC?)A`]^;BJ<7>:@Z Y <>BJ]

l

:1+D:Pr : R→ Q

5J?79D:);=<ACBJ<A`7SGB8Y2:K5JN>9a7>:T]^;=L 587>:<=LC:V5I+DZ^79D:275'S98#34+50:34275;N#3 _B8Y27>:T]^;=L 587>:<=LC:@? 5J?)79D:MN@BJ]^;B?A`7ACB6+gB8Y6A`]^;kBJ<7;=<>:@N@:@Z=:F+DN@:I5I+DZ ;=<ACBJ<A`7S

a

a a

a

#default #default

<apply−templates mode=’#default’ .../>

<template mode=’#default’ ...>

<apply−templates mode=’a’ .../>

<template mode=’#all’ ...>

<apply−templates mode=’#current’ .../>

<apply−templates mode=’#default’ .../>

<template mode=’a b’ ...>

#default

#default

\<7 0)2i52h)S5;;5vu +)2'J,

r1 ≥ r2 ⇔ P (r1) > P (r2) | (P (r1) = P (r2) ∧ Pr(r1) ≥ Pr(r2))

5 BKFMVA Y lr(r) AC?79D:?>7SLC:@?9D:@:T7LC: 3:TLk79H587 N@B6+.7\58A7+D? 79D:7>:T]^;=L 587>: rV5I+DZ

lri(i) = lr(ri(i))V.F#:4NK5I+

;=A7+ Z=BKF<+ 79D:GL 58<W3:@?7I?>:T7fB8Y)7>:T]^;=L 587>:_<=LC:@?f79H587f]_5KS<>:@N@:TA3: HB F Y <>BJ] 5 7>:T]^;=L 587>: A7+3B .A7+=WA7+D?7<DNT7ACB6+ 5J?&Y 58<5J? "" # $ "#$ %& '& #( % % ') AC?N@B6+DN@:T</+D:@Z

v(i) =

RA Y

i = "" # % " % &#

r ∈ R : Pm(lri(i)) ≤P (lr(r)) < Pm(lri(i))

A Yi =

"" # $ "%$ %'&r ∈ R : lri(i) ≥ r ∧ r 6≥ lri(i)

A Yi =

& %( % % *) Q&9D:1+H58L

Φ Y>+DNT7ACB6+:@N@BJ]G:@?

ωa(m,a, r) =

liveA Y

r ∈ v(a)dead

BJ79D:T<F)AC?>:

φi(m, q, a, r′) =

Σd

A Yωa(a,m, r′) = live

∅BJ79D:T<F)AC?>:

3 :@ZM;kBJA7+.7$58L`W3BJ<A`79=] B3:T<j79=AC? Φ Y >+DNT7ACB6+MF)A`L`L39H5!3: 5J?2A`7>?2L 5877ACN@: 7 D?7(done,notdone, done w

notdone)V=LÀ`]Â`7A7+=WG79D:j+ =] :T<4B8Y .AC?>A`7>?)7>B^:K5JN>9 7>:T]^;=L 587>:f7>B

%"!' %' '

Q&9D:IY BJL`LCBKF)A7+=WY >+DNT7ACB6+D?M58L`LZ=:T7>:T<]Â7+D: : 595 3 - 8#3 71#-0/8#34+ 9 + +.3" k:T7F :@:F+U7>:T]^;=L 587>: A7+3B .A7+=WA7+D?7<DNT7ACB6+D? 5I+DZ 7>:T]^;=L 587>:f<=LC:@? .S : 3 58]Â7+=A7+=WaN@BJ]^;H587A=A`LÀ`7S ;=<>BJ;:T<7AC:@?B8Y & % 5I+DZ % *) P5879 : 3 ;=<>:@?\?ACB6+D?

U:,F)A`L`L D?>: 79D:j+DBJ7\587ACB6+

up7−→

xv

]G:K5I+=A7+=W A3:F+ 5 $'& 7<>:@:4Y <\58W]G:F+.7xV=5I+DZ 5+DB.Z=:

uA7+ 79D: 7<>:@:V=: 58LH587ACB6+ B8Y$79D: P5879

;H5879: 3 ;=<>:@?>?ACB6+ pF)A`79

u5J?f79D:aA7+=A`7A 58L)N@B6+h7>: 3 7w+DB.Z=:a<>:@?=L`7>?IA7+ 5c?>: D:F+DN@:_79H587^N@B6+.7\58A7+D?G5+DBZ=:

v Q&9=AC?+DBJ7\587ACB6+ F)A`L`Lj58L`LCBKF%Y BJ<&?A`]^;=LC:T<&Z=:@?>NT<A`;=7ACB6+B8Y79D:47>:@?7>?79H587)Z=:T7>:T<]Â7+D: A Y:@ZbW3: HBKF?&: 3 AC?7Y <>BJ] ?>BJ]G: 7>:T]^;=L 587>: A7+3B .A7+=W A7+D?7<DNT7ACB6+ 7>B_?>BJ]G: 7>:T]^;=L 587>:M<=LC: +D:@N@:@?\?\58<S_<>: =A`<>:T]G:F+h7&Y BJ<5I+ :@ZbW3:HB FY <>BJ]/7>:T]^;=L 587>: A7+3B A7+=WGA7+D?7<DNT7ACB6+ i

7>B^5f7>:T]^;=L 587>:<=LC:

r′

5 5 : : 8%2' 265+.265 - 5 ;3 1#2 : 5 5 3 - 8 3 71%-,/ 8#34+ 9+ +43"Q&9D:T<>:E: 3 AC?7>?5I+ $'&7<>:@: Y <\58W]G:F+h7 x

N@B6+h7\58A7+=A7+=Wa79D:j+DB.Z=:@?n1Vn25I+DZ

n3V=?\B

n1select(i)7−→

xn25I+DZ

n3match(r′)7−→

xn2

+ 5D?7<\5JNT7ACB6+ B8Y79=AC?I7>B >+DZ=:@NTL 58<>:@Z-+DB.Z=: 7S;:@?EAC?I79D: H5J?AC?RB8Y79D: ?>N\9D:T]_58LC:@?>? Φ Y>+DNT7ACB6+

A7+ 79D:]+D: 3 7 ?>:@NT7ACB6+ +DBJ79D:T<5D?>7<\5JNT7ACB6+%7>B Z=:@NTL 58<>:@Z+DBZ=:g7S.;:@? AC? D?>:@Z%A7+%79D: 5D?>7<\5JNT7: 58LH587ACB6+

Φ Y >+DNT7ACB6+ A7+ :@NT7ACB6+ 5I+DZ2V.F)A`79_Y =<79D:T<<>:1+D:T]G:F+.7>?KVbA7+_79D: 5I+DN@:@?7>BJ< L 5I+=WH58W3:

Φ Y >+DNT7ACB6+ A7+ :@NT7ACB6+

' ! Φ &'

Q&9D:W+D: 3 7 Φ Y >+DNT7ACB6+A7+ B=< HB F 5I+H58L`S?>AC?&AC?#NK58;H5=LC:,B8Y 1+DZbA7+=W =;=;k:T< B>+DZ=?Y BJ<&79D: J58LD:@?&B8Y

79D:&Y >+DNT7ACB6+Ch79D:)N@B6+h7>: 3 7 ?>:T7>? Y BJ< 7>:T]^;=L 587>:<=LC:@?KVh5J? F#:TL`Lk5J?6Y BJ< 79D: 58LD:@?B8Yk79D:)Y>+DNT7ACB6+ F Q&9D: 58L`W3BJ<A`79=] AC?E5 ?9H58<;k:F+D:@Z 3:T<>?ACB6+XB8Y)79D: 8 Q$:T]^;=L 587>: 5I+DZ ?\?>B.NTA 587ACB6+ <\58;=9 W<\58;=9g58L`W3BJ<A`79=] ;=<>:@?\:F+h7>:@Z hS Q&9D: 7>:T<] <\5@F <>: Y :T<>?&7>BI79D:M58L`W3BJ<A`79=] ; 1 3 N@B6+D?ACZ=:T<A7+=W

d 79=AC? AC?,Z=: Y :T<<>:@Z 7>B 5_L 587>:T<KV +;%/3 : 5- 8 8 8%275Φ Y >+DNT7ACB6+ Q&9D:E;=<;B?>:^B8Y Z=BJA7+=W79=AC? AC?7F B8Y BJLCZ $A`<>?>7KVhA`7F)A`L`L 1+DZ_5j+ =] :T< B8Y58;=;H58<>:F+h7L`S3:T<SI;=L 5D?>A=LC: HB F?79H58779D:4?>N>9D:T]_5 5KF#58<>:

5I+H58L`Sb?AC?)F)A`L`L?>9DBKF +DBJ77>B^: 3 AC?75 Y 7>:T<58L`L F)9H587 B6+=W &58A`LC:TS NK58L`L A7+J58LÀCZ7>:T]^;=L 587>:fNK58L`LÀ7+=W<>:TL 587ACB6+D?9=A`;D? \VP5I+DZ F#:^7>:T<] 5D?>:F+.7HBKF? #B6+h7<>BJL 5I+DZUN@B6+.7>: 3 7f7S;k:HB F?M79H587MZ=:T;:F+DZUB6+?7<DNT7=<\58L Y :K587=<>:@? B8Y279D:A7+=;=7 7<>:@:F)9=ACN\9 58<>:J+DBJ7;:T<]Â`77>:@Z.S^79D:A7+=;=7 ?\N>9D:T]_5bV=5I+DZG]Â`W9.7?=<;=<AC?\:f5 D?>:T< .Sa79D:TA`<45D?\:F+DN@: Q&9D:#?>:@N@B6+DZM<>:K5J?\B6+MY BJ<jF#5I+.7A7+=W 7>B;k:T< Y BJ<] 79=AC?65I+H58L`Sb?AC? : 3:F+fA Y1+DBJ7A7+.7>:T<>:@?7>:@ZEA7+I5D?>:F+.7 HBKF? AC?j79H587$A`7AC?65

Φ Y >+DNT7ACB6+f79H5876NK5I+ :A`]^;=LC:T]G:F+h7>:@Z 3:T<SM: _NTAC:F+.7L`S3V3?>B)79H587PF)9D:F+EZ=:T7>:T<]Â7+=A7+=W

79D:g5D?\:F+DN@: B8Y,5I+.S HB Fi587a58L`L&Y BJ<G?>BJ]G: N@BJ]=A7+H587ACB6+B8Y 7>:T]^;=L 587>: A7+3B A7+=WOA7+D?7<DNT7ACB6+ 5I+DZ7>:T]^;=L 587>:a<=LC:VP79=AC?,Y 5JNT7fNK5I+ :G?7>BJ<>:@Z2V65I+DZX?\53: D?MY <>BJ] N@BJ]Â7+=W 7>B79D:a?\58]G:GN@B6+DNTLD?ACB6+ A7+5 L 587>:T<f?>7\58W3:^B8Y 79D:G5I+H58L`Sb?AC?KV2F)9D:F+D?>A7+=Wg5_9D:K5.AC:T<

Φ Y>+DNT7ACB6+ [+ ;H58<7ACN =L 58<KV79D:R<\5KF Q

$)( "!$#%&'()# ) +*,#%(-$'+*,!#%.()/,0 #*! $"1 *2!3'24.$56&478*,#%98:<;,=#%>7=%'!#74?=%76"' 1@#A? !,#/*,=% 1 #%24B2C:

Φ Y >+DNT7ACB6+ AC? 71#;3 5#3 +.;: 5 ;: +434+%5 A`7RZ=B.:@?+DBJ7RZ=:T;k:F+DZ B6+OA`7>?IN@B6+h7>: 3 7R7S;k:

q ;H58<\58]G:T7>:T<KVF)9=ACN\9g9D:TL`;D? 3:@:T;A`7>? 5J?>?>BNTA 587>:@Z L 5877ACN@:,LCBKF Q&9=AC?

Φ Y >+DNT7ACB6+ D?>:@?,5 ?>:TLC:@NT7 ]_587>N>9XN@BJ]^;H587A=A`LÀ`7Sc7>:@?>7 Q&9D:R7>:@?7>?,58;=;=<>B 3 A`]_587>:^7>BKF&58<>Z=?,7>BBL 58<W3: N@B6+h7>: 3 7 HBKF? 5 G<]_587A3: <>:@?=L`7aY BJ< ?>BJ]G: N@:T<7\58A7+ N@B6+h7>: 3 7 7S;k:V]GB.Z=:V7>:T]^;=L 587>:A7+3B .A7+=WaA7+D?7<DNT7ACB6+ 5I+DZ 7\58<W3:T747>:T]^;=L 587>:,<=LC:,AC?<+DBJ7N@B6+DNTLD?>A3: +D:TWh587A3:f<>:@?=L`7)AC?

Q&9D:_5I+H58L`Sb?AC?,]_5 3:@?f+DB D?>:^B8Y&A7+=;=7f?>N>9D:T]_5 s+DB F)LC:@ZbW3:V =7,A`7MAC?,?>7A`L`L 5JN@N =<\587>:GZ=BKF<+X7>B79D:LC: 3:TLB8Y :TLC:T]G:F+h7 5I+DZg5877<A=7>:f+H58]G:@?

H$

QAC?E79D: A7+1+=A`7>: ?>:T7IB8Y 58LÀCZ@+H58]G:@?>;H5JN@: H58LÀH:@Z %$ &%:TLC:T]G:F+h7RBJ<I5877<A=7>:+H58]G:@? Q&9D:; 5 8%275 + 78#2g:TLC:T]G:F+h7 7S;k:

e∗<>:T;=<>:@?>:F+.7>? 5I+.S+ =] :T< B8Y:TLC:T]G:F+.7>?KVH:K5JN\9gF)A`79gF)A`79 5I+hS

+H58]G:Vk5I+DZ LÀ 3:TF)AC?>:Va∗<>:T;=<>:@?>:F+.7>? 5I+.SL+ =]k:T< B8Y 5877<A=7>:@? V :K5JN\9gF)A`79c5I+.SL+H58]G: Q&9D:@?>:I58<>:+D:@:@Z=:@Z 5J?1+=A`7>:G<>:T;=<>:@?\:F+h7\587ACB6+D?^B8Y >+ s+DB F<+ :TLC:T]G:F+.7>?I5I+DZ 5877<A=7>:@?fA7+ 5 L 5877ACN@:a5I+DZA7+ 5I+

A`]^;=LC:T]G:F+.7\587ACB6+ Σu

AC? 79D:I?>:T74B8Y&58L`L ; 5 8%275 ; 1 5 3 /5 : V F)9=ACN>9X58<>:IZbAC?7A7+=W=AC?9H5=LC:IA7+ 79D: P5879 ZD587\5R]GBZ=:TL +DBG?>N>9D:T]_5GAC? D?>:@Z2VD?>BR79D:T<>:E58<>:j+DB^Z=:@NTL 58<\587ACB6+D?

Eu = e∗ ∪ eq|q ∈ QAu = a∗ ∪ aq|q ∈ QΣu = Eu ∪Au ∪ root,pcdata, comment,pi

D?7<\5JNT7A7+=W 7−→ 7>B >+DZ=:@NTL 58<>:@Z+DBZ=: 7S;k:@?KV

Up−→ V

]G:K5I+D? A3:F+ 5R?\:T7B8Y >+DZ=:@NTL 58<>:@Z]+DBZ=:,7S;k:@?UV=79D:T<>:E: 3 AC?7>?45I+ $'&7<>:@:MY <\58W]G:F+.7 x

F)A`795w+DBZ=:

nB8Y6?\BJ]G: >+DZ=:@NTL 58<>:@Z 7S;:

∈ UVn

p7−→

xv5I+DZ

v ∈ V

?A7+=WI79D:45D?7<\5JNT7ACB6+jVD5I+DZ 58L`LCBKF)A7+=W^79D:7S.;:@?#B8Yn15I+DZ

n3B8Y 7>Bk: 5I+hS >+DZ=:@NTL 58<>:@Z 7S.;: 79 D?+DBJ7#<>:@?7<ACNT7A7+=W^5I+hS79=A7+=W V=5M?>:TLC:@NT7 ]_587>N\9

i, r′ N@BJ]^;H587A=A`LÀ`7S N@B6+DZbA`7ACB6+_Y BJ<#5I+ :@ZbW3: HB FB8Y67S;k:q′:@N@BJ]G:@?

Σuselect(i)−→ q′

5I+DZΣu

match(r′)−→ q′

#4

U : XPathpath → 2Σu

U stepa::t , Uaxis

a , U testet , U testa

t : 2Σu → 2Σu

(k$*/k0#"1 23

Q&9D:@?>:GY>+DNT7ACB6+D?I?A`] =L 587>:a: 58LH587ACB6+OB8Y45I+ 65879O;H5879 : 3 ;=<>:@?>?>ACB6+OB6+O5g?>:T7fB8Y<+DB.Z=:@? EQ&9D:TSA`7>:T<\587>: ?7>:T; .SU?7>:T;jV$Y <>BJ] 79D:_LC: Y 7M7>Bc79D:G<A`W9.7KV5I+DZY BJ<E:K5JN>9 ?7>:T;jVP79D:TSU?A`] =L 587>: 5gN@B6+h7>: 3 7HB F B3:T<479D:f5 3 AC??7>:T;jVH5I+DZc5 DL`7>:T<A7+=WaB8Y'+DB.Z=:@? hS 79D:j+DBZ=:,7>:@?7B8Y 79D:M?7>:T; DBJ< $ & % #$ & %: 3 ;=<>:@?>?ACB6+D?KVk5RW3BB.Zg58;=;=<>B 3 A`]_587ACB6+ AC?;kB?>?>A=LC:V k:@NK5D?\:f+DBZ=:@?A7+c5_N@B6+DNT<>:T7>:f: 58LH587ACB6+cA7+.7>:T< ?>:@NT7ACB6+aF)A`L`LHN@:T<7\58A7+=L`S^9H5!3: 5 7S;:)A7+G79D:)A7+.7>:T<>?>:@NT7>:@Z_7S.;:?>:T7 Q&9D:T<>:)AC?U+DB,W3BB.Z_58;=;=<>B 3 A`]_587ACB6+Y BJ< #( " % VD79DB=W9&[7]_5@S ?7A`L`LP?>:TLC:@NT7J+DBZ=:@?4B8Y5G7S;k:,A7+c79D:M<>:@?=L`7 B8Y 5D?7<\5JNT7L`S : 58LH587A7+=W79D:,<A`W9.7 9H5I+DZc?>ACZ=:

U stepa::t (Ω) =

U testat (Uaxis

attribute(Ω))A Y

a = attribute

U testet (Uaxis

a (Ω))BJ79D:T<F)AC?>:

U (ε) = root

U (a :: t) = U stepa::t (e∗, a∗, root,pcdata, comment,pi)

U (P/a :: t) = U stepa::t (U(P ))

U (p1 intersect p2) = U(p1) ∩ U(p2)U (p1 except p2) = U(p1)

Q&9D:GY>+DNT7ACB6+U(p)

N@BJ]^;=7>:@?R5I+=;=;k:T<kB>+DZY BJ<X ⊆ Σu|Σu

p7−→ X

V658L`79DB=W9 58;=;=<>B 3 A ]_587>:TL`S A`7,?7\58<7>? Y <>BJ] 5 1+=A`7>:R<>:T;=<>:@?>:F+h7\587ACB6+ B8YΣu

Vj5I+DZ <>:@N =<>?\:@?MB6+DN@:IY BJ<,:K5JN\9X?7>:T; Q&9D: ε]_58;=;=A7+=Wa]_58;D?LC:K5JZbA7+=W 6 ?)7>B^79D:j+DBZ=:,7S;:

$* 0

Uaxischild (Ω) =

e∗, comment,piA Y

root ∈ Ω5DZ

Ω ∩ Eu = ∅e∗,pcdata, comment,pi

A YΩ ∩ Eu 6= ∅

∅BJ79D:T<F)AC?>:

Uaxisparent (Ω) =

e∗A Y

Ω ∩ (Eu ∪ comment,pi) = ∅∧Ω ∩ (Au ∪ text) 6= ∅

e∗, rootA Y

Ω ∩ (Eu ∪ comment,pi) 6= ∅∅

BJ79D:T<F)AC?\:

Uaxisancestor (Ω) =

e∗, rootA Y

Ω 6= root ∧ Ω 6= ∅∅

BJ79D:T<F)AC?>:

Uaxisdescendant (Ω) = Uaxis

child(Ω)

Uaxispreceding(Ω) =

e∗, root,pcdata, comment,piA Y

Ω ∩ (Eu ∪ pcdata, comment,pi) 6= ∅∅

BJ79D:T<F)AC?\:

Uaxisfollowing(Ω) =

e∗,pcdata, comment,piA Y

Ω ∩ (Eu ∪ root,pcdata, comment,pi) 6= ∅∅

BJ79D:T<F)AC?>:

Uaxispreceding−sibling(Ω) = Uaxis

following−sibling(Ω) =

e∗,pcdata, comment,piA Y

Ω ∩ (Eu ∪ pcdata, comment,pi) 6= ∅∅

BJ79D:T<F)AC?>:

Uaxisself (Ω) = Ω

Uaxisancestor−or−self (Ω) = Uaxis

ancestor(Ω) ∪ Uaxisself (Ω)

Uaxisdescendant−or−self (Ω) = Uaxis

descendant(Ω) ∪ Uaxisself (Ω)

Uaxisattribute (Ω) =

a∗A Y

Ω ∩ Eu 6= ∅∅

BJ79D:T<F)AC?>:

Uaxisxslv (Ω) = e∗

Q&9D:@?>:gY DNT7ACB D?a<\5879D:T<?7<\58A`W9.7 Y BJ<F&58<>ZbL`S%?>A`]=L 587>:5 3 AC? ?7>:T;D? Uaxischild

Uaxis

descendant

<>:T7=< D?: 3:T<S79=A =W 79H587 NK5 k: 5XN\9=A`LCZ2V)A YE5hS DBZ=: 7S.;:cA -79D: 58<W=]G: h7?>:T7aNK5%9H5!3: N>9=A`LCZb<>: Uaxis

parent

<>:T7=< D? 5hS :TLC:T]G: h7 Y BJ<^58<W=]G: h7_?\:T7>?IB8Y47>: 3 7^5DZ5877<A=7>:@?GB =L`S3V5DZ5JZ=Z=?R79D:<>BBJ7DB.Z=:R7S.;:IA Y 79D:T<>:_58<>:G58LC?\B :TLC:T]G: .7>?KVN@BJ]^]G: .7>?fBJ<,;=<>BN@:@?>?A =WA D?7<DNT7ACB D? 479D:T<F)AC?\:V79D:f58<W=]G: .74AC?:T]^;=7S BJ<A`7)AC?)79D:f?A =WLC:T7>B root

V=F)9=ACN\9g9H5!3: DB^;H58<>: h7>? Q&9D:,<>:@?7B8Y 79D:5 3 AC??7>:T;Y DNT7ACB D??9DB=LCZ D:@:@Z DBRY =<79D:T<: 3 ;=L 5H587ACB

D?7<\5JNT7 DBZ=:R7>:@?7>?MZbAC?>NK58<>ZU79DB?>:^7S;:@?,F)9DB?>:^A D?7\5DN@:@?fNK5DBJ7f;H5J?>? 79D: 65879 DB.Z=:G7>:@?7 Q&9D:T<>: Y BJ<>:V)79D: <>:@? =L`7a?>:T7GAC? 58L`F#5KS? ?]_58L`LC:T<a79H579D: 58<W=]G: h7 ?>:T7KV)BJ<G]_5JZ=:c]GBJ<>:g?;:@NTAHN79=<>B=W9c79D:M? D?7A`7=7ACB gB8Y5 DZ=:@NTL 58<>:@Z F)A`LCZ=NK58<>Z Y BJ<5RN@B DNT<>:T7>:f7S;k:

U testaq (Ω) =

aqA Y

a∗ ∈ Ωaq

A Yaq ∈ Ω

∅BJ79D:T<F)AC?>:

U testa∗ (Ω) = Ω ∩Au

U testeq (Ω) =

eqA Y

e∗ ∈ Ωeq

A Yeq ∈ Ω

∅BJ79D:T<F)AC?>:

U teste∗ (Ω) = Ω ∩ Eu

U testenode() (Ω) = U testa

node() (Ω) = Ω

U testetext() (Ω) = U testa

text() (Ω) = Ω ∩ pcdata

U testecomment() (Ω) = U testa

comment() (Ω) = Ω ∩ comment

U testepi(...) (Ω) = U testa

pi(...)(Ω) = Ω ∩ pi

U testaattribute(q) (Ω) = U testa

attribute(q,t) (Ω) = U testaq (Ω)

U testaattribute(∗) (Ω) = U testa

attribute(∗,t) (Ω) = U testa∗ (Ω)

U testeattribute(q) (Ω) = U teste

attribute(q,t) (Ω) = ∅

U testaelement(q) (Ω) = U testa

element(q,t) (Ω) = ∅

U testeelement(q) (Ω) = U teste

element(q,t) (Ω) = U testeq (Ω)

U testeelement(∗) (Ω) = U teste

element(∗,t) (Ω) = U teste∗ (Ω)

U testaschema−element(q) (Ω) = U teste

schema−attribute(q,.) (Ω) = ∅

U testaschema−attribute(q) (Ω) = U testa

q (Ω)

U testeschema−element(q) (Ω) = U teste

q (Ω)

U testadocument−node(.) (Ω) = ∅

U testedocument−node(.) (Ω) = Ω ∩ root

Q&9D: ZbA2:T<>: h7 H58]Â =W B8YM79D:testa

5DZteste

H58]G:c7>:@?>7>?a?>:T<3:@?a7>BXY BJ<F&58<>ZA bY BJ<]_587ACB 7>B:K5JN\9 H58]G:g7>:@?7^Y <>BJ] 79D:c5 3 AC?G?7>:T; ;=<>:@N@:@ZbA =W A`7KV#F)9D:T79D:T<_79D:g;=<A DNTA`;H58L DBZ=: A DZF#5J? 587 7<A=7>:GBJ<,:TLC:T]G: .7 Q&9=AC?MA D: DN@:@?,79D:^?>:T]_5h7ACN@?fB8Y H58]G:R7>:@?7>? %% $$ % hV & % .V& *) %% $ $ % M5DZ &*) & % 58<>: P5879 ?>;k:@NTAHN DBZ=:7>:@?7>? V.F)9=ACN\9 ]_5@S_: 3 58]Â D:f79D:M?>N>9D:T]_5 Z=:@NTL 58<>:@Zc7S;:@?B8Y6:TLC:T]G: .7>? 5DZc5877<A=7>:@?KV 5J?)F#:TL`LP5J?:TLC:T]G: .74? D?>7A`7=7ACB W<>B=;D? ?>:@: #:@NK5D?\:&79D:&7>:@?7>?Z=B DBJ7 D?>:&?>N\9D:T]_5 A bY BJ<]_587ACB jV.79D:T<>:&AC? DB,N>9DBJACN@: =7 7>BM58; 3 <>: Y;=<>B 3 A`]_587>:,7>BR79D: L 58<W3:T< & % 5DZ %% $ $ % A`WDBJ<>: 7S;k:@?5DZ 7 D?7&]_587>N>9cB H58]G:@?KV5DZ &*) & % (q) ]_587>N>9D:@?RB O5.SU:TLC:T]G: h7KV ?A DN@:_5.SU:TLC:T]G: h7IAC?,;BJ7>: h7A 58L`L`SU]G:T]k:T<B8YP5E? D?7A`7=7ACB W<>B=; 9D:K5JZ=:@Z hS

eq L`L?A`WH587=<>:@?#Y BJ< "$ && $ & $ & & % $ % $ & g58<>:<>:T;=<>:@?>: .7>:@Z 5J? 7 D?7 " $

9D:T<>: Q&9D:GZbA2:T<>: h7IB3:T<LCB35JZ=?fY BJ<,79D:GA`7>:T] 7>:@?7>? & *) & % .V &') %% $$ % 7S.;:@ZBJ< DBJ7KV =A`L`L 5=LC:GBJ<DBJ7 58<>:_58L`L 7<>:K587>:@ZX79D:^?\58]G:V$5DZU7<A.A 58L <>:T;:T7A`7ACB D?M9H53: k:@: OBJ]Â`77>:@Z 79D:M? 58]G:,W3B.:@?#Y BJ< & % & ,79H587]_5KS 7\5 3:E5g:TLC:T]G: h747>:@?75J?5I;H58<\58]G:T7>:T<

*Φ

ωu(m, i, r) =

liveA Y

U(select(i))∩U(match(r))dead

BJ79D:T<F)AC?>:

φl(m, q, i, r′) =

Σd

A Yωu(m, i, r′) = live

∅BJ79D:T<F)AC?>:

Q&9D:∩BJ;:T<\587>BJ<AC?5 DB D:T]^;=7S A .7>:T<>?>:@NT7ACB 7>:@?779H587N@B D?>ACZ=:T<>?

e∗5DZ

a∗?>:T]_5.7ACN@?

[7G]Â`W9h7 ?>:@:T] F&5J?7>: Y =L7>B<>:@Z DN@:c?>:TLC:@NT7ACB D?GY <>BJ]Σu

7>BU:T]^;=7A D:@?>? BJ< DBJ7KV#79=<>BKF)A =W5@F#5KS79D: 7S;:aA bY BJ<]_587ACB BKF#: 3:T<KVF)A`79DB=7^]_5 A =W D?\:aB8Y,5hSX?>N\9D:T]_5 DB F)LC:@ZbW3: 587G58L`L V5hS

A bY BJ<]_587ACB Wh58A D:@Z AC?R<>:K5JZbA`L`SXLCB?7 $cB?>7 & % : 3 ;=<>:@?>?ACB D?RN@B .7\58A -?7>:T;D?RB3:T<GBJ79D:T<G5 3 :@?79H5 & VF)9=ACN\9 NK5D?\:@?5 LCB?>?B8Y58L`]GB?7#58L`LDA bY BJ<]_587ACB a79H587 N@B=LCZ^9H53: :@: _?\53:@Z #:@?>ACZ=:@?KV5D?7\58A =A =WfY <>BJ] <>:@NTSbNTLÀ =W 58L`]GB?7F BJ<79=LC:@?>? A bY BJ<]_587ACB aLCBKF :T<>? 79D:&L 5877ACN@:&Y BJ< 79D: 3 :@ZR;kBJA .758L`W3BJ<A`79=] I79D:BJ79D:T<P9H5DZ2VJA`7]_5KSM?>:@:T] D:@N@:@?\?\58<A`L`SMN@BJ]^;=LC: 3 7>B: 58LH587>:#: 3:T<Sf?7>:T;EB8YH5R: 3 ;=<>:@?\?ACB jVWA3: 79H587)5hS_A bY BJ<]_587ACB 5kB=7&:TLC:T]G: h7>?)?\:TLC:@NT7>:@Z.S H58]G: :T7>N A 58L`L =7 79D:4L 5J?7&?7>:T;D?)58<>:LCB?7 5hSF#5KS BKF#: 3:T<KV 79D: Φ

Y DNT7ACB cAC? ?7A`L`L$?>LÀ`W9h7L`S]GBJ<>:E;=<>:@NTAC?>:M79=AC?4F#5KS F)9=A`LC:M<>:T]_58A =A =W?A`]^;=LC:EN@B DN@:T;=7H58L`L`S3Vk5DZOV=A 79D:fF)9DBJLC: 58LÀCZD587ACB g;=<>BN@:@?>?KVH5.S;k:T< Y BJ<]_5DN@:fN@B?74B8YP79=AC?4F)A`L`L9H58<>ZbL`S ]_5877>:T< [YPZ=:@?>A`<>:@Z2V U A 79D: φu

: 3 ;=<>:@?>?ACB N@B=LCZk: <>:T;=L 5JN@:@Z hS U ′

U ′(P/a :: t) = U(a :: t) Q&9D:,<>:@? =L`7>?A 79=AC?)<>:T;BJ<7F :T<>:fB=7\58A D:@Z F)A`79 79D:MBJ<A`WA H58L V 58L`L ?7>:T;D? 58<A 5h7B8Y

φu

DBJ<I79D: 3 :@ZO;kBJA .7R58L`W3BJ<A`79=] B3:T<E79=AC? Φ

Y DNT7ACB jV679D:_L 5877ACN@:aF)A`L`L :MVPF)A`79 79D:a? D?\:T7

<>:TL 587ACB 5J? BJ<>Z=:T<A =W Q&9=AC? F)A`L`L,NK5D?>: HBKF ;=<>BJ;H58Wh587ACB :K5JN>9 7A`]G:U5 D:TF ]GB.Z=: <>:K5JN\9D:@?g57>:T]^;=L 587>:f<=LC:

$ ' & Φ & '

& ! #"$%&(' $) *+,$Φ-'$) .$/ 0"$% 1! #2%)3(45 #,6"6687.%9*:',;;

& ,<= >) 3%%)>? 71#;3 5@#3,3 /5A BCD ,4,E! F)#'+( 5 #"67G$ IHJK;% ,"6L)#'+,$%IB,4M B,N) O 3 #"E)#'PE%) Q 3 NR7Q4ST45 #;& #A;

q HJ$B,9 )#'S ( ;& 3 U #( V #"5 #$) A"$% 1! #A%)3(45 #,6"66R7D%U)3;6<V 5 #%P'W;)3YX #Z [D5 !(5 #;4M %BC69*S 3 B,%BC6'-)3; U # * B*S 345 #;T)#'\] 3 $) ^)#'\D< ;& #" &QH_& #$! 5 #"67G$D #"6<)3;6,`'W;)3`"$)9 #" 1874M!) ,<V"$1R7Q4S!&! "a ,<5 #<%b*P #"6;%Bc6)Dd+)3;F); 5 8%275 ; 15 3 /5 :*G 9 3B/)#'U); B,%"a #;%B )QB, ; 8%- 5 :E 3J9 #;"6$; 5 )B,%+d 6Ee #A5 #AV* ,NB,%"a #;%BOBG; >"67* 8%275?BG$ ,<,$%B ;& 3 ,< 7−→ )!f 5 Hb*

Up−→

dV

A9 g O! d B[8d)0K)#'hf 5 H U

BV*;F 3 $K )QB, n

)#'hf 5 Hu ∈ U

O %$ &[;%L'i;& #<VA Qx5 # $ 3 #"6$Bd ; d

*,)]5 #

np7−→

xv B

v ∈ V

5 #;4S %B;$) D)#'%BG< 5)bdj%) BG6$) * )9dg%) $B,; ,<T! h;%;$$) 9*3$ HJ; 3 $ $'&0;%I'i;& #<VA Q x

d ,$&k$ 3 #"6$BFd ; ) d*d 6O )QB,

n1)#'UB,%"a #;%B=874S

q*,

)B,n2

)#'UR7Q4Sq′ B )QB,

n3*,)]5 #

lnm * 0 no #'=%.*2 =%4!Uo @#% #%U ′ p )=%'"!Ko)=% 76)='0 2=%9 1 'o .!B$@# #%356 '.B2#%rq '>7=%().' *2! '.B2#%sq

t8usvewMxRy #%*2! #% 2=%B2.!*2 p )=%'"!C:

child::b/child::d

child::c/child::d

d

b

x a y z

c

!"#$&%')(*( +,"-.(*/(0$&(12 34,5 0&((0( 6$,4/478,",5 0&((0(9:8 !;<=,)($.,>.4,?%A@B=,;-8C!!(0$.&(9$,D1E D&4 (0$.:F!D$G4H&.,I 0&((0J<$8K:88 0L=*MLD>ONP,Q#$&%':# 0LR(0("4+$R D$,S-.(*R(0$&()4%( *#) R&>*MNT7#G$,Q(*(:8 !@+$&> 4%U(0$TNH,Q*V9W($:(X4#4S,D$JY&>*MZ#$.($&[8P@5\ 4!Y$,4$,(/(0&4.!MN(=G$,) (*8[= 4!4$I$&(0&ND%L&(=/%:&[1,":8>D$ !*M@

n1select(i)7−→

xn2

Bn3

match(r′)7−→

xn2

d ,$&O6(4,"6$%

qselect(i)−→

dq′

BΣd

match(r′)−→

dq′

HJL' $) S(p,Ω)

,4,4S; S)B,]X : Ω

p−→

dX

)3(45 #,6"66R7F% ,<D$J%)3(4S)V%B/'i;)3 ;& 3 V #"5 #$) )#' ,<V"$X^ P # 3 4,;%&$) J6 4,"67 3

q′ ∈ S(select(i), q) ∩ S(match(r′),Σd) _R?),"$B S()$)K5 #?f 5 H )3E [A >;%$) )#'J!"$%K B^! #& V #"5 #$) 6; #; )3\4S)V,"$N;%,"6\)#'h&"$%$) / 3 4,;%$) *>)3;B,))3\! #&!h! #F45 #; `)9d ;9* M%9 KE%I4S; 'W)3;AIK8d+)k ;& 3L V #"5 #$) I B,4S B, >"67*S6%I 3 4,;%$) j B !45 #; j) ,"67 B ) B Q7c S%D5 # +; 71%-,/ 8#34+ 9 5 +; 3 52 - 5#+48#3 5: 3 5 /:?! 97k5 !?) %)3(45 #,6"6687$h"$)V P #6;I)#' ) 5 #"4h)#'T8d)!45 # 3 4,;%$) 5 #5 !L F(4,R7A >;&%$) =)#' 3%%4,%B )B,N874S%9* B/ S%"67!! hI 3 4,;%$) %)3(45 #,"$ 6<,; aF$] [6"6";& #$) g)#' ) ! %)3(45 #,"$F >;A%BGa #=4[<)3 ,< )3$%%B HJ,$K"$)VE"$%Bc)[X #Z 6 KB, "$)34,A >()#'h cA)3;!4,;%$A%9*B,%;S%B[ '-)3"6"$)9d ,<!&%$) HJL4,;% > % 6J6"6";& #; 4M)bd+; ' ,"1*,),<V_R5 3h 3 %"6"$ QN6AE BAA)3;7k%)3(4,"$ 3 687 6 $N%) %4,5 #"6"676(4,"$V* Bk4,;%$$) $N6"6" ,6T<))B HJJ ;& 3P 3 #"5 #$) D%d)3;P6(6"a #;"67T)I\) \'-)3;\&! #"$%5)9dg<V;& #4,;9*V 3 %4,5 #E6E%) $B,;T(%) ;& # >D)#'J =&! G*"66(6 ,<OAT)#'J874M%L5 #?9 3& 3 $T4< ;& #%9*M BO9 3& )QB,E%I 3%%4, HJE< ;& #" 3 4,"a 5 #$) N'-)3;h9 3&O<V;),4O)#'P' $) #;? 3 'W)3; E&! #"$% ;& 3h V #"5 #$) k'$)

#b

S : XPathpath × 2Σd → 2Σd

Sstepa::t , Saxis

a , Stestet , Stesta

t : 2Σd → 2Σd

Sstepa::t (Ω) =

Stestat (Saxis

attribute(Ω)) '

a = attribute

Stestet (Saxis

a (Ω)))3;d $

S (ε,Ω) = root

S (a :: t,Ω) = Sstepa::t (Ω)

S (P/a :: t,Ω) = Sstepa::t (S(P,Ω))

S (p1 intersect p2) = S(p1) ∩ S(p2)S (p1 except p2) = S(p1)

HJA' $) S$E!;%,;/ ;& 3I^ P # V #"5 #$) ' $) HJ ε

! #4,4, ,< ! #4"$9 3BG ,< 6 % )A )QB,TR7Q4S

Saxischild (Ω) =

⋃

n∈Cd(ω)∧ω∈Ω S∗d(n)

Saxisparent (Ω) = n|n ∈ Pd(ω) ∧ ω ∈ Ω

Saxisancestor (Ω) = fix (Saxis

parent(Ω) ∪ Saxisparent(S

axisparent(Ω)))

Saxisdescendant (Ω) = fix (Saxis

child(Ω) ∪ Saxischild(S

axischild(Ω)))

Saxispreceding (Ω) =

Σd\Ad

'Ω 6= ∅

BΩ 6= root

∅)3;d $

Saxisfollowing (Ω) =

Σd$Ad ∪ root) '

Ω 6= ∅∅

)3;d $Saxis

preceding−sibling (Ω) =

Saxisfollowing−sibling (Ω) =

Σd\(Ad ∪ root) '

Ω\Ad 6= ∅∅

)3;d $Saxis

self (Ω) = Ω

Saxisdescendant−or−self (Ω) = Saxis

descendant ∪ Saxisself

Saxisancestor−or−self (Ω) = Saxis

ancestor ∪ Saxisself

Saxisattribute (Ω) = n|n ∈ Ad(ω) ∧ ω ∈ Ω

Saxisxslv (Ω) = "6""$A QIB,%"a #;& #$) N! 3B,K #h87"$%%h6(4,"659 #$)

HJ ⋃

n∈Cd(ω) ∧ ω∈Ω S∗d(n)

3 4,;%$) =) = *) $ A 3 $ 4F$ ) L)#' ,"$% ,<L)#'6^ &! Q6:&"$%+ #"6"B,%"a #;%B! 6,%:)#' #"6"5"$A >\B,%"a #;& #$) W 3 4,"6$6$3;:6(4,"6$%B]'W;)3B,;V #$) Q7F 3 $) Ω

fix (f(x))A9 ! 3 %BA4S)3 >Gh' $) f

$J #4,4,"6$%B!;4S9 #%BG"67!)?6 3 #"">6"fn+1(x) =

fn(x)*,d ,$$NT;%,"6 "6")#' Cd

*Pd

BAd

BS∗

d

d+;KB,#%Bk %$) $&% %

('

\ #;a ,"$ 5 #A%I #;S) B=d ;TA >$) %BC) kT"$ 'W 5 B$B,V*)3;d $& S) B

Stesteq (Ω) = Ω ∩ ei

q ∈ EdSteste∗ (Ω) = Ω ∩ Ed

Stestaq (Ω) = Ω ∩ ai

q ∈ AdStesta∗ (Ω) = Ω ∩Ad

Stestenode() (Ω) = Stesta

node()(Ω) = Ω

Stestetext() (Ω) = Stesta

text()(Ω) = Ω ∩ pcdata

Stestecomment() (Ω) = Stesta

comment()(Ω) = Ω ∩ comment

Stestepi(...) (Ω) = Stesta

pi(...)(Ω) = Ω ∩ pi

Stestaattribute(∗) (Ω) = Stesta

∗ (Ω)

Stestaattribute(∗,t) (Ω) = ai

q ∈ Ω|Td(t, aiq) = true

Stestaattribute(n) (Ω) = Stesta

n (Ω)

Stestaattribute(q,t) (Ω) = ai

q ∈ Stestaq (Ω)|Td(t, a

iq) = true

Stesteschema−element(q) (Ω) = ej

q′ ∈ S∗d(ei

q ∈ Ω)|Te(eiq, e

jq′) = true

Stesteelement(∗) (Ω) = Steste

q (Ω)

Stesteelement(q) (Ω) = Steste

q (Ω)

Stesteelement(∗,t?) (Ω) = ei

q ∈ Ω|Td(t, eiq) = true

Stesteelement(q,t?) (Ω) = ei

q ∈ Ω|Td(t, eiq) = true

Stesteelement(∗,t) (Ω) = Steste

element(∗,t?) ∩ q ∈ Σd|Nd(q) = false

Stesteelement(q,t) (Ω) = Steste

element(q,t?) ∩ q ∈ Σd|Nd(q) = false

Stestaelement(q) (Ω) = Stesta

element(q,t)(Ω) = ∅

Stesteattribute(q) (Ω) = Steste

attribute(q,t)(Ω) = ∅

Stestaschema−element(q) (Ω) = Steste

schema−attribute(q)(Ω) = ∅

Stestaschema−attribute(q) (Ω) = Stesta

q

StesteDNTs(Q) (Ω) = Stesta

DNTs(Q)(Ω) = Ω ∩Q

Φ

φa(m, q, i, r′) = S(select(i), q) ∩ S(match(r′),Σd)

HJ]"a #$%]'-)3;LA 3)a #%B 3 %B04S)3 >? #"6<)3;6,`$L;A%) $B,;& ,"67C,6<V;E5 ^ ^4,;$) K #"6<)3;6,A

(2Sigmad×M,⊆)* #<> # [; 5% ,<O5 #E(& #;<?)#'N 5)9d B,4S B,?)

S)36N%) Q 3 NA)B,? Bk6h%) > 3 N874M(%

<> # *G! >7/' $) hB,#%B= %$) $&% #;%BHJ874ML%Td

BTe

5 # (6($ 5 2 + 5 :.2 1%- )#' %$) &% ' % b )#'Q^U #h%%)3(A B #$) X Z *S B

Nd

5 #L9 "6" '

$

(f 5 H $h D4B,)1R7Q4SL'-)3;I ,6"6"$%B"$A >I874M(%HJ,$?' $) 4,;% QK M%?A)B,"6 ,<C)#'"^U #8^ &! O%) ;9*: B[6K64,"$A Q& #$) $ ;7^!$ > - BcB,) / #"6" ,] 'W; )Q) c'i;)3`/ S)('-)3; ,"a 3 * ,6\5 3+Nd9 %J)#')3JB,% ,<K %)3(45 # ,"$ >;A%BGa #T4 %PHJ 3 - B/"a 3) 8%)3(4S)V6 ' $) 4,;% Q%Bd 6"6"6(4,;) ?) k5 # %

! "#IΦ$%#

%%)3;:"a ,<(5 #<I"$%&1! #F%)3(45 # ,6"6687(% ,<E$+ #"6;9 3BG7( L"a 3&$J !& #$ ^ QH 5 #"'7G$ X #Z X Z * BL' $) 4,;% Q%B;T;#%h' ,;;",4M) 6 % K ;& 3IV #"'5 #$)

Φ-' $) *,$Nd 3h(G B,%Bk'W;)3 d+)3; ,</) ,"67=);B,%"a #;%B )B, ; 8%- 5 :E)(d)3;Q ,<

) ;EB,%"a #;%B )B, 3 /5 : * 3T F%) %D)#'+ ,4,<V;& 3B,D'W;)3 "$)9 #"P)/ ,<V"$1874M]&! "a ,<(5 #<%9*M6$ )!"$) ,<;I4S)V ,"$?)/6(4,"67k! #4 5 #A%)AR7Q4S%9*S 3 S '-)3;(%NHJ,$d 3B,9 #"6d 6 Q7= >;)B& ,<F D;& #;h4S; '-)3;! %8%)V"67=874MT9 #;&*5 #NdJ 3 "a #;N6(4,;) %B %HJ,$I4,;)) %d 3)3;6<V 5 #"6"67O%) % %B ) ) I(G B?;& 3BG6$) 5 #" 5)9d 5 #"67$b* ,</,$' $) .%)3(4M)V&%Bgd 6 FA)B,V* "" # $ "%$ %'& & %( % % *) Bj&! #"$%D' $) b* B d 6^)3A?)#'\K >; 5 #"PA%&5 ,$%T)#'\D ;& 3V #"5 #$) C' $) ^ 3h"64S;L%)34S) >Td ; %%%&& #;7 %EH) S] ,"$])S;T%)3(45 #;],$E #4,4,;) 3[d 6[ d ) D5 #5 3I,4M;&%B,%B=6*,+V*Gd+Td 6"6"B,%&; MT6 B,& #6" %HJD' B #A >& #":$B,9 =)#'+D' $) ^$9* 3d]5 (% ^ %$) $&% $G*5 # 8%; 5 :3 1%2 98%; - 8 - 5: +;/.10%. 8%;2 35476 8 5- 8 8%265 275 - 8%2 8%; - 3 8 %+ ::9 1#+;3 %6^ P #I45 #((4,;%$) 5 # &) ,"67=B,)9d Qd #;BC (G% i)VL5 # ! #4 )QB,%J)]6;NB,%% B Q)B,%N B=6;I #&; ,% *+)3;] & ($b*:9 . #"$) M/;& "a #%Bg >)0;<(,"a #;A(G4,;%$) b*: Bg g. dJ %7 5 #D/"a ,<(5 #<%A)#'h%& Dd 6"6"5 k ) (4,R7c Q;%$) .d 6gF %%)3;"a ,<(5 #<%L)#':?f;HI5 #h! #& ?45 #C(G4,;%$) % _ O45 #;$,"a #;9* A&"$%&1! #0%)345 # ,6"66R7 %]9 M/! 3B, >7[;& "a # ,<0="$%$) . B /! #& ^ P #j(4,;%$) )!8d+)!;<(,"a #;h"a ,<(5 #<%9*S Bk >;% ,<F )A) ,& # 0 ( ,<V"$T"a ,<(5 #<D%) >& # , ,< %%)3;I; ,< )#' )B,%J5 #h #;=<61#3:8"$%& ,"$ Q7/T&"$%$) O(4,;%&$) *8%;F! #&! #&O45 #; %HJ,$%$+,4M;$)3;+)?L ;& 3J3 #"5 #$) =%9* M%9 &h %)3(45 # ,"$ >;A%BGa #T48%275L%) $B,;%B*G BA;h$ L' ,;;5 #;4M , ,<D%, L V #6"a ,"$ '-)3;\69*d ,$&/dhd 6"6"M9 #"6"/ 8 3:8 5@#3 5;:+41%; >L ,<AA)3;E4M)3 Qa #" %)3(45 # ,"$E Q;A%BGa #?4J'W;)3 ! #O45 #; )#'I(4,"a #;,"$h5 # 71#;3 8%+.;:II(4,"a #1 )? ,<( ;$) =5 #J$\) ,;%)#'@ )bd %%B %BA 6c% 5 #"66$%9*,$E%E$9*U 3K #"6;9 3BG7^B,A) ;& #%B >7jX DC Z *!$ >"674,;%$T'W)3;h #"6"9 3&%N% k ;9 #"'1"6 '-^ QH (,%4,NL'-d ;7FA)VN45 #)3"$)3<V$9 #" %lFE #% 0 4!()#%2!. !o=%94! *2!# 1 54# #%.HG?#% ! #% ?"!#'=-*,#%,=*,77(9* #%.2! 1 *,! (9*,!9*2'rq 56 7.4B"B29

! *2<#%>*,()#% p Io *,.B22=%@#%$:

J a

child::b/child::d

child::c/child::d

b

x a y z

c1

d2

2B=,)4&(0$=!'4848/&(0/%:&:(145<&8(0 !V"L(Σ∗

dbd) ∩ L(Σ∗

dcd) = ∅

8 #! N! U $ ,U

HJEB,%6;%Bk;<(,"a #;h(G4,;%$) N N5 TE%) ; V # Q6R7=4,;)34M;R7

qp−→

dq′ ⇒ anld(q

′) ∩ Σ∗dR(p) 6= ∅

>L))B=4,;%$$) $ E%) ;

anld(q′) ∩ Σ∗

dR(p) 6= ∅ ⇒ qp−→

dq′

fL#Γd

) ML? N)#'Σd

)#' )B,TR7Q4S% 5 #N! 97k #4,4S9 #;I 3N%) Q >

Γd = Ed ∪ pcdata, comment,pi%

_ E;<(,"a #;U(4,;%$) '-)3"6"$)9d ,<*#d+\d 6"6""$)Q)V&"67\ B?"$A >U)#'Σd

) ;4,;% Q ; 8%- 5 :k)#'h)V= &D)3;("$A Q9*+ 3 )3]) ",; ,4gF;<(,"a #;((4,;%&$) Dd 6µ(· · · )

#%

#;?) $) "67* ) 8B,)bd >dJ #;B 4? #;(< ;& #"6"6706(4M)V& ,"$])k;& "a #()=;<(,"a #;K"a <(5 #<%+); %%)3;\; ,<9* 3,$:d) ,"$BA; ,6;N)3AN)3;:)#'<> # 1"$ ,<VF"a ,<(5 #< ,4>dJ #;B4;9 #T %%)3; ; ,<*G ,"6 ,<(4 #"6;"a 3 7 S)3"$9*G B M '-)3;)3;( 'i;D4K5 k #"6"+)3;D)#'h % % )3;5 #"67*^ H 45 #; A #;/%)3(4M)V&%B )#'h) ,"67B,)bd >d #;B04b* B9 O #"6" SL;& "a #%B % ,A'-)3;)9d 5 #I #"6" ^U #]45 # (4,;%$)

p%N) ,"67=B,)9d Qd #;BC4 - (F'W)3; )

B,)bd >d #;Bc4hd 6"6" SE! 3B, #% ,6K4,;%$E;& "a #$) *S "BG ,< )B,?%5 #;4S , ,<*' ,""6"6 ,</%) ; V # 687=$

JDJ

R(p) =

R(p1) + R(p2) '

p5 3N'-)3;

p1 | p2

ε '

p5 3N'-)3; & :: t

ε '

p5 3N'-)3;

q & :: t BR(q) = ε

R(q) ∩ Σ∗d.R

testself (t)

'p5 3N'-)3;

q & :: t BR(q) 6= ε

R(q).Raxis(a) ∩ Σ∗d.R

testa (t)

'p5 3N'-)3;

q a :: t B & 6∈ a B

R(q) 6= εRaxis(a) ∩ Σ∗

d.Rtesta (t)

'p5 3N'-)3;

a :: t B & 6∈ aR(q

& & & % t) + R(q & t) 'p5 3N'-)3;

q & & & % $ & :: t

root '

p5 3N'-)3;

d ; & ∈ aA9 5 #

a$ & )3; & & & % $ & %

Rtesta (t) =

n '

a 6= %% $$ % A B (t = n)3;

t = & % & )3;

t = &*) & % & )

@.n '

a = %% $$ % A B (t = n)3;

t = %% $$ % & )3;t = &*) %% $ $ % &

)

Ed '

t = B a 6= $ Ad

't = B a = $

Σd

't =

& root

't =

& & )3;t =

& & & )3;t =

& & *) & pcdata

't = %(

comment '

t = & pi

't = ?)3; t = ?)3; t =

σ|σ = µ(q) ∧ q ∈ Q '

t = DNTs(Q)

Raxis(a) =

Γd

'a = ')

E∗d .Γd

'a =

& & Ad

'a = $

HJL' $) O$N< ;& #"69%Bk'W;)3 5 #h)#'JX Z )! 3%%4,h(G4,;%$) N5 # M<V k (G$4 % '-d (4,"a 5 #$) HJ;:4A)#'S 45 #A(G4,;%$)

p$P;& "a #%B])E ;<(,"a #;:(G4,;%$) (;4,;% Q ,<?N (G$

%) Q( @ )bd.)#' 4 %PHJJ(G4,;%$) ($P A5 #;4S %B >7K;%;$ ,<E6 (D"a ,<(5 #< ) #"$) M T ,"a ,<(5 #<h)#'MJ"$ ,<V h;<(,"a #;:"a ,<(5 #<J'W;)3

Rtesta

' $) *>A)QB,"6 ,<?5 # )B,T%h,;)9dNL %d 97)3A)B,% %\HJ,$h$N;4S9 #%B='-)3;NE)3;I49*5 BkT;%,"6 ,<"a ,<(5 #<%L #;T%) 9 # 5 #%B %A[04,;# ( ;<(,"a #;45 # ;& "a #$) >720"a ,<(5 #<

Σ∗d

*L #"6"$)9d ,<2 Q7 4,;# ( )#'] %%)3;; ,< %HJ,$+$JB,) I !'-)3"6"$)9d ,< ,4=) k ;& 3 ,< )QB,%) 3 /5 :T B )3, ,<("$ 1%;3 5@#3 G'-)3;! #$) *\&g 3( %%;7*: #;F,;)bd g) ,])#'h/A)QB," %7;)3!5 #],$]B,)Q% )3];,

J

K S%)#'P E4,;# (G ,<* 3 K) ,"67O #4,4M9 #; 3N ;h7 S)3")#'\ %%)3;I; ,< Q7QdJ %7 %HJ )B,T% $ Q;)QB&%%BO k(I%$) % "$%&1! #&C%)3(45 # ,6"66R7O)#' ]9 BG$B #K%BG<Td 6 ]%) Q( @ )bd 'W;)3

q)

q′$N6"6"

qselect(i)−→

dq′

BΣd

match(r′)−→

dq′

;& "a # ,</)iT"$9 3BG ,<Σ∗

d

$J'W)3; 4S;(6 ,<F Q7= %%)3;

anld(q′) ∩ L(Σ∗

d(qΣ∗d) ∩ LR(select(i))) 6= ∅

B


dR(match(r′))) 6= ∅

_ O ]d+)3;"$BO)#'PB,)bd >d #;B 8) ,"67C"$%$) O(G4,;%$) 9*G,$Φ-' $) Od+) ,"$Bkd)3;

φd(m, q, i, r′) = q′ ∈ Σd | anld(q′) ∩ Lmcs 6= ∅

d ;

Lmcs = L(Σ∗d ∩R(select(i)) ∩ Σ∗

dR(match(r′)))

J%9 K"$%$) C(G4,;%$) #; )3I< ;& #"6"67B,)9d >dJ #;B 8) ,"67*,$ V #;a >$)3 ' ," % ;45 #6;Id 6"6"ML! 3B,E)3;"67 %

HJ( S)D;<(,"a #;L"a ,<(5 #<]%B,)%L%) $B,;L %)3(45 # ,"$] >;A%BGa #A4S)9d;9*6'1 #6"$E)k! A)#'J( G'W)3;! #$) 5 #?! 97 SAB,; %B0'W;)3 : 1 2 5=(4,"a #A;,"$A)#' @ )bd EHJ(%) >(G )B,] T5 (45 3%B06E45 #; rE%9* BC'W;)3 ,$9*A)3;!%) >(G G'-)3;! #$) C S) ,N6h %%;7=(%! 97 STB,; %B * % 6<,59 >(6(4,;) A >/9 S!! 3B, Q7 5@ 3 5;%+.; - 3:85 : 5 5 34+ 1%; / 8#3:8 5@ / 275 : :+41%; >7 ! #&O45 #; )#'

ri(i) BkT%) >(GhR7Q4SV*G 4,; 64,"$

select(i) 7→ match(ri(i))/self ::µ(q)/select(i)

; @ % ,<k5 # )B,%I5 #T #;D ,6a #" )QB,%I'-)3;V #"5 #$) ^)#'\K&"$%$) ^ #;]%) Q( )B,%)#'N/(4,"a #!;,"$V*: Bc D5 /! #%B 6K! #g45 #; %OHJ

self ::µ(q) ;%B

5 #;4S L >7kd 6"$B,9 #;B, )3; & N)#'i C% O E"a 34 )#':45 #; b*5)F 3%%4,) ,"67l (2!#% G?#A!? *2 *,' 7*2''9 *2 #%#%/20 7=%9?.(*,#% ! #% 7 * #'#%)=%!C: !?0 2=%+* #%"!To24. 56 4' 0 4

0 ,=&0 4='#%)= '*,=%76!!B0 ,=>HG*27. 1 * 7?=%9(9* #% #%#%!B !"?:.:: ("4 $##% =&"4?#>*2 54?# 2!&%'( #%*,#=%'4@#%9 0 =%" * #q?76 =% p 9 5%q HG#%!'2!3!$)+*$,.-?(-+*:0/ 9* p #% 0 2= #%/0 4#%4?=%":

child::b/child::d

child::c/child::d

b

x a y z

c1

d2

$, 4$, L$D(0PN9,W.., $$ 4" $&>!4$W! :88.4 $,($!&:$ $?($($ Q'(C$&D&%&%W$J$,&(($8PND&4 !II!C4D:&(0$8/!'4848&(09>%:$&$,1 V V1!!O8)$"!';!/V1$,G$$&$D@ E,4$,5L($8PNL$,"4$ !*MJV9!'%J,D!;;4&%A@

)B,%Nd 6kEe #A5 #A? 3 T%) Q( )QB,V*' ,;;N;#, ,<AT;%,"6 ,<!( B,%B45 #(G4,;%$) % "$%$) 45 # ( $) 2d 6"6"T #"$) (G B. "$ ,<V )#'E ; ,<! 2;<(,"a #;k(G4,;%&$) ;& "a #$) g)#'J/"$%$) c45 #* B*P 'i;

Σ∗d

$?4,;4M B,%B*U!&?)#'h; ,<E Q;%$) C)#'PT"$%$) "a ,<(5 #<?d 6"6" ST! #"6"$;) $B,;I8d)A;<(,"a #;h(G4,;%$) I);

Σd

*r B

rext.r%1_8N) ,"$B M?) $) N5 #I Q7=; ,<

s ∈ L(Σ∗d.rext.r)

$N #"$)? L(Σ∗

d.r)* ,J%) ;L$)3J< ;& #"6"67/; HJ;! %7=(G$J

; ,<s = x.y

L(Σ∗

d.r))( (F)#': ?4,;# (

x ∈ L(rext)(G$'-)3; Q7k (

y ∈ L(r)%

"(G BG ,<F D45 #p) L"$ 'i >7k (4

td 6"6"( B

R(p)Q7

R(t) ∩ Σ∗dR

test··· (· · · )

#%

P #C(G $) CB,)Q% )3h& 3;5%?%) &; 3 # 687 56hA;"67O #4,4,"6$%h%) >(G5 #"U G'W)3;! #$) C)%) Q(TR7Q4S% %_RId 6"6"P4,;)$B,A 06(4,;)A QE 04,;%$$) C'W)3;E #"6"%)3 , 5 #$) E)#'

i B

r′*

d ;?select(i)

5 3J'-d+;h4N5 match(r′)

%

HJT S)%) 9 # 5 #$) (4,;%$) /dJ 3J k #4,4S9;+'-)3;\< ;& #"M$B,9 G* ,+6$)3$# ,6%)3;;%;I)3U #"6" )B,:874S% #;\%) ;%B?) 4,;)34S;%9*3 BK &)3",\"$%$) D45 #d 6"6"Q<hd ;) ,<D! Q$% 7 h;)Q)3 )QB,V* )3\I%) >(G )B,V* 3\6;\ ,6a #"S%) >(G %HJT4,;)34S; ;$) OB,#%I ]%)3 , ;N' $)

c'W)3; ! #& B"$%$) O(G4,;%$) %1_1'U

"$%$) C(4,;%&$) k$ ;"a # V*6 4,;4S B,N)]6 ]5 #;4M %B ;$) O)#'PL! #O45 #;

c : XPathpattern ×XPathpath × Σd

c(pm, ps, q) =

ps

'ps

$I )3",sc(pm, q)

ps

)3;d $HJE5 #;4M ; ' $)

sc

$

sc(p, q) =

sr(pr, q)

'p =

pr

$I )3",sr(p, q)

)3;d $

sr(p = p1· · ·

pk, q) =

p1· · ·

pk−1

$ n 'k > 1

Bq = ai

n

B( pk =

$ )3;pk =

$ $ )3;pk =

$ $ )3;pk =

$ ') $ )3;pk =

$ ') $ )3;pk =

$ & *) P $ n '

p = $ B

q = ain

BPd(q) = P

*) P $ n 'p =

$ & Bq = ai

n

BPd(q) = P

*) P $ n 'p =

$ n Bq = ai

n

BPd(q) = P

p1· · ·

pk−1

a m '

q = eim

B( pk = a )3;

pk = & )3;

pk = & )3;

pk = *) & )3;

pk = *) &

p1· · ·

pk−1

a m '

pk = a & D B q = eim

p1· · ·

pk−1

a ( '

pk = a & D B q = pcdata

p1· · ·

pk−1

a & '

pk = a & D B q = comment

p1· · ·

pk−1

a '

pk = a & D B q = pi

p)3;d $&

HJ ,"664,"$IB,%"a #;& #$) /%DNTs(Q)

5 #+ 3%%4,+6;\)#'Mhf ;H\ ! T9*V$'W)3; Q; 5 #" 5 #"679;"%N B$ )3h7 >& 3$9 #"6"67k(G4,;% ,"$T U^U #&%

"

HJ % S)h9 A) ,"67K5 BG"$NB,)bd >dJ #;B/ B ($4b*Vd ,$A$ ; h4,;) ,"$ d 645 #; 9* ,$ )3!$ Q'W)3;L"$%$) 0(4,;%$) 9*5d ,$&0! %7 SD Q745 #0(4,;%$) % (/'-)3;N5 # $

l(p) =T"$)bd+%I B,(

i)#' ]& # %E&)]5 #

pi

· · ·

p|p|

#"6"5 ?B,)9d Qd #;BC)3; (G% Bg,(4( %dJ %7 'i;)3 =(4,;%$) *:)C) ,"67 ;6<VQA)V(45 #j)#'IB,)9d Qd #;B2 B 4b*)3;

ε*G$ "$ 'W

wp(p) = p1/ · · · /pl(p)−1

dp(p) = pl(p)/ · · · /p|p|

A[T%) ,"$BF! TB,)Dd 6 ,<Σ∗

dR(dp(select(i))) 3N K;<(,"a #; "a ,<(5 #<'W)3;JL"$%$) * ,

(5 #;4M , ,< ,<(E%) >(GN874Sq B

wp(select(i))$ 4S)V ,"$

Rany : XPathpath × Σd → Reg(Σd)Rany(p, q) = S(wp(p), q)Σ∗

d ∩Σ∗dR(dp(p))

SdJ 3NB,#%B %$) C&% J JHJ5 #" %%)3;&1"a ,<(5 #<

Φ-' $) S%%)3A%

Rs : XPathpattern ×XPathpath × Σd → Reg(Σd)

Rs(m, s, q) =

R(c(m, s, q)) '

l(s) = 1S(wp(m)).Σ∗

d ∩Σd.R(wd(m)))3;d $

α = Σ∗d.Rs(match(ri(i)), select(i), q)

β = Σ∗d.R(match(r′))

φr(m, q, i, r′) = q′ ∈ Σd | anld(q′) ∩ L(α) ∩ L(β) 6= ∅

"

φr

*> =65 '-)3;*Q5 3 D;$) 4S; 'W)3;! %L4,;) ,"$ 'i;L(α)∩L(β)

$J%)3(4 ,%B - 3 A ,)3! #) *V6(A%BGa #"67D #4,45 #; Qd 97?)"BKB,%"a #;%B )B,\R7Q4S%Ud )V %%)3;"a ,<(5 #<T Q;% d 6

L(α) ∩L(β)$)]% ;7FB,%"a #;%B )B,L874M rN %%)3; "a ,<(5 #<

,)3! #) ^d 6L(α) ∩ L(β)

'W)3;L ) (4,R7O >;&%$) % ;I(G4S;6A >L;9 #"$%BC5 #,$L%))?,40 S) , ' )#'+K6AD)#'\Dd )3"$( %%)3;L"a ,<(5 #<( 5 #"67$ )3;9*S4 ,BG; >"67*5 #"6;9 3BG75 #;"67F 3%%4,& ,"$ '-)3;) 1"6 & + #"6<)3;6, 5 3B S% =! 3B,L S) , 6A%I"$)9d; %X DC Z ))?F 3B V >& #<L k,$ V #"6$B #$) )#'UfLH f 84S%5%B ^ H 5 # 5 #A%h B=874M%d;T& #AJ, ,<*Q B]"$)Q9 #%BA #"6"G 8%BG<%)T 3%%4,\& #%)

L(α)∩L(β) ,)3! #& B,%"a #;%B

)B,ER7Q4S%h) ,<VQ 'W;Nd+;? 6(4,"67 #"6"R7Q4S%N5 #I5 3Bk6; 5 #AK) O&C O%BG<V*M 3 /;& 6$) ^"a S" %A[( #; )3E 3",7*S) ,<V*S%9 DA)3;D5 0) DR7Q4SD! %7O5 ]& #A 5 #A(% )3",$) d 3h'W) B ,</ ;& 3LV #"5 #$) '-)3;h"66(6 ,<FE874S?9 #;& %)34S(%"_8 5 3'9 #"6"67T%) $)#',;, ,<

φa

S 'W)3;φr

*3 BT4M; '-)3;( ,<hR7Q4S:9 #;&E ?φa

;%,"69*#d ,$K$9*%'-)3; #"6"45 #O(G4,;%$) ,h)V ,<(L874S%B ^ P # D B **%b*5 ],4S;N)#'U

φ′r

;%,"6

φ′r(m, q, i, r′) = q′ ∈ φa(m, q, i, r′)|anld(q

′) ∩ L(α) ∩ L(β) 6= ∅

' ,;;0;#A >c$0) & g%BG<1"a S"(%, # . 'i;[ #"6"1*( B 4M; '-)3; ) (4,R7 1 Q;%$) %J) ,"67/) 5 #A%N5 #5 #AA)3;L5 D ,<V"$LB,%"a #;%B )QB,R7Q4S(%HJ,$hd 3)3 ;$%B %l-l !Io .(-$(9*,'&7=%().'2! . 2!rq37?=% p 9

C

8 R $% L_ ! R

A[ )bdj5 Φ-' $) P5 #A)QB,"GA)B,%9* D ! >$%+ B B"$%&1! #& %)3(45 # ,"$(45 #6;Ld 6c # ,6(B,%% >T4,;%$$) * "BG ,<;%%)3<,6$) c)#'J)3A

%)3(45 # ,"$K >;A%BGa #D4 % L%)3(4S)V6

Φ-' $) /'W)3; @ )9d 5 #"67G$ i 'P 3B #4,%B/) I& #Ah"a #$% +%) ,"$B S

φ1 φm ∩ φi ∩ φ′r

WHJ5 #=$9*JCA)B,k' $) *N ' $) *I B C %%)3;"a ,<(5 #<E' $) E&! #"$%I BkK ;& 3IV #"5 #$) k' $) #;)3h "B,%B* %E7= #;T< ;& #"6"67="$%N4,;%$T5 E %%)3;I"a ,<(5 #<L' $) #% Q$) "67*S;D$ ) %%BO)/;[ #"6"' $) ^ #"6"P9 3%9*S BCK%)3(4 ,& #$) 5 #"6"67 '1 3;' $) I #;S; %BF'-)3; ,4,4S;& M) BG ,</T;%,"6N)#'PE"$)bd+; %A[T 9 3B4,"66 (,%Bk4S)3 >I #"6<)3;6, Q)/ ] # %E)#'P,;%? #"6<)3;6,A

(% (G%Bk4S)3 >L #"6<)3;6, d 60 ("a #$%K)#' h)#'M* ,<

φm ∩ φi

* B%)3(4 , ,<3 #"% 'W)3; L' $)

Fm : I →M→ 2R

&% (G%B/4M)3 QJ #"6<)3;6,_d 6k T"a #$%)#' )#'M* ,<

φl

3J E%) ;& # Q BFm 3 6N%) Q;)3" @ )9d <V;& #4,*5 B%)3(4 , ,< V #"%J'-)3;

Fl : I →M→ R→ 2Σu

Fl

)3;%+ V #"% )#'U(select(i)) ∩U(match(r′))

)D,4,4M)3; B,9 3B @ )9d ;4S)3; ,<! #N "a #;h& #<(%

C&% %) >(G&8 6 (,%B!4S)3 >N #"6<)3;6,*Gd 6 ?"a #$%)#' J)#'Σd×M

* ,<] 36N%) >;)3" @ )9d <V;& #4, Fu : I →M→ 2R

Fu(i)(m) = r′|Fl(i)(m)(r′) 6= ∅

% Qa #"6"67F?& #AE 3φl

* ,N; ,<Fl

rNB #& (;,;(%

))? ,< 5 3, # U6<(,; C&% G*J,$A$/φpre

4M; '-)3;! %O ,5 %A QF Q;)QB&%%B*Nd 6φpre = φl ∩ φm ∩ φi

%

A25 #A(, 3"67g%) 6,%BjO%) >(G&8 6 O #"6<)3;6, dJ 3Ak )%A)#'&)3Ak(4S;'A Q % U6;9* 0(G4S;6A >Ld 6"6"B,A) ;& #D5 #D,;%8& #<]%)3(4S)V6$) ^)#'\] #"6<);6,Ah$N) BG"67k ,<V %;%B %

b

H%h9 3l t e a n1 n2 n3 n4 a $ $ C C($ C

b C $ ' '(' C ' a

b J ' b b

!#"$ C ' C b ' J a a b C J a J ' a C($a"%& ! ' a '#b C b ' b $ $ b C'( !#"$ J C b C b C b J ' )!* )+,!-" JDJ a C ' ' a b b C b b ' ./0 b b DC J DC J DC J JDJ "1,2!-"3 C ' b a DJ DJ J b '('4 J $ C $ b $ C (, !-"3 J C DC J a 56 246 ' J b C C C J '!!( 4 7 ($ ' a C ' b (' b ' C '8 8 ,2!#"$ a Ca a J C J C J ' a b a , !-"3 /0 $ a b $ J DC ' $ b C J C b C , "$ 4 ' J C J b $ ' $ C($a #b C ' a C C ' J

B4 !:9D<;F#L>= D(0&(0$ !)4!M(0'(1,@?+ABCH$?(* :(&@=/.4!P<85 D8,"$?(*&!L$8#&N($:DL?[8SE@@l(J$,Z! :8#J4",Z8$!/(**ML!&($,&N

t'(J$,SLR 3I4"$&!4$S$!?(Q $,GFHJILK)MNH OQPSR

(0*ML!?(0,&:?Ne'( ,CLX D&FP!#=%&!4$( Q,&(0=&($1($.,)4D%

a'(6$,;LR 3

240$ $)%&:!'4.8(FG$, $&(0/8(0 /(.,&@n1

'(G$,ULX D&Y4:88L>= !&((I?%?(G4UT+$&!4$(= !7L (0$:$(&NC%8N $!' $!#V.,?.7?%Q<81>%"%G$*MQ:4$ !*M@n2

(/$,XLX D&CF(0D.,Y$!?(C($ !# !L$,WTωm

Nωi

V1$&(0&Nn3

(C,XLX D&C6:88L>= !&((&%&(&(0$&%G LMQ,)(.,4!&((=4!8$$,K%

n4

(=, LR 3/($ !L !LR,ωl

$?(*?@B=,G!'4

n1

<X$,YXZ[X\]#^_:`A$?(*8(0I(R$,G&($!XR#A-B5!'$(= !87#W(0$[8(X D&.,?.7?%Q<81>%" !E*MIV1E,aR$&!4$"!&(&@

H%h9 3tm sm tl sl t s km kl !#"$ $ ' C $&% a % b J ' % C (%Ea?C Ca ' a?C($

)!* )+,!-" $&% C b % J % b J % b % b a % ' $ $ b $ b '#b J!!( 4 7 &% C % DC&% J C&% ' % ' % b (% #b ' J b 8 8 ,2!#"$ a % b % % J &% '#b $&% J % $ (% J J b ', !-"3 /0 $ a % ' C ($ ' % JDJ b J a (% C (%

, "$ 4 J DC&% J $ J % C $&% (% a ' C b

B4 !bE2\ !!4$542:88L>= (0&($E !8 V 4!8$$, cQ:M@tm

'(=$, $> <8=$,"%"4D%E*MJ4$ !*MJ4!M($(&N

sm

(1$, &(0/(0 !L !!AD&#Ntl'(1($.,&4!&(( DV 4D4!ML($'(9$>

%sl

(($ !# !4!O3.:#.48@t4D%

s$;4!P(0(/4%IL%[.(@

km

4D%kl

4;7L!!A.&(dT &%8&(e($&-V <=, *V9X&(0(&@BH&(0;&($&(9$,D;4!Mf?%IY!&((1$,D4U-a(C4"4C($,V1P@ $,Y,)8Y42$,hg_b` Zij-kR($N,

φm

Nφi

%φl

<[8(9!&%Q !8 al A$,;!4$& V ($&.,Q($8:NLJ!&(( ,4ZC($&%A@

'

!

=9 SC% HU ,"$ b *hC;"a # "67 6(4,"$CA)B,V* D B&! #"$%h 5 #"679;J"66( 5 #L V 3! ) )3;6R7/)#'; a #"9 3%9* S 'W)3;I9 $;9*,%) >(G& 6 5 #"679;: #;+&"$))V(%HJ7D #"$)I%)3(4,"$A Q:9 3()3; ;7Ed+"6"1* S)3D"66( 5 # ,< ?"a #;<N'W;& 3$) =)#' G'W9 3 ,"$ @ )9dN id ,$&F$+5 #;BG"67!,;4,;$ ,< QIA)B, '-9 #,;hdJ 3B,%6<%B) ST%)3(4,"$A >& #;7O)()3; @ )9d1;"a #%BO'W9 #,;%##%_R(6<V> MJd)3;>d ,6"$I)L;7K >A)3;N6(4,"$N 5 #"679;:)E 3B,B()TJ4,64S"6 V*>)3;,4,<V;& 3B,! #"$%&U 5 #"679;)h "B,B,%"a #;%B )B,:R7Q4S% D6"a #$%i6%U)#' )bd 9V* ,NEN)#'"$A > 5 #A%N5 #N! 97 ME 3B,B,%B,6 i"66(6%B Q7=d 5 #N$J'-) Bk (R7Q"$%% B[ F45 #;a #"\)3;B,; ,<* B0"$9 3,4,4S;? B0<V;9 #%E"$)bd+; S) B[ #;A #"6"B,#5 ,"$ #% ) "$) =HJ=%)3 , 5 #$) )#' A)B,V* D Bg! #"$%&! #"679;D$D #4,4,;)34,;a #/'-)3;] k'i;) Q&8 Bg 5 #"67G$ % HJ;F #; )4S; '-)3;! %/4,;) ,"$AD &! #"$%I 5 #"679;9*5B,%4,6T5 # 6I #4,4S9 #;%B%)3(4,"6$9 #%Bd d ;6 C) ,J'W)3;! #"6"67 %

Φ

HJ (,%B^4S)3 > @ )bd #"6<)3;6, $5 3&%B[) ^(d+)3; 1"6$K #"6<)3;6,*d ;((6AE [d)3;/"6$ #; - ,4,"$% )#'U KA)QB,V*, DB,%"a #;%B )QB,I874SV* E(4,"a #1 )?Q ,< ;$) g Bc =& #;<E(4,"a #!;,"$V*'-)3;T% ,<d 6

Φ-' $) % BG$B #!%BG<%D #;

'-) B ,</D%) >;)3" @ )9d <V;& #4, ' $) Fu

< ;& #%B >7K6(4,"$] 5 #"679;9*Md 6Cfm

' $) )#' %$) C&% b BFE #"6;9 3BG7FA >$) %BkR7Q4ST9 #;&*'W)3; %)3(4 , ,<ALA)B, B%) Q(I874MT)#': O%BG<V*,<V O)VT)#'U?)3;6<V 5 # ,<!(4,"a #E;,"$(%_ 9 3B()#' 3B,BG ,<d.9 BG$B #h%BG<%)Jd+)3;]"6$BG6;%"67*>4M; '-)3;! %N9 S ,5 %%B%) $B,;& ,"67 >7 !#"$ - d-'-) B09 BG$B #% ;9*M"$9 ,<k)3A])#':K G'-9 3 ,"$D) %T) ,)#'T=d+)3;j"6$ %jHJ,$! % "67g%)3;;%4M) B,!) ,< % &'" ' $) )#'A)3;O5 ) Φ-' $) *5 BV #"5 #E) E) ,"67F 'U?)3; 'W) B @ )9d

f(φ1, φ2)(m, q, i, r′) =

∅ '

φ1(m, q, i, r′) = ∅φ2(m, q, i, r′)

)3;d $ J4,;Q$) h(4S;$ %T5 3 )bd *5 BO 3Jd+Ld 6"6"%T #<> # "a #;9*G

φr′' $) k$J4,;%$&V*

,hV #"5 #%N;& #;I"$)9d "67*,! ,<A"6;

f(φa, φr′)

(9 BG$B #E'W)3;h K'1 3; 5 φr′

i k4,;& 3$% J' $) * ,h6"6" #N"$9 3h 3N4,;%$(%

$

! "

J)3 X DC Z BX Z 4,;)34S)Vh E)3;\)#' "6; ,< S 'W)3;h%) >(G&8 6 L 5 #"67$b*d 6F E%) >(G& 6 ? %%)3;N"a ,<(5 #<?% %_R\d 6"6" )3ShB,%; S%BA FB,& #6" ;V* S%9 N6+$\;& #;J6(6"a #;+)E%) >(G&8 6 T %%)3;P"a ,<(5 #<J%9*3d 6]J(,%4,$) (5 # )%) >(G:5 #;4S , ,<L$UB,) N #U45 #(( $) T45 # ( $) O5 #Nd+T4,;%& >%B 3I D;#%B ;$) O)#'

(select(i), q) 7→ match(ri(i))/self ::µ(q)/select(i)

$N6(4,"65%B)

select(i) 7→

match(ri(i))/select(i) '

select(i)$ ;"a #

select(i) otherwise

_ >;% ,<V"67*+X DC Z B X Z %BCD%TBG; >"67 "$%& C [ F%)3(4,"$(& B R #"$) (,%B4S)3 >= 5 #"67$ * *+6(6"a #;/)^kdJ %7jd+

φl

*J B ) (d 62 c"a #$% * * B 3"6"$;? 3T "6;L) ^( %%)3;T"a ,<(5 #</ 5 #"67$b*M9 3&, ,< ,)3! #& F'-)3;L; (% B Q;% ,<V"67* 6;I4 , ;7F O'- #6O ;& 3hV #"5 #$) J)3%B=6I) ,"67= 3 D"a 3;%)3;hd O;7Q, ,<F"$'1 #6"$%B*G'W)3; ) 8B,)bd >dJ #;B^4k;45 #6; % C(G4S;6A >Ld 34S; 'W)3;A%B*S%)3(45 #; ,<kK4M; '-)3;! %K)#'J W%) >(G&1 6 E %%&)3;]"a ,<(5 #< "6;D' $) *\ Bj j ;& 3(3 #"5 #$) "6;D' $) %CHJ=(G4M;6A Q]$ Q;% ,<* S%9 D]8d)=' $) T5 (BG; >?;) ,<O B d9 4S)3 > HJA %%)3;"a ,<(5 #<J' $) (5 3P #"6;9 3BG7DB,%&; M%BA 3B V >& #<N)#'M"66( 5 # ,< @ )9dNd 6( %)3(45 # ,"$ Q;A%BGa #F49* Bc6E%) >(GK & 6 Q6R7[ #"6"$)9dNK; A)#' A& #A! ,)3! #& '-)3;K #"6"%) Q(+874M% %UHJh ;& 3+3 #"5 #$) (' $) A5 3N 3B V >& #<I)#' S ,<E%) >(G&8 6 V*d ,6"$E6"6"4M; '-)3;( ,<Ad"6" %HJE&& ,4k'W)3; ?(4S;6A >Id 3:HJEA)QB,V* BO! #"$% 5 #"679%Jd+;L; ;J)?4S)34 ,"a #LB #& K;,;%J5 #6(4,"$A QNh' $)

Fu

%HJRd+)!BG; >""6; d+;K S 'W)3;

φ′r

*5 3f(., φ′

r)%

HJC%) "$) 6(A%BGa #"672 #4,45 #; Q='i;)3 H ,"$ a^$/5 #k c%) Q(&1 6 0 %%)3;"a ,<(5 #< "6;h& #6"6<> #%IE&! #"$% 5 #"679;;_O #"6"U)#'U?"a #;<;I( #(4,"$%9* C )3;hA)3;)#', @ )bdN5 #45 3&%BT:&! #"$%% #"$&) 45 3%BL\ %%)3;"a ,<(5 #< "6; %9_ T< ;& #"1*D ;& 3IV #"5 #$) "6;%)3;%N C,6<V; 6"6";& #%I5 O? %%)3;h"a ,<(5 #< "6;9* B=6h #"$)/6"6"$J G'W9 3 ,"$9 BG$B #?%BG<% &k'- 3; % )39 ,"$T(,%4,$) k$J ,2!#"$ /0 %9 3V*d ,$&O5 3I)(! >7 B,%"a #;& #$) h 6h&! (5 # !%) >(G&1 6 "6;hd) 4S; 'W)3;! %1d $& >6" M9 # O #<> # >7=9 3, ,<= ;& 3hV #"5 #$) O;%,"6 #% C;9 3) 5 ,"$^(G4,"a 5 #$) 2'W)3;k %) >(G&8 6 "6;=)c4S; '-)3; A)3;C4,;%$"675 c F%) >(G&1 6 !) K$LD,6<V , M;K)#'\< ;$](4,"a #1 )? ,<O ;$) "6 %%% B %%% % HJ7 #;%B ;7.)#'i *N B OR7Q"$%%F6(4,"65;k 3B,B,l !#"$&%!'$&)('*+%,-/.0,1$2-34 !0%,-056'7)98!:*;":-<l:= / "> )(-,@? !),@"A(B-;CEDGFIHHJBKML#$&-*N%B,-%0.O0"-(P-Q7'-(!:"A*B),

a

H%h9 3n1 n2 n3 n4 !#"$ b bb b C J b bb b a $DC

)!* )+,!-" b C b C b!!( 4 7 $($ '(' $($ '8 8 ,2!#"$ ' a ' C ' a b a, !-"3 /0 Ca b J C($ J C J $ C CDC, "$ 4 C C #b a ' a?C $ J

B4 !2H!V ($ !L !4!34$&( <F$, :8#$L[= ($($E !8/4D:&(0$86!'4848 !(@,; (0$.[F!4!8-!$&(&@

n1

'(1,)LX D&/4 DV(=$?(*&%Y LMQ,X:?(*!'4;-!$?Nn2

'(1$,)LR 3;(0 !L !L@n3

'(=$,"#R 314 V(9$?(*&%G LM$,)4 (0$.:=!4!8Q-!$&/4%n4

'(=$,"LX D&(0 !L !#D@

H%h9 3tr sr tl tlc sl kr kl klc !#"$ C($ b % bb ' a b $&% C % ' a

)!* )+,!-" C J % J a % ' C&% J &% J J ' % ' % J ' a b !!( 4 7 a (% b C&% C (% a % $ ' a % '#b $ b '(' C b 8 8 ,2!#"$ J a % $ C&% $&% b $&% b J &% ' b ' %Ea ' $DC ' $DC, !-"3 /0 Ca $ ' % ' J b C J J % b a %Ea J (% C a, "$ 4 $ a C&%Ea b a '#b a C % $ (% b bb J

B4 !R L2$<4/4H$,"#$#[= ($($$ !C:?(*9!D4 !(@$, (0$.[=!!4$J-!E.(@tr'(1,")Y(($&%5 LMQ,X:?(*1!'4848;-!E

sr

'((C(0 !L !!AD&#@tl($,)$>

($&%> LM),4 D(*8[ !4!4$>-!$?N%tlc

'(2$,1$1(0?%> #MR$,&.,?%X (0$.[ !!D$X-!$&sl

(1(/(0 !L !!33.:&#48@kr

4%kl

4 7L!!(=3C(0?:D%JH?:8J <=, $,$&@ Y4!!P8(0?(=:& g]#^_:` \>V1$,/&.,NL,)4 D(*8[=!4!8J-D!EV=(=($D&$?@

DJ

A)3;(% )3;N9 3C)#'U%V* ]%) Q(&1 & 6 "6;hd 6"6" #4,4,;)K Q7=(4,"a #T;,"$T! #, ,< "$A Q!R7Q4SV*+)3;F >7 874MO #! #"6"1*;%4S% "67*,"$%(k(4,"a #;,"$%) >& # , ,< (4,"a #1 )?Q ,<k ;$) 05 3L A5 #;4 45 #; %hHJ,$I4,;)34M;R7k$h"a #;<"67 5 #;%Bd 6C&! #"$% @ )bd 5 #"679;9*d ,$&jd 3(; S 'W)3;/ 5 #"67G$ ,< "6; ,< % g=)3;5 B* /%) >(G&8 6 "6; &%%) Q(T G'-)3;! #$) ^ 9 3B0)#' Q7 i< ;$ %) >& # , ,<! #&C45 #; *S B* d 6 K6(4,"$?6(4,"$A Q& #$) [)#'\ ;& 3V #"5 #$) *M6 %%B, )3 S(G4M (% B,BG ,<T 9 3+5 #! #4U9 3K(4,"a #\;,"$\)h ,4,4S;&R #4,4,;) (G6! #%B])#'f;IH! #, ,<T45 #; C)#'UL;,"$V* BO )3;h9 3

XPathpath → Strings → Σd → 2Σd

)3; ,< 3 #"5 #$) E)#'J"$%$) c(G4,;%$) 'W;)3 45 #;$,"a #;?%) >(G?f;H9*"64S%B^4S%%B ,4( ;& 3TV #"5 #$) "6; %THJD9 3& 3 #"%T #;D;%BO'W)3;T #"6""$%$) ^(4,;%&$) 5 # #;T(G5 #"6"67=T& #ATd 64,;%BG$9 #%I;64,4S%B) % ) "$) F'W;)3 (G4M;6A Q +"$9 3d ,6"$I /"664;9 #Y)#'I&! #"$% 5 #"679;9*/%) >(G&8 6 = ;& 3KV #"5 #$) "6;K4M; '-)3;A S;E5 !%) >(G&1 6 %%)3;T"a ,<(5 #< "6; %J_CD4,;Q$) T(G4M;6A Q9*d+]& 9d 5 #;]$ )F;9 3) )3L)/!&! #"$%A 5 #"679;9*)k'-)3;?/"a #;](4S;6A >9*P= %%)3;D"a ,<(5 #< "6;KdJ 3 5 B,) %BO k'- )3;h)#'P? ;& 3hV #"5 #$) "6; %

! ! !

HJk4,;$) ARd+) (4S;6A >!'W)%Bj) j Q6;) ,A QF)#'L%) Q(&8 6 5 #" Φ-' $) * ,Id+K5 )3h7I"$)Q)?%BO >)/E4S; 'W)3;! %D)#':5 #N' $) 4,;)34S; %A26

NB,%$$) A)Jh ;& 3+3 #"5 #$) Φ-' $) ! 3\ "6;9*>5 #:"$9 %+) ,"67KN%) Q(&

6 %%)3;"a ,<(5 #<Φ-' $) /'-)3;\I& 3%PHJ5 #$ )D%)3 $B, %V*G)#'%) ,;V*, 3\,$

$ EA)VN4,;%$ ,I #"$&)]E"$)9d%Φ-' $) %

%;TdJ 34S; 'W)3;A%B*#6"6"Vd 6?%)3(4,"$\A)QB,V* BE&! "$% 5 #"679%\4M; '-)3;A%B ;:)E4S)34 ,"a # hB #& ?;,;%:5 #+6(4,"$A > ' $) Fu

*'-)3"6"$)9d%B >7 (,%Bk4S)3 >I 5 #"67G$ ,<(

Φ-' $)

φx = f(φ′r)%

9 S\% *#4S; 'W)3;! %+d 3 # ,6:<))QB? ] #"6"9 3%9*3(G%4,\"a #;< ,2"3 4 B ,2!#"$ /0 9 3% %1_8$ #"$)]Q$B, Q5 #JL%) >(G&8 6 K %%)3;J45 #F%+5 3N '"!"$)bd 6"6"M;& #V*"$9 3BG ,< )], k)#'UdJ %7GN)(6;, Q)3;I%)3(4,"$"67="66( 5 #D ,)3! #) O% ,< % 6(4,"67k;A) Q ,</T%I BO 3%%4, ,<= #"6" @ )9dNb* 3 '-) B Q7F?%) >(G&8 6 K ;& 3V #"5 #$) "6;T$ )3E& #$ '1 3)3;7*M'W)3;8d)k;9 3) X_%)3(45 # ,"$( Q;A%BGa #A4Ld) ,"$BSL;<> #;B,%B 3N%)3(45 # ,"$V*5d ,$$N5 #;BG"67= 3%%4,& ,"$E'i;)3 & ,6"66R7 Q$d 4S)3 >9*M B=;dJ 3)3I D"$)bd+;&R #4,4,;) (G6! #]%h 3 #6"a ,"$E'W)3; # $ T) SL4,;% >%B %

H%h9 3a k k/t1 k/t2 k/t3 !#"$ aa $ b

!!( 4 7 $

, !-"3 /0

, "$ 4 CDC J C $ % J % bb % b $'( !#"$ $ C ' $ 56 246 C $ #"6")3;

B4 ! <&8(0 ! V 7#!!(Q<J:?(*!'48485#$L>= (0&(0$ ! V 4D4!Mf&?NF4+$I4 (0$.:!!D$W-!END< (0&!?[$?%5$?(* 8(0?(@

a'(,>#R 3;4 &% V(/<%AN

k'(,RLX D&C

?%V(1($ !# !LX,;-!$?N 7#!!?%I LM,)4D:&(0$8=! 4!8$$,5@k/t1

'(;$,X7L!! .R4F$,>&.,?% !8E,5Nk/t2

(C$,>7L!! .R $,α= &.,G4!$, 4D%

k/t3(9,"7L!!P.;T,

α4D%I&($!.,4!8$$,

H%h9 3tα tβ tαβ ts tt tns mmax !#"$ C ' b CDCa bb C b $ b b $a a

)!* )+,!-" C ' b b J b a !!( 4 7 C '#b C C C&% C 8 8 ,2!#"$ a a J b Ca , !-"3 /0

∞

, "$ 4 b J a?C ' C ($ J a ' a $DC b '( !#"$ b ' '#b C 56 246 ' C $ b $ b

B4 ! 2$<:"2:?(*!'4":88L>= ($($E !8V 4!Mf&&N4+$C4 (0$.:!4!8-!$&$DN4%IV1$,G$,"&($!14$,) (*8[=!4!4$5(1X*MLD)($&.,G($3;!>&@tα

'(,>$>>($&%Z:&α= $84N

tβ'(C$,X$(0?%W:&4$

β= $84 T+$,MW4X&.,?%

41$,&1&($D?[ !8C!'&(SV=4%tαβ

'(9$, "($&%G8.(0?[α=64%

β4$4@

ts(C$,R($&%W3$<Q*MLD($&.,PN

tt'(/,>$4!>(0?%W LM5$,>:?(*;!"&(0(

%tns = tt − ts

'("I!V9C$> 3% 8 ,Q4D:&(0$8 !R$&(0H$,$>)VF8!'%Z(0$!!2.478!G 1f&= $>C*MLD)($&.,IV98(=!8#$?%A@mmax

V98(F$," R ,&G!!4$&%PN(1($I< ,:; 8:8@B=, !8M!$8 g]#^_:` \ X$?(*/&($ ,%J$ 3" !&I E/%'%G4/!:;!&54+$&(0!.4!3,8(&@

H%h9 3tα tβ tαβ ts tt tns mmax !#"$ b $a b $ aa bb a '(' a a b $

!!( 4 7 b C b b b C&% b , "$ 4 DC $ J $DC b $a $($ ' J b C C C ' b ' ($

B4 !-a ;9.,α= $8@!!P.4 !):8!5,?%&(=,!8;$,R(4"&(1YBH !#B@8@

α&.,J,D%W!0$!O&:;8W$,>($4!! Z>^#^ k ` #Z ZC&($ O$,X&% (0&f%XZ*X\]-^_b`($R?%

%84$?%Q LM>$,;(0?4..,$>8NLV1,!;$&$7 !MX!0!;,D&&%JV1E,Q,/!'4& g_:` Zij#k42V ,L$?($($8Q:8R 8( 4D?%$",C(4/&.,/7M(&@B=, g]-^_:` \R(0$!!O%'%46$D$CV1E,,"!E.(1421&:8@

H%h9 3tα tβ tαβ ts tt tns tmm !#"$ ' C ($ ' C b bb aa a?C J ' $ b $

!!( 4 7 bb C Ca a $ , "$ 4 a a $ b J $($a ' ' J b Ca C ' J a '(' a

B4 !G ;98.,α= $8J4%W$,>$?(0!E.(/ *MLD(0?4.., T<78M?%Y LMYI(0$J,8(0, % !8&%5<

, $,J&((0( $,4α4%

β4:8>$?%<$85NL%>$,C:8#$LF*M#3#V:@ B=,C($4!!2Z>^#^ k `

Z Z*\]#^_:`#&($ (0$!!T($V !0!)., T 4%IEV=(18% 4$&!M 8(*!&8%MV L$,">?% XZ[X\]#^_:`8&($V :8>$?%J R($&%(NLV1,'.,5(14.4 !CV1E,I, $).,!8&%J #M ? ABCPG,

tmm:8!>

T !?% D(RZ*?[$$J$,4X,54!'(0Z.,&%V:@ZB=,G!$8hg_:` Z(ij-kJ&($I(0$!!=($3&$?% < ,!L !8!#%?%E.(1,#(*:8$&&@

_R!dJ 3A'-) B.5 # T%BG< Q6"6"$F%)3;%B Q7jO%) Q(&8 6 0 %%)3;!45 #2 ,)3! #) % d;E) k'-)3; "$%$) O(4,;%&$) i4S)V ,"67F%)3(4M)V&%Bk =45 #(G $) %)3(45 # ,"$Kd 645 #; & %

I%9 #"6"6 ,<I; # ,6;A >U'-)3;%BG< @ )bdc %$) C&% $G*V N&5 #;& 3;% ,<I'-9 #,;\)#',\4,;) ,"$$k5 #O45 #; O%) %4,5 #"6"67 ;9 3B ;6<VQ&1)1"$ 'i0& #; ,<j'W;)3 )3A )B,V*d ,6"$(G4,;%$) =;9 3B "$ 'W&1)1;6<V>9*T B & #;F'W;)3 %) Q( )B, T03 #"5 #$) )#'D #"6"S)36"$IB,)bd )! 5 #" )QB,%"$%%B0 B! #&%B*M&)AERd+)=(G4,;%$) ) ,"$B;9 #"6"67 S #"66<%B "a 3N4)]"a 3N4 d 4M%%B='-)3;N%)3(45 # ,6"6687 %_ B,%%B*, 'P;%;$ ,<!) B (,%9* B , M; ,<F4 5 3 QdJ #;B,

S = asn :: tsn · · · a

s1 :: ts1

M = amm :: tmm · · · a

m1 :: tm1

6 S%%)3A%h #4,45 #; QI5 #9*G'-)3;N)3A )B,

•_1')B,\'1 #6"$ ' :8 '"h)B,%

ts1"h)B,%

tm1*3 ]6U$6; )3P&"$%%B*

)3; )3N! #%B* )S B

M #;T %)3(45 # ,"$T'-)3; )B,(%

•_1'

as1 6= am

1

* 0) K (G$4 "$%%B ) ,"67%) > Q9* BD)3;) ,"67O #; ,% %S B

M #;L %)3(45 # ,"$ '-)3;h >7 )QB,E # #"6" #%

•)3j4(9 .) ,"67 "$% )QB,%]5 #! #;k&,6"$BG; )3;A #; ,%A)#'I45 #; Q % _1'

asn ::

tsn · · · as2 :: ts2

$L %)3(45 # ,"$(d 6am

m :: tmm · · · am2 :: tm2

'W)3; B,%"a #;%B^45 #; >?)#'J) ,;)QB,V*G C B

S B

M #;T %)3(45 # ,"$(%

HJE #;<(,A QN<)Q% ) = B& "67* >6"mk)3;

nk4*d ,$&;h$"$%9*, # d ,$

4S)3 >N;D #; )(A)3;E)34,4S)3;,6$%N)A%) "B,E %)3(45 # ,6"6687 % h #"6<)3;6,*5 BO3 #"5 # ,<!'W)3;h ]N)#'P4S)3 >a #";%,"6N874M%N 9 3B)#' ) ) "6<)3;6,

incompatiblePaths(S,M,Ω)

i← 1Ωs ← Ω

Ωm ← Ω i ≤ minm,n

as

i 6= | asi 6=

I;,; 9B am

i 6= | ami 6=

I;,; 9B as

i 6= ami

;,; 9 Ωs ← Stest

tsi(Ωs)

Ωm ← Stest

tmi(Ωm)

Ωs ∩ Ωm = ∅ ;,; 9 Ωs ← Raxis

asi

(Ωs)Ωm ← Raxis

ami

(Ωm)i← i + 1

;,; 9B

HJR (G$N4=' $) I #;T

S ($ 4 ;;%B

Raxischild(Ω) = n ∈ Σd|ω ∈ C(n) ∧ ω ∈ Ω

Raxisattribute(Ω) = n ∈ Σd|n ∈ Ad(ω) ∧ ω ∈ Ω

) $B,;h)9d T%) Q(&8 6 K %%)3; "a ,<(5 #<T%N%)3(45 #;%Nd 6k,$ %J'-)3; B (,%N) ,"67 \HJE %%)3;N"a ,<(5 #<E% d 6"6"% '


dRtestam

m(tmm) · · ·Rtest

am1

(tm1 )) ∩ L(Σ∗dR

testa

pn

(tpn) · · ·Rtestan1

(tn1 )) = ∅

- #"6"+Rtest

··· (· · · ) #;("$ ,<V "a ,<(5 #<% #%U_ c)3;?d)3;B,9*U"$ ,<V

(min(m,n)) (,%K #;

! 97 ST %)3(45 # ,"$K k? %%)3;N"a ,<(5 #<%4,;# (G% #; )3 % "$)D%) $B,;J)9d ; $J%) ;%B/'W)3;J&k (G$&1('(!45 #k(G4,;%&$) 9 #;"67 %Q_RI5 3L) ]& #KA)3;D5 CD"$ ,<V^)#'\](G4,;%$) * BC;& 6$) E #;"a S"$%B^d 6["$A >D)3;? #; , 5 #A% % ) $B,;?d 5 #T5 #4,4M ?d ^;; ,<O&[8d) ,)3! #& G* B Q;% ,<= +HJ5 # S%%)3A%h$B, Q$9 #")

incompatiblePaths% ),*,'-)3;h

6(4,"$?9 3T)#' (G4,;%$) N)#'P # 5 #""$ ,<V*,L8d)!%)3(45 # ,6"6687k%h #; # 5 #"6"67=4,;%$(%HJ5 #I"$9 %L ,)3! #& Ad 6C) ,"67 * B 4I 3h9 3&%)! #;<(K M) ,Nd ;E7/! 97=6"6" 5 #;4S;N5

incompatiblePaths* ,

• h tr $N # , 3 #"$ Qh) h

tr• h

tr $I # , 3 #"$ QL) h tr h

tr ,<V %

N) LA)3;E9 3E)]%

'-)3;U&)3A:4,;# (?45 #](4,;%&$) h*# (?45 #D(G4,;%$)

r*3 (G$

a B )B,\%

t% ) $B,; ,<

;<(,"a #;I;& "a #$) *,d+K9 O #"$)AB,)

• ha t1 tr2r$N # , 3 #"$ QN)

ha (t1 ∩ t2)r

•"$9 3BG ,< tr 5 TEe #AL;& "a #$) C 3 r

Bk9 ST;64,4S%B %

HJ(t1 ∩ t2)

)B,T%L$h k Q;%$) )B,L% L;%,"6N$h ]& B #;BU^P #)B,%9*>)3; % ! ,;B 5 #AJ%9*V '-)3; * #"6"5 #AJ%: B * B VJA)3;N 3B V %%B5^P #L6 %: #4,4,;) (6! #)5 #AE% k;<(,"a #;h;& "a #$)*5 B9 SL;9 #%BO 3N& %

&)F'W)3;E%)$B,;& #$)] S) ,T6;E;<(,"a #;?;& "a #$)*d+A(6<V>K 3Td"6"+%)$B,;D #"6"45 #(G4,;%$) 3\%)3(4S)V%BA)#' ) t * t B 4 % ,;;A)3;V* #;<(,,<A M) ,J"$%&1! #%)3(45 # ,6"66R7S8d%k8d)D=(4,;%$) F"$%$)c B[ /45 #;*dA #;?'W;%D)=d 6c #;) B0D8d)O #Ld 6"6" 6;ED;<(,"a #;%D)3;

incompatiblePaths! !)#'h Q7[4M%a #"\45 #; 4,;)34S;$% * B^d+F9 c;A)

Q7F"$9 3BG,< ]4k'W;)3 T45 #;,6hA9 )3,,<D*! (% ,AL5 #h&)3AEf;IH

q′$ M)3 "$%& ,"$? Bk! #&5 ,"$


dR(S)) 6= ∅ B


dR(M)) 6= ∅

,AL5 #NincompatiblePaths

%J'1 #6"$%Bk)(B,%N%)3(45 # ,6"6687

incompatiblePaths (S,M, q′) = unsure

BO #"$&)(5 # T;<(,"a #;N%)3(45 # ,6"66R7%NdJ 3N5 #;4S;9*5 BB,%%Bk%)3(45 # ,6"66R7


dR(S)) ∩ L(Σ∗dR(M)) = ∅

%

kS]("a #;<%

k′ [5 #E( (0(G4,;%$) Sk′ · · · S1 B

Mk′ · · ·M15 A),"67

)3; (,% %HJ6;N;<(,"a #;N;& "a #$)L #;

R(S) = R(Sn · · ·Sk+1).R(Sk · · ·S1) B

R(M) = R(Mm · · · Sk+1).R(Mk · · ·M1)

HJ;?$N (;,<a ∈ anld(q

′) : a ∈ L(Σ∗dR(S))

*5 Ba5 3h ] (

ak · · · a1 ∈ R(Sk · · ·S1) ∩R(Mk · · ·M1)i; #;<(,A>

HJ*5$J STT9 3E5 #a|a| · · · ak+1 6∈ L(Σ∗

dR(Sn · · ·Sk+1)) ∩ L(Σ∗dR(Mk · · ·M1))

%

BO #"$&)A)T)#' l#" 9> B-/8!. Q:8,%B,":"(!./ q $+( q q ': B') 8 !-, *-N(!-0 ,"%$' < !&'&)( vxRt !*M)7) ! *)3 08!> %B,"-,"> q !-8!./ ,+

- C

Sigma

Sigma d*

d*

d*E

L(R(M))

L(R(h))

8hAa !!(0$.8IΣ∗

dR(h)E∗dx ∩ Σ∗

dR(M)

•"6;

Sn · · ·Sk+1 = ε)3;

Mm · · ·Mk+1 = ε g(4,;%$)*(& %7

M*D5 3^ (4,87 4,;# ( Fd 6) , %,< >7,,<*]d+ &

3 J4,;# (9 3B*# BT6;& "a #%) Σ∗dR(Mm · · ·Mk+1) = Σ∗

dR( ) =

Σ∗dHJL4,;# (k6(4,"6$9 #$) S%%)3A%

a|a| · · · ak+1 6∈ L(Σ∗dR(Sn · · ·Sk+1)) ∩ L(Σ∗

d)d ,$O%)Q;& 3BG$a ∈ L(Σ∗

dR(S))

•)3; W& 97

Mm · · ·Mk+1$L)C?'-)3;

h *Md ; h

5 3T #"$9 3N)E4

R(Mm · · ·Mk+1) = R(hdescendant :: node()) + R(hself :: node()) = R(h)E ∗dΣd +R(h) ∩ Σ∗

dΣd_ Q;%,<d 6Σ∗

dR(Mm · · ·Mk+1)5 3 )h%P)

Σ∗dR(Ss · · ·Sk+1)

# #"6" V% 6<(,; - 'W)3;h O6"6";& #$)* B=d? 3,A%Bk5 # a ∈ L(Σ∗

dR(S))%


dR(S)) ∩ L(Σ∗dR(M)) 6= ∅

#<> #D%)Q;& 3BG$,<T 3&,(4,$)] S) ,J %%)3;U"a ,<(5 #<% S,<5 #;4M;5 incompatiblePaths

%

I9 #"6"67*,d+E6"6" %%Bk)A)bd 5 #

q′ ∈ S(S, q) ∩ q′ ∈ S(M, Σ∗d) ⇒


dR(S)) 6= ∅anld(q

′) ∩ L(Σ∗dR(M)) 6= ∅

)3"$B,:)(J6(4,"65%B!(4,;%$)9*V)5 #\ ;& 3\V #"5 #$)A9 (;4,"a 3%N ,)3! #& T>6;"67* ,T5 #T) ,"$B SK;& #;T) Q$) % "$&),*5'-)3;E )3",D45 #^(4,;%$) id+A #;<(%B0),"67'-)3;;"a # (4,;%&$) S)(%%% *

incompatiblePaths9 S:! 3B,+ 35 #;4D 3:;<(,"a #;U"a ,<(5 #<

% >7=5 ,<!6N;,; 9! 'P6N;9 3&%hT"$ 'W&15 BB )#' &)3",E(4,;%&$)*, ')3;h(G4,;%$)O$ "$),<; %A25 #N$JT6(4,"6$9 #$)C)#'U,$ (d9 %& '-)3; L4,;%$$)O)#'PL)Q)3" A["6"1*'W)3;I (45 #;

h

r? ,)3;)#'UK87"$%%N h5 Ed Q%BO)!"$%h),"67 )QB,%

5 #N5 K O %%;7=45 3,<(h%9*5 BA" %N45 3N

r% %

HJL& #$L ;& 3$)*G)9d;9* 3%%4,JhR7Q4S)#' >7 )B,h5 #J45 3&%\r%9*, B!5 3

#&" g %%)3;T5 #?45 3%Lh%THJ(),"6709 3]dA9 [%)3A ,4^d 6*d ;A

- b

incompatiblePaths #"6<)3;6, d 3 @ !5* ,LD %%)3;"a ,<(5 #<]%%) ,"$B0"66(5 #A

@ )bd )#'f;IHq′*S$d

SB,)Q%)3T^"$%

q′*)3;

MB,)%)3T0! #

q′5 #T9 3

d 6"6" ST9 ,<V>IE ;& 3hV #"5 #$)"6; >7d %7 %HJ %)"$)()T #"6",,$P$U5 #;$)"$)V)#'54,;%$$)(("66(5 #,<K %%)3;"a ,<(5 #<%Q6;"67A'W;)3 @ )bd 5 #"67G$QI6(4,"$;J ;& 3JV #"5 #$)k B

incompatiblePaths%\5

K& #AE4S)9d; %NHJ,$hdJ 3N' ,;;I%)3;;) S)3;& #%BC(4,6;$9 #"6"67 %N; ;%,"6%B ' W(G;A"67 ; M)V& @ )9d <V;& #4, B&,(4h'W)3; #"6"%h9 3%",<!K %%)3;h"a ,<(5 #<K% G %,<!

incompatiblePaths% %

A[S"6$Td? #;T ;N)]4,;%&>h,$QBk)#'=^P #O45 #O%)3(45 # ,6"6687k% %

# #

(

(

- '

g( #(4,"$k)#'L C%);(5 #(d 6"6" 9 C4 ,;$) 3 #"6$B #$).;;)3; ,4,4S)V=,4 ,:"a ,<(5 #< 5 3:NB,%"a #;%B!"$AQ:874M% L B * S)3(d 6 AB,%"a #;%B &,6"$B* d ,$&0 ,;C5 3 /B,%"a #;%B0 # %?)#' &,6"$BG; %LHJ*r1(6<V>h45 3 "$AQNd 6 ?45 #;QN) r3

% d $&V*r2(6<V>N45 3&

"$A>d 6 45 #;Q) r3% ;Q6AV* :45 #;>"$AQUBG$$)

S8d+%O "$AQ @ )bd ,<!) r3$ ! #Q& #%B 5)bd+;9*) ,;I& #$E 5 #"67$

6:$\"$)V9* ' - "' " r1

r3 %

r5)? #4,4M9 #;9*G #"$),<?d 6=

#4,45 #;> @ )9d 'W;)3r2

a r3)

r4%:HJL;%,"6N$N ]%)3(4,"a #Qh'W;)3 ^`IH V #"6$B #$)

5 #?/,6"$B 874M $?6"6"$<> #"\'W)3; # ,*P B !'-)3; *Uc) ,<V ,$('( ,4[d 6"6" ;K5 #4,4M #K;>6A(% 5 #"1*,$B[)#'N4 ,;$) ?;;)3;K! %7 S%)G' ,<())1$B,; % 4S)V ,"$D6(4,;) A>K)#',$L; # ,6;%K #& 3,,<A)3;]G'-)3;! #$)[)k%)>(GT874S%)#'%BG< @ )9dN9*, B ,<K5 #G'-)3;! #$)/'-)3;J5 #;4M,,<]"$%&1! #&%)3(45 # ,6"6687 ,)3;Nd)3;B,9*,6<V>,,<FL"a #$%?)#'P (,%Bk4M)3QI 5 #"67G$ %HJ(5 #;4S%L"a #$%A9 BG$B #(d(6! #<V%B^d 3?)()#' <' - - '' " - - *;4,;%Q%B. 3?;<(,"a #;]"a ,<(5 #<%( Bg)3;B,;%B Q7["a ,<(5 #<F"$) % . "a #$%kd) ,"$B 9 kO%)>(G!874S%A)#'T @ )9d 'i;)3

r1)

r3)SkBG$A'W;)3

)Vh'i;)3r2)

r3iI'W)3;A;r %%)3; ,"a ,<(5 #<L%;& #,"67!5 3 ? 3 BO"a 3h7 S)3"O6I;,<5T"a #;rI;,<N5 ] *5 BE8d+)BG ;>874M%d+) ,"$B C,; 4,;)345 #<> #]BG ;>T%BG< @ )bdNL) ,)#'

r3*M"66(5 #,<k

4 ,;$) K;;)3; % ,?& ="a #$%! #"$)5 3E& ,6(6<VQ9*U9 ,< =4S)V ,"$ )>;&(5 #$) )#' (,%Bk4S)3>L 5 #"67$ ) h%)$B,;I (f;H B,%"a #;%B0 3h (B,%%B Q)#'6" '*d 6 F! #&,,< ?)#'J;%,; ((4,"a #A;,"$% #% #$% # - %) ,"$Bc)3" ,$&G'-)3;5 #"67* )A!$Qhd $B,,,<!)34S;& #$)O(G$J'-)3; ;<(,"a #;N"a ,<(5 #<%9* )] #4,4,;) 3 d 6"6" )3 d+)3; % )3;A9 BG$B #k$! C ("a #$%) ;A"66(6%B 1"$,<V2 %%)3;("a ,<(5 #< (,%9*&D5 #P ' ,<T (K"$,<V("66(6 C)3;UA)3;JD) ,;:( #(4,"$V* )B,%U;4,;%>%B>7 % % M%%)3A BG$,<(,$5 ,"$k'W;)3 % % )B,% % C D"a #$%Td+) ,"$B&)3" L5 #" 'P)#'P) ,;N4,;%$$)4,;) ,"$*,! ,<(6N4S)V ,"$)((,"B,@ )9dN)#' % % ) r4

* ,6"6" )3)#' R %%)3;%B )

t5*,'W)3; ;9 3)h(4,"a #%BO %%% %

)3;5 #"67*+1QBj%);]4,;) )?Q,<cF4 ,;$) A;;)3;(B,%; S%B ;k&%A)^)%,;()Q)0;& #;"67g)1) 'i7 k;9 3%B.%)3(4,"$(G687j)#'T R,4M; "a #$%%9*J B;Fd+; )^ 3B,BG6$)5 #" 4,;) ,"$A]'-) B F;& 6$) 'W;)3 "$)Q9 #"'1R7Q4S=) ,<V"$874SK"a ,<(5 #<%?^,$T;%4S% %5_1'\]($&,<kd $B,,,<O)34S;& #$)[$LQ%B*U)3;L 'J6$L(4S;$%%B05 #E4 ,;$) T;;)3;E)#'+,$ QB0%)G' %;L)#'J /))3" 5 3%B^)0,$ #"6<)3;6,*5)T)#'PT"a #$%T6<VQ,,</%&, # %I%) ,"$B SE 3B,B,%B %

$%! ! n

U6;9*,T(GB,%B45 # (4,;%$)p

p = c(match(ri(i)), select(i), q)

$N"$9 %B ,4 >7=L' $)fold

*GG'-)3;! #"6"67

- $

H%h9 3ta ti tfast tcomp tnc mmax !#"$ $ ' JDJ b C b % '

)!* )+,!-" - % b J C &% !!( 4 7 - % J J C&% 8 8 ,2!#"$ - % b a C ' % $ , !-"3 /0 b J b - C '#b $ ' - b C $&% C , "$ 4 b Ca b &% $

B4 !#A&0<8$: 42(0&!?[[= ..,G4$ !*M$?(*($Q4 (0$.:9!4!8GR ?%GV1E,incompatiblePaths

N!(0$!M"(03T"=4%"&>8$M;3$<: $,68!'4T:?(*T!'4&(0&@ta("$,($&%Z!4!4$

φa

Nti'( $,($&%Z!!4$

incompatiblePaths4%

tfast'( $,

"($&%G!!4$φf

T<V1,'.,5$(= D$,54H$,"$!#D(*V:@tcomp

($,R$>X($&%Y3$<I(*U) $,>:3:E8 4!M($((0completeCoverage

Ntnc

(,/D(0?%D&0<8$)(0$YA 4O$,C:8D$$J4!M(0'( ($

completeCoverage4%

mmax

( $, R ,&G($8: ($&%AN&8(0$?%JG$,)(4 V9MQ8(9<=,)4&(0$89!'4C$&(0&@

• ($N4 6(A%BGa #"67F'W)3"6"$)bd+%B Q7 (G$N4h #; M)3k;A) %Bk'W;)3 p

• 4h #;L;A)%B'i;)3 p

* 3 "$),</ 3 5 # d 6"6" )3h! p(4,87

"64,,<incompatiblePaths

(,"B,EA)3;TG'-9 3 ,"$ @ )9dN9* >7k%); V # "67k;d ;6,<F&)3Ap)(5 ? ,$%; ()#' 4 %

HJL'1 3 @ )bd #"6<)3;6, $

φf (m, i, q, r′) =q′ ∈ φa(m, i, q, r′)|incompatiblePaths (fold (p),match(r ′), q′) = unsure

! n !

I ) %+5 3 S%/d4,B,; ;,< Q6" )bd )>(G @ )bdN\5 # ;+! #;a #"69L #;Q6AV* S%9 T7k #;T);;$B,B, >7=%)>(G @ )9dNh)()3;N(4,"a #%Nd 6 ]%)3(45 # ,"$A)B,V* !%)3(45 # ,"$]! #&045 #;c BC !,6<V;L6(4M)3;L4,;%%%B,%()3;4,;$)3;687 %;%%BG"$%)& 97*, @ )bd 5 #"67G$+5 #B,)% )3J 3%%) Q'W)3;,$d 6"6" SN!$Q"67!4,;%$V*, B=%)G' ,<'-)3;!; %UHJJ ) %Ud 3PB, '-;;%BD)h;V* S%9 J KQ;)QB&$)A)#'6Ud 3)3 %%%& #;7'-)3;E 0(G4,"a 5 #$)[)#'+ 5 3$ @ )bd #"6<)3;6,A9* B0d+) ,"$B0B,%%B1) I'W) ,"P6Ld 6[ ^"a #;<;Id 6"$B,;%h)#'P%)%4, % ); V # 687O M?! #>& #%B*SA9 ,,<F5 #I6 S?%)$B,;%B ;7O9 #; ' ,"6"67k5 #$9 3%J #;h%);%B* S 'W)3; 8 ' - F%BG< @ )bd $:'W) B!) Sh);;$B,B,k%)3(4,"$"67 Q7! ,6<V;&14,;$)3;6R7 8 $ ' - '" @ )bd _8'UT&5 #"6"$,<; @ )bd rN& #;<N! #&O45 #;! #&%I),"67k &N)#'Ud 5 # T&5 #"6"$,<%B @ )9d rh& #;<N! #%b*G'W)3; ( #(4,"$V*,;T(6<VQ ML)3AT9 3&%d ;?6NB,)Q%)3I);;$B,K 'W;h #"6" %

- a

_ kE"a 3$E %%)3;N"a ,<(5 #< @ )bd #"6<)3;6,*5%)3(4S6$)C 5 #"67G$ dJ 3hB,)? 3

match(c)$J4,;%BG$9 #-'W;%>* B

Σ∗d.R(α) ∩ Σ∗

d.R(match(v)) ∩ anld(q′) ∩ (Σ∗

d.R(match(c)))c = ∅

d ;v$?A5 #"6"$,<%B @ )9d rK& #;<9*P B

c$E/5 #"6"$,<;rD& #;< % J)3 #"6d 97K5

(& #AD) ,;%A B0%)>(GT874S(%THJ(& #A>T! 97 S?;9 3B[ 3 )3;T;7 %)Q( )B,5 #N! 97ST"$%%B Q7/T) ,;%V* ' @ )9d ! #%

match(v)*6h #"$)]! #%

match(c)%

_8'L5 #"6"$,<;h5 3 ,6<V; 4,;$)3;687*5 #"6"& @ )9dN )DT&5 #"6"$,<%Bk& #;<N9 MLB,"$%B G 'T&5 #"6"$,<%B @ )9d 5 3N K& #;<NBG S;QJ'i;)3Y5 # )#'T&5 #"6"$,<; @ )9dE* , S)3F5 L& #AE4,;$)3;687* DdJ #;,,<F S) , ,;%)3" %Bk(4,"a #K%)3(4M6$) $ $%B %_ ) ,;S)3;I)A;A)] ,)3! #& !'i;)3 @ )bd 5 #"67G$ #"6)3<;9*M;?$ ()3; '- #"6"d 6%)3(4S6$)O 5 #"67$F`)9d 9 F5 # SB,)hd 6) ,N ,)3! #& HJ d+;J"6$%\k KB&5 #"M)#'

incompatiblePaths #"6<)3;6,*d ,$Od 6"6" ML4,;%&>%B (G %

;) ,"$ > C U^P #45 #(G4,;%$)

S* D45 #;

M* BO ]

Ω)#'Uf;H9*Gd 6"6"

M! #&O;7

)B,/)#'h 874M/Ω5 #

S9 "$% HJA;%,"6K$K)/)#' 9C)3;9B *d ;

$L%)" V* B 9BF$ )3 % incompatiblePaths

*M6;& #$)C$L);K(G4,;%$);;?)3;B,;9*5 B)]$ ?4 , M;,< "6<)3;6,

completeCoverage(M ∈ XPathpattern, S ∈ XPathpath,Ω)

M = amm :: tmm · · · a

m1 :: tm1

S = asn :: tsn · · · a

s1 :: ts1 _8': >7=4O)#' M5 3 4,;%BG$9 #%

;,;9B M

5 3NA)3;E4 5 Sm > n

I;,;9B

M

$h )3",? BS$)3 I

;,;9B i← 1

Ωm ← Ω

Ωs ← Ω i ≤ m

Ωm ← Stest

tmi(Ωm)

Ωs ← Stest

tsi(Ωs) Ωs\Ωm 6= ∅

;,; 9B

am

i 6= asi

- J

;,; 9B Ωm ← Raxis

ami

(Ωm)Ωs ← Raxis

asi

(Ωs) Ωs\Ωm 6= ∅

;,; 9B i← i + 1

;,; 9

d ;

Raxisdescendant(Ω) = fix (Raxis

child(Ω) ∪Raxischild(R

axischild(Ω)))

Raxisdescendant−or−self (Ω) = Raxis

descendant(Ω) ∪ Ω

HJO$B,9 ^$() %,S* 4 Q7.4j'W;)3 & #6"I)*+d ;FM

! #% #" )B,R7Q4S]5 #

S! %70"$% %;I)B,]%E #;A #4,4,"6$%B^^(e #A]d %7^ 3T0)3;! #"\ ;& 3

V #"5 #$)* ,? (G$T4? #;];;&%B %(HJ]%Td 3K)3;6<V5 #"6"670B,$%BC'-)3;E 3? /'- 39*S"$)9d+; #4,4,;) (6! #,< R S; '-)3;= %)Q(&8&6 0;<(,"a #;O %%)3;="a ,<(5 #<0% - 3

M

U6<(,; C&% *5 h #4,4,;) (6! #,<F6 S)3='i;)3 S)D B M"$)bd %HJ,$(%(4M; '-)3;A] & S;(5 j %%)3;A"a ,<(5 #<k%9* 6(;& #(4,;%$$)* #"6) ,<Vg,$D6A!dFd 6"6" )3 ,;,<0 O4,;))#' * ,]),"67c& #/5 #K6D$?1; ;& 6$)' $) '-)3; '"' 0"a ,<(5 #<% % _8/) ,"$B S9 37g)c%;, )#'T,$A'W)3;A45 #;%)3(4S)V%Bc)#'N),"67 B (G%9*U B[5 #E!<;& #"\5 ,6"66R7c)#' ,)3! #)Q;%$) %N)]4,;)B&%K >7,,</%)" T'-)3; / #"6;9 3BG7=5 3 S%)bd %> g =(4,"a #1)?,<^;$)

i*U O%)>(G?874S

q′ B^8d)O(4,"a #/;,"$%

r1 6= r2d ;r2 ≥ r1

*Q;T #;hRd+)])34,4S)3;,6$%J)K%)"B,5 # F%BG< @ )9d2'W;)3id 6F%)Q(

R7Q4Sq <)E)

r29 3BF)#'

r1*)3;9*> ' #"$)

r1 ≥ r2*Q5 #+;I$J ,;%)3" %B=%)3(4S6$)

4,;) ,"$

%completeCoverage(match(r2),match(r1), q

′) = true*#A9 ,,<T5 #

r2d 6"6" 3%%4,\ >7

@ )9d 5 #r1d 6"6" %

&%completeCoverage(match(r2), select(i), q

′) = true*A9 ,,<.5 #k;^! 972(G$

%%)3;h)#'q5 #

r1! #&% B

r2B,)%)3N! #&* ,I )QB,Ld 6C %%)3;

d 6"6"))3 S="$%%B %cHJ="6 "66))B )#',$D%];,;,,< ^d 6"6"J;9 3= 'I45 #($)k$ %B)kE&"$%$) %

IA),<]%BG<%+d 6"6" )3 )%)345 #;BG9N<;& #") B %)#') ,; (,%B/4M)3QJ 5 #"67G$ 'W;;A) 3 #")#'N %BG< @ )9d d 6c%)>(G @ )bd

q))3A](4,"a #V*

q$?6"6""$ 'WE[A%)Q(

J)#'I(4,"a #V*G4M)V& ,"67A);&-' ,""6"6,<(hQ<V;687=%);& #>N"66<V>"67 % 6(4,"$I5 3, %,<( #<> #+(4,"a #%+F4,;$)3;687/)3;B,; 9 !A'1 3+"66(5 #T #"6" ;A)V #"$)#'%& ,"6$%B

-

@ )bdN9*, B!,;I5 #+%)3(4S6$)F),"67A"66(5 #% d %BG< @ )bdN9* M '-)3;I ?%)>(G+R7Q4SNdJ 3)3;d $D 3B,B,%B %

! ! #I

HJ @ )bd 5 #"67G$ 4,;%Q%B6"6" )bd d 39*d 6='Wd (,%4,$)9*& '-)3;NfLH f]* , 6hB,)%)3!$Q"67?4,;%; +\6(4,"$+B #& N874M%U)#'P^ ! 9` Q,<L 1<V;& #%BD874M7G'-)3; R6(4,"$ R7Q4S% WB #& L874M%# *VA)QB,"6,<D #"6",( )B,%\ 3N,<V"$))QB,JR7Q4S M ]$));) ,<V^ 0 #4,4,;) (6! #$)S;K$ )!4,;) ,"$ d 6 =6(4,"$1R7Q4S%B B,%"a #;%BC"$A>)B,]874M%b* ,d ;?()B,%T"$%%B >7 )3; >7 #;! 3B,A%BG< @ )9d %)Q(ER7Q4S%9*V #"5 ,"$]G'-)3;! #$)c$L"$)VTH\7Q4S]G'W)3;! #$)c$? 3)a #%B)3d 6]()B,V* ,Pd 6("$AQ )QB,J%)Q& #,,<E6 % ;& #"( #(4,"$%)#'M4 ,;$) ;;)3;L9 %B >7k,$Id+;T'-) B*S B*M #"6) ,<VC,$hdJ 3)3L ;7k4,;V #"$> QB )#':;;)3;9*6 dJ 3h%)$B,;%B&;$) J'i;)3 L4S;4S% E)#'&;N(4S;$% :HJ;E) ,"$B SE 3J'-d 34S)V ,"$T%)G' ,<!;;)3;NA%&& #<%h #;$,<('W;)3 ,$ Bk)#'6(4,"$TG'-)3;! #$)O"$)V %HJE&)3",$)O(4,"$)97%BOd 3N6(4,"67F) "] M kR7Q4SV*, ,874,,<A6I B=45 #;& #A;99 3&! ,874S >7D ! ,)3! #)/);:JR7Q4SJ;4,;%>%B* B])L;<> #;BA 3:BG ;>874S%\ >7Rd+) M /f;H+d 6FBG ;> ,)3! #& &%:H( )QB,%\'W;)3 ^ ! D%)3(4,"$(!"$A>R7Q4S% BD #"6"fH f ": #;\45 #;& #;! "%B >7#!$%

char∗"a ,<(5 #<&(%9^ ' $%!

! 6(4,"(R7Q4)*"+IB ' "a #;& ,! $)%q)bd- 6(4,". ' ."67/45 9d (B ' "a #;& ,! $)

q′ = pcdata(t)*d0 .!$

t = Dd(q) = Dd(q′)

!;! 1T! 97 )]B ' "a #;%B d0 .!$[B2 ;R7Q4)13 M)4!$0fLH f_ B ^ ' $%! G* ! ' ,!;! 5( ?45 #;!?)#'6!$%/ ,!;! )BV* B )4 ' )& , %%B7 7 M )B19*U ,!;! B ' "a #;& ,! $)% %1%B ) ' )3"$)3;! ,< % ' ' ) ,;V*8!$ 9 874 ,<5)3"! $) d0 6"6":$% 6<;$<!$%?"a ,!! ' >7 - ,IA);! )%E'W)3;99 ' $<! 6(4,"R7Q4)JB ' "a #;%B* )3! 6< ' +4=; '-)3;! ' 4=5 #".R7?d 4P) %; &%BK'-)3;P Q7?4,;& ' ! ' #"( #(4,"(%

&;& #">!87"1!$%1?;! 6<V<&;%B2 , );F)#'#4 ,;! $) %5;;)3;!1e #<&1/ S) !4,;! $)3;! .87 ' ) @ ' #A),<@(4,"a ,=;,"1A! , ' $ ,<[4,;) ' 1! ,<< %!; ' ! $)% % 9 #"6"67*!$%;=dA; )%V* 4!$% 6; 45 ,!;%hdB;D #"6"U)C!$% target '-)3;* ) ,<! 5 #"6"67D( ' "%! &(%\H6$%T4,;) ," d 4)3" &%B >7kB ' "a #;! ,<*)E!$% @ 7*,)% 874=T)#' '-)3;09 ' $OB2 ! ' & #;<& 5 #V*d0$ 6"F!! 6"6" ' )%! $B;! ,< #"6" 874=1E)#'# ) ) ' )3(45 ,! ,"Ad0 .!$G!$%F& #;<&"1H .I1! %

-

H 1! ' 4tf2 m2 tf1 m1 mg mDin !#"$ JDJ b b % ' $ b $ C($ C &%Ea

)!* )+,!-" J &% CDC($!!( 4 7 C&% $ - % ' -- 8 8 ,2!#"$ a ' % $ b - a, !-"3 /0 '#b $ $&% C ' JDJ C J J - , "$ 4 b Ca &% $ ' -- ' a $ b - - !- ! 7 C ' DC&% ' J b

B4 !Q#BFB=R4D%5>&MJ3$<:" * (0 V 4!8$$, :84&%I$,;4 ?+ABC @tf2%

m2

4 DV 4!M($(C4%Z R#!J!!&% ,&S($R<8 )!8E,5NO%tf1%

m1

$;,8($ 4<? ABC @mg

4%mDin

4 C&>8$MI(0&f?(142&% V .4,D(%5 I C($.,(*$D[$$?(=<1,R#$#[= ($D(0$ ! !4&(0$1!'4V!8E,5N$?(03&:$ !!M T<V1$,C$8NLC(.,>(*$:$&(1($ !&$M!E$$!)MV[@

7! #

H6$% @ )9d6<)3;! .!$ %%B ) ' ' )(4M); . (2%B=4S)4 6<)3;! .!$

% ' )+(&( %% .! &V*A)QB % .! & (2%Bj4S)4 6<)3;! .!$ d0 .!$φm ∩ φi

*+) ' 67' )% ' %B ' )+;) @ )9d <V;!#4$

&% ' )(2&( %%! .! &V*"A)QB H%! .! & (2%B 4S)4 6<)3;! .!$ d0 .!$φl

*SB,)4 ,<#/4,;! F .! &$(4%, ' )(4)! .! $)&672! 9*,)/!$%L;1.I)#'!$%S)&

C&% ' )+(&'B(A)B>%! .! & (%B/4S)4 )6<)3;! .!$ d0 .!$φf

*Q4); '-)3;*F ,<F!$%>$(4%,' )(4=! .! $)&67! h)#' ' ! $) C&% CG*)/!$%L;1.h)#' !$%S)&

A@ $ &D;%B& ' %B ! +B,$A)3;7 ' )(4(2 .87C)#'^ H @ )9d-67! ' )%! $B;!67 'W;)$#;B.67 '1' 4! - ' )BA'W)3;?!$% ,2"$ 4 1! ' 4 X DC Z ' $) ' &%B ' - ' )B ) % b ' )Bb*/B['i;)0M) ($ - ) &% $ )#'1$A)3;7 %H6$%;? )#$);?)#' 4,; ' ! $)*)3;2>7)4!$%;FdA3%1F)#'#!$% %d4#4,4,;)5 ' $ !$,!dB )9d)#' % _ .' ' 9*J4,; ' ! $) 5 %!! % 67)!;!$ X DC Z *d0 .!$6 .! 64? M <874)19* !$%D' ' %4T)#'B ,< (874=7%,<(#<&1# ,4,4S)3;!%B %H 1!\)F!$% d0$) ' ) ' ! $)!)#'=1 ' 41 %%B Q7=X DC Z $)9dA%B?!$, S)4!$6<)3;! .!$:4,;)B& ' %B ' @ )bd <V;!#4$% % )(4#;! ,<5!$%T;1.N)#'P; ,<?!$%%#;<&101! ' 41

•264 0 " " ' " &" - $ # %

•264 0 " "264 08 %

•264 0 ' " :8 2354 6 8 9 :8 " 9@ %

! "$#%

)'&)(+*5B2 )'&+ -,.(/&! .!$ % ,9!$%0( 21 )(+*%!$% @ (bd -,.(/&! .!$ B 3 ' $ ' (2&! ! ,3( 41+&!5(+*!$% ^ H %B2 .3(/&3(! 6( +&71&1H%B98Pd0 .!$ 21= ' %6$:1$4! 5( ;( + , !$%!!,! ' ^ H . $B ,! 6("1&3( $*<(/& ^ QH BQ^ ' $%$0&H ' (B.-=.8 !$%A3(d0$, :1'& ' -,.(/&! .!$ %

>)? @BACED FGIHKJ'LGNMOJQP5R

!,! 'OS T &% - . $B ,! 6(/ 0!$%U1&! +11. ' ,! 6(V(+*)( & @ (XW -=2! Y&1. %

& S ZT . $B ,! 6(5W[(/&2\W0 .!$]*^(/&*. * (B$. , S =B( ' +_,&%'&!,! 6( " - " 8 #%a` S T !b= 1$%1 . $B ,! 6(c83dW0( ' $-7+&2=$,e&!+1$% +& ' (%!2& ' %B98f(%,&%'&!,! ,!$%f1g(;! N( ' (h(+*!$%92&!%2*^(/&*8i,; &E!$,0 1 B( ' +& . $BjWY&! %!$% 1 A ' $%$i8 B(%],&%'&!,! ,*!$%)%,(+,&](+*!$%]( 21 B ' $%$&%)T6$%k*<(/&*'& !$% . $B ,%B,+, , %!!$% %,!'&X8 %! , C(2 !! ,-,.(/&! .!$%

l #

*3m T6$%IB# .! 6((+*:7+&2=,e&!+1$%k1&1%B $%'&3 &'&! 6( 3Bn*^(/&B!$% S T )&3()! ' BI*<(/&0!$%U1&1+1&3()! ' *3o % 7+&2=",e&!+1$% ' )!$p( ,;$+\(+* 4 %!2&! ' )q 2&11 rT6$%'= %!2&! ' *-= - # '" q . &92&110&!,!$%'&A!$ <'$ - 2&11 %A@W0 p(4B1 ' &! )37+&2=:,e&!+1$%B /B!, B$%'&e82! ' !$%'=IWA'&# &%B BB!, %B(D$'W0$%'&G2s.8 WB&! , &! t*\& .'&!,! 6( 7+&2=7,e&!+1$ B# %%Bj&$%,! &>3(25 1 0 ' $%$

Din

B S T !d= 1!$%1T !$%

( 21 * ' $%$ p(4 %%B=& #% NE

8NA

8NT

8NS

8 BNC

)FU(+* Zu I p(B1X8 wv p(B1X8 yx p(B1X8 yz 9I M p(QB1Q8 B/ M p(B1X8i&121) ' ! &$-= %` .! &$-=.8!$%"*<(/&*'&>!$&1+ Bf(+* p(B1N&'1&1!$%E1g(;! $$X8",!2&! 1Q8"B' $+&! ' '&JB ,!O(/&',!2&! %1!$, =( '1' &KW0$%|& ,*!$%9!d= 1!$%1[(5 1 . $BWY&! %93(

Din

%]T6$% yz 9I M B< p(B1+& %H%B*<(/&)(B$. ,E$$ ' (+B,!2&! . ! %4T6$%5%Bi,&1* !$%7,e&!+1$gB1 ' &! )$p(QW !$% ' (%!! .% ' = ' (:1g(;%B 3(<~ !":8!$&$+,<+.,10%! "(G:,-*B8B7)"-/(P"A0,.' Q7'-% B-0,;3 ,-/$ B%B,-3" **n9(!*B), *N A ,< 9"

B,-8!./ G$&-/&- %,-3"A*#Q7'-$&%!)#"(G:,-*B8!7 "A-( - :8B$&$+0,<&.0,1%B !'<< 9(!*B), *N A),er^ -^

*<(/&* S [B( ' % (/&f1& ' $-=.8 " - " 8 SG 1

SG = (NE , NA, NT , NS ,NC , R, S, contains , seq , choice)

W0$%'&

• NE8NA

8NT

8NS

8BNC

+& .:B2 ) (4 + c(+* [(+*2!$%:B2 )'&+ B ! 6(%%B( & i*<(/& %,'& fWA?B# %

N = NE ∪NA ∪NT ∪NS ∪NC

• R ⊆ N )H(+*PB1! -,,%B "

• S : NE ∪NA ∪NT → 2char∗ 8,B# %1 & < '

• contains : NE ∪NA → NB# %1 -

• seq : NS → N∗ B# %1 ' - B

• choice : NC → 2N B# %1 8 - '#%

T6$%& - - L(SG)(+*' 7+&2=4,e&!+1$

SG !$%*N(+* S 72&119!$, ' ="( !, %%B

Z= i*<($B2 ,!$%U,e&!+1$c88!!+&!! ,:*^&3( E&3(Z(4p(B

L(SG) = x | ∃r ∈ R : r ⇒ xA@$%'& 0!$% $ - " ' 8 ⇒ 8 )dWA1 7+&2=5,e&!+1$ p(B1'B S /2&11Q8.W0$ ' $ NB# %%BC B %' ! &$-= 4k*^( 6(QW

n ∈ NE e ∈ S(n) contains(n) = m m⇒ a1, . . . , ak m

⇒ c

n⇒e a1 . . . ak

c

e

n ∈ NA a ∈ S(n) contains(n) = m m⇒ s

n⇒ a s n ∈ NT s ∈ S(n)

n⇒ s

n ∈ NS seq(n) = a1 . . . ak ai ⇒ bi

*^(/&) i = 1, . . . , k

n⇒ b1 . . . bk

n ∈ NC a ∈ choice(n) a⇒ b

n⇒ b

T6$ B# .! 6( 1B!$%N(/1='&!,! 6(% ⇒8 ⇒8.B

⇒3((2&! ' ,!2&! 1X8 ' (+X8 B (2 %

T6$%1h&$%,! 6(% +&EB# %%B#4Y*^( 6(QW

C

n ∈ NA n⇒ a

n⇒ a

n ∈ NE ∪NT

n⇒ ∅

n ∈ NS seq(n) = a1 . . . ak ai

⇒ Ai

*^(/&) i = 1, . . . , k

n⇒

⋃ki=1 Ai

n ∈ NC a ∈ choice(n) a⇒ A

n⇒ A

n ∈ NE ∪NT n⇒ x

n ⇒ x

n ∈ NA

n ⇒ ε


⇒ bi

*^(/&) i = 1, . . . , k

n ⇒ b1 . . . bk

n ∈ NC a ∈ choice(n) a ⇒ b

n ⇒ b

n ∈ NT n⇒ x

n ⇒ x

n ∈ NE ∪NA

n⇒ ε


⇒ bi

*<(/&) i = 1, . . . , k

n ⇒ b1 . . . bk

n ∈ NC a ∈ choice(n) a⇒ b

n⇒ b

T6$%%, +,&"(+* 7+&2=j,e&!+1$% +&h(+* D&4,e&3,'& ' %40!$ ,&%'&! 2&1%, +,&1 %;N(4! ' U* 'W2B!, B2 '& ' 1 =bWA1q B 7+&2=7,e&!+1$% S ,!2&! p(B1B3(p(4 ' (!, 7(p(QB1 % 7+&2=V,e&!+1$ ,!2&! p(B1>$ &%Bi,&1>3( (p(B1X8=!$p( ,;$ % 7+&2=4,e&!+1$%IB( p(41(QB$:!$%# u u B/ p(B + BQ8 40!$%1+&$+&B.-=IW0(/&!!$' (%! $B'&!,! 6( . $B2 .d= 4H1*+ ' (+(jT6$%'= +&j1)'&*F .!%B (;! y=W0$%'& y= W= %T6$%'&7+&75* 'W. F .!,! 6(% +11-=+ , 3(', 7+&2= ,e&!+1$% p(B1)X=V(-=+11)3+& 46!$% ' (+p(BU(+* /$$+ p(Be8 BE$$ ' (+ (QB$ ! )! , b=Z1)(%6( %( % !b 0, (!-0N% ),$&">:*P0N71 !"A*,'( -3 ''$&'(G@*B'7) ,* .!8rQ 2O (B O),9 !,1* -3

(E$+56-,Q*B"), 78B:*5!8 :-/$& -*X -3O ,A-G-"A(B.P < / &:% )7'8!A0+ "_Q:"$&%B 3 -,./-0:'( - G %!"7'"> % ),$&"> B'$ "( ! )+*$, :% )7/<

C(2 !! , -,.(/&! .!$ n` ' $%$,3(( ' ' $% ' g8*<(/& y= bW[( 7+&2=I,e&!+1$%(SG1B

SG2)8W0$%!$%'&

L(SG1) ⊆ L(SG2)

` ?!$%%', ,! & ' 4e8. . !0(+* '&2&3(/&'1 +,&1 [1&3(QB %' %B98 . !! , &'&2=$$+ ' ((B$W0$p(; ' (%!2&!, +& + 6(%,%B98pW0 .!$,C( :1h(+* 6(%,! 6(W0$%'&O1(; (%

A@OW0 ! :1-= !$ -,.(/&! .!$ *<(/& . $B ,! 6( 0T6$%* 7+&2=4,e&!+1$ ' (%!2& %' %BC3( (B$( 2&!% *<(/&* ( 21 X89,; &@!$,>2&!% *<(/&* $ . $B WY&! %

Din

SG1

8"B<!$% ' $%$:W0 ) %B 4) 4 k*^(/& ' (%2& %' ! ,

SG2%

l # #

, ' (%!2& %' %B @ (XW ,e&!+1$c8nWAW0 D!$%< i*^(/&*,! 6( (+**!$,j*<(/& ' (%!2& %' ! , 7+&2= ,e&!+1$c8),&%'&!,! , C 1)'&E(+*!$% S 2&1 *!$, !$%|,; & 2&!% *<(/&*0=,&%'&!,]*^(/&

Din !$ A!+,&e8&!$%hB ,!EB1 ' &! -1! 6(|,.(1)*^&3( "' ^(%],e&!+1$ p(B

*<(/&B3 ' $ $:1%,n& B $:1%,( .(? ,F %!2& %' ! 6(c82$:1%,p(QB1 +&B ' (/&!,%BjW0 .!$' (+(?H B %Bi,&1:W0 .!$ ' ((2 @ (XW3( # "' ",e&!+1$ !$%'& p(QW (% p(QB"*<(/&33 ' $

(templaterule, contexttype)1, -&X8"B p( ' ((2#TB ' (/&!,! 6(%

( p(B1(/&%Bi,&1

T6$%< 7+&2= ,e&!+1$ W0 >(B!$% @ (QWB,e&!+1$ dW0( B2 % 6(%X8Y*^&3( B1 ' &! ,(-=@ (QW (+* ' (2&3("B ' ((26d=1=1 )dWA1E$:1%,N& 1JB &! ,F!d= 1!$%16 .( ' ,! 6(c82 .kW0 B1 ' &! )#&'&2=!$ , F ! ,? E!$% @ (XW ,e&!+1$ 6(%

•T6$% p(B1 EB &! ,D!b= 1$%1* .( ' ,! 6(!W0 )7(QB$%B

T6$% &'&2= &34;(*<(/&

+ ,9!$%A 7+&2=U,e&!+1$"1g(-= +&! % 3( 11g(/&!:!$ X8Z= + , , % 21) ' '' ((2d=1)f*^(/&3 ' $C # ' ' (%!2& %' 3(/&

•T6$% ' ' (+* p(B1X854\,; & y=*!$%6 1 ' $%$i8.WB'&1+11&3( (2 ,%B ' (5+&$-= E!$% @ (XW-=2! ) i*<(/&*,! 6(C E!$% ' (+B ,!2&! (QB$](+*\q;NT:YW4!$&3(XW W= D!$% @ (XW -=2! X8=( ' '1NW0$%!$%'&3( d=1="W 4 X= )+ ' $ $B(/&,!2&! (+* p(4!$%'&

6(XW:WB'& (B$%B ( !$% %+&2,&/ $Be8 B %&'&!B1$%B p(4

3(F( X8 1H0!$, ' ( $B )1!!. !$%%BIW0 .!$#%3( ' '&!!, +d=T6$% 7+&2=j,e&!+1$

' (%!2& %' %B5W0 3( %+&2,&6(2 ' (:1=% ,K*<(/& !$,X8/& 1!!. !$ ,!$% . F . B !$% = =1 -,p(/&%B/3+&*. '& BE!! ' (%'& ,! &$-= _T6$%h,e&!+1$4& @ ' y= ' '&!!, b=!$,3( @ (QW(/&]( 21 W0 ' -= $+11),,02&!% *<(/&*,! 6( & (!

T6$% '&21%X= =bWA1 !$% @ (XW -=2! "B#!$% 7+&2=f,e&!+1$ ' (%!2& %' ! 6( ' 6(Z(;$-==f1 0!$ ]W X= 6(XW -=2! 6!&1 ' +&>3(2(B$"y=j& (! .( ' ,! 6( (+* $:1%,1!$,1=' 84( 21 *^(/& . $B2 .d=

T6$%9 7+&2=7,e&!+1$ ' (:1g(;%B|*^&3( '" - ' $t8!$, +&4$ %BI( !$% 4 (+* i*<(/&*,! 6(4*^&3(I!$% ' (2&3( @ (XW ,e&!+1$

'

choice

sequence

1

b c d

:A "!"#$%'&()*%,+-*./1032345b 6 c /+

d 7 89,.: /&)%;*9&* )'9*+)%; 6 <! =*?>A@B>ACD>AE;FG*'"*"*'>=8/H=*+) 7

T6$%# B2 $B 7+&2=4,e&!+1$ *w&!+, +)(B$: .( ' ,! 6(%f(+* $:1%,# %2& %' ! 6(%X8 ! , ' +& 3( 3( (B$!$,F .( ' ,! 6(%= $+11=c8 ' ! , h( 21 Y*<(/& . $B2 .d= +

0 8 - # " " - " 859 - ' - " 8 # 8 /I 0 8 " - " 8% ' " ' - ' '" - 8 '" - - :8 & - - - # '" <:8 # 8 # 9 - ':8 $ ! "#JI :8 #8

Din

T6$%51&3( ' 1U(+* ' ( &'&!! ,/!$%5,e&!+1$G >3('W0$, .( &%B98 B< !$%]B$(%!2&!,3(/&* :1+!,! 6(c8 . '1' ( +0*^(/&B!$%n,e&3,'&01+&!Y(+* !$%>3( & ' ' (QB

q>121 . +11)3+&! , ' (:1( ,

1% ' 1X8)!$% ! 7B<21 ' ' (:1( .b=V(+*6 7+&2=,e&!+1$ ' (%!2& %' ! 6( +& ) !LKg( B%BMKy=!$% NK='&h(+*A$:1%,"& 1 .! -1. %BOKy=/!$% K)'&h(+*\B ' %+&%B p(QB d=1=1Q8 W0$%'&3 ' $$:1%,O& ' ( 40!$% NK='&N(+* (B10 .0 H%BI*^(/&

T6$%PK4! ' K $B2 ,DK6( ' %BG *!$%% " - " 8 " - ' <8rW0$ ' $ WA:W0 +B1 ' &! QK= . .!*(/&?B!, :R

l # $

" - " 8 " - ' '* 7+&2=:,e&!+1$ (B%BPKy= # " B +11 ,*^&3( q ;NT: 3( 8 '"

% ' $p($B'& +1% '&TS& 3( 6(QW 21) ' ' M p(B14(+*+

7+&2=j,e&!+1$j*w&!+, +3(UK= 43( ' %,%BjW0 .!$q;nT 7+&2=|,e&!+1$j*^&!+, X8 .!$p( ,;$

S&'&2=E! :1e8+& ' +1 K"(+* . ,|( !$%1f&3(1R

• (B$. ,CVS ,! 6( (+* S /,!$XW/!'1 (1&1 6(%X89*^&3( I,; QS& ' ((2+B &1!2&! ' %BKy= F ' $%$

• (B$. , S T1WH # ' ' (%2& %' 3(/& BE$:1%,ZY( <S.(?+ , %!2& %' ! 6(%

E !"#% ),7)'%B"-/(E"#(!-"[8B">Q7'-$&%!)Z\('$&%BA0Q$+ 7)-/(G1"( :-$& "(!:,8B7)"-/( 0N-/8B%B8B'I G 0(8!(!*B'7'A,*;)A)$&'(G !"7 ", 9] -G-$Q8!71 '^<0 '$&%BA0,8!N$+ & 2O"> "('_ I -2 :8B7bO'*+8B%n+0(!-0 !),'$&%!A/!-0,"$+ ] N$&"::"(!.&0>-/./ !),!78B:"A(B.+G] -G- ">:A^1< 8 3 -0,N B,'_ ">'$2:8B$&$+0,<GG">c"A *B-<8` - -!8B(!': ! CaAb,b $&-*N"8!:*M )$&%!A0N"458B9 '$&%!A/<

c

• 6( ,? ' $%$ ' (+)(B$

` (S&'&TS 'Wh88 7+&2=I,e&!+1$ ' (%2& %' ! 6( ' (%! !](+*!$%1'1%R

&!+, ' (%!2& %' ! 6( R (/&?3 ' $ (QB

m ∈ M8_*<(/&?3 ' $ $:1%,&

r ∈ R8K*^(/&

3 ' $ ' ((2d=1)q ∈ C(r)

8E*^&!+, fr(m, r, q)

' (%!2& %' %B98&'1&1! ,rW0$%

/S.( %B B'&1(QBm8iW0 .!$

q40!$% ' ((2d=1=

T6$%)*^&!+, rW0 (B$!$%K( 21 (+*r # ' ' (%!2& %' 3(/&/4c*, .!$i* -= 4 1&! ' ! '

" ' $5$:1%,ZY( /S.( ,F %!2& %' ! 6(i : ri(i) = r

$4'*'1+&!,Y*^&!+, ' (%!2& %' %B98W0$ ' $ = K=I&t* '& ' %B %,'&(4

fi(m, i, q)!$ 5*^&!+, |W0 $Kg(QBi= i*<(/&*,! 6(

K( 0!$% p(QB10!$,i

=E$ ' X8 B'&!$%h&1!2&! ' ! 6(%](+* !$% 1 ' $%$

W&!+, 74$NK-=R"T6$%F i*<(/&*,! 6( !3(/&%B@ @!$% @ (QW,e&!+1$@ %B*<(/& 4$NK. ,!$%k*^&!+, A 3( ' (% ' %B? 7+&2=:,e&!+1$c8y&'1&1! ,!$%Y1g(;! QK]( 21 [(+*!$%! -&2&!% *^(/&*

T6$ 8 7+&2=5,e&!+1$? !$% S . $B ,%B +, , %!p(4!$%'&A 7+&2=

,e&!+1$&'1&1+! ,?!$%h( 21 ' $%$

! #

T6$% 7+&2=,e&!+1$ *w&!+, +$% K(/&!,%B!(7$%'& (QB$B!$%7( 21 7B!( 2,.(4 , @ (QWa(+*3( $:1%,4& %$ H ?!$,!$% $:1%,I&

r <S.( %BW0 .!$ !$%

' (+b=Z1)q8 B'&>!$% ' &2&(B

m T6$%"*^&!+, U&'1&1+! ,/!$ NW0 K="&3( ,;$-=

3((/&21$ ' W0 .!$-!$%G # ' ' (%!2& %' 3(/& (+*r8B .E +11&3(/1&! %,$-= 2&!% *^(/&*%B-

& ' &! QS&KB1 ' n(S&'&!$ R

yz 9I M : +& 2&!% *<(/&*%B/3( yz 9I M p(Be8W0 .!$D!$% ' $ $Bi& K) ,!$%>2&!% *<(/&*](+* !$%# # ' ' $ $Bi&c88 /!$%!h(/&B'&

: +& 2&!% *<(/&*%B73( .x p(QBe8W0 .!$ C %, +,&( 3(,3(' (%!2& %' %B#4NB!, %BC ' ! 6(

+& 2&!% *^(/&*%B 3(6 v p(Be8)W0 .!$ ( 3(,3(' (%!2& %' %B#40 ' ! 6(

+& 2&!% *^(/&*%B 3( Zu I p(Be8 W0 .!$ 7 3(,3( ' (;Y!2& %' %B#40 ' ! 6(

: +&62&!% *^(/&*%B3( > M p(Be8eW0 .!$choice

%Bi,&63(>!$%02&!%2*^(/&*(+* 3 ' $ ' $ $B

+&>2&!% *<(/&*%BE3(F!$%2&!% *<(/&* (+* !$% -& ' $ $BD # '

! +&#2&!% *^(/&*%B/3(F!$%>2&!% *<(/&* (+*!$% -& ' $ $BCH # '

+&>2&!% *<(/&*%BB'1=B2 ,j(qR

#"

uI ' (2 b=Z1)1O&1 .* Zu I p(QBe8 ' (%!2& %' %B !$%?!7W = 4*w&3( %2& %' ! 6( wv ' (2d=1=1"&1 . v p(QBe8 ' (%!2& %' %B !$%5 7W=4n*w&3( %!2& %' ! 6( .x p(B 3B,B%B64 ' (X8:$HS ,E!$%%, +,&

Dd(q)84NB %%BE ' ! 6( c

J

M l ' (2b=Z1)1Y&1 . # yx p(Be8iW0 .!$/!$%%, +,&

l ' (+ b=Z1)k&1 . ?!$%62&!% *^(/&*(+* !$% ' $ $BF %!2& %' ! 6(? # ' (+*)!$% ? %2& %' ! 6( C u u I ' (2b=Z1)U&1 .0 &yz 9I M p(QBfW0 .!$ p(?%Bi,&1

C ' (2d=1=h&1 .0 # Zz : p(BfW0 .!$ p(%Bi,&1

T6$%B2&!%*%,! 6(:(+* y= ' (_(+* !$% %!2& %' ! 6(F 3B ' (+K(+* . 2&!% %,! 6(

Zu7 +&2&!%2*^(/&*%B 3(2"&!,!$%'&B <S.(QS&%BE!2& %' &e8 ' (!, ;Y ,2,'34!k(%]1% ' $p($B'&k*<(/&A3 ' $Iq;NT !$, = K=9$ ' %BPKZ=!$%9 %!2& %' ! 6(c8 B((B$ !$,KB1 ' &! QK)1X8 ! ,C 1 ' $%$/ i*^(/&*,! 6(c8$p(XW y=G! 1 3 ' $ q;NT= K)$ ' %B X=OK=FH$ ' %B98/B@ W0$,O(/&B'&"&$%,! QS&3( (4!$%'&"q ;NT:

T6$ *

B1 ' &! QK)%BE'1+&!,$-= ' ! 6(

T6$ 5 %!2& %' ! 6(%(-W =2 VS ,153( @ p(Be81B .? 2&!%*%,%B3( yx p(B K=1Y g(/&!,!$:1 23B 3( Kg( B .7%, +,&E3(W0$,F!$% 1&1H! 6( =

VS ,3( R

@ .x ! &1 .0 /!$% 6( %, +,&h(+* !$%%, +,&1n(+* 3 ' $D K;Y i1&1! 6(

! * ' ! 6( ' Y&1 . E!$% ' ( ' ,,! 6(,%, +,&O(+* !$%+&2, %, +,&1 * ' ! 6( ' Y&1 . E!$%# , 3( %, +,&O(+* !$% h(+* !$% ' (2b=Z1)G * ' ! 6( ' _&1 . !$%! , 3( %, +,&](+*)!$% 6( ' n(+*=!$% ' (2

d=1= * ' ! 6( ' O&1 . !$%5! , 3( %, +,&I(+*!$% 131 ' ]`f(+*

!$% ' (2b=Z1) &1 . E!$%#! , 3( %, +,&"(+*!$%$H$QS&1

^ !@7'-/-,"(B.;-03 D a!Laf G %B 0"(!* "( - '7)"-( ? < ?"! <: 9 -(!#$&"./ G !3/N./8B'::* <= !3 8B(!7)"-/(;" :% '7'" # '* 0 :,"(!.3 8!(B7)"-/( (!-G[G80A" # *;(!$&3 8B(!7)"-/( < !" 2O':$+ %B,-!'$

-k !"71 ($&):%7)#%B, #G -&8B:Z\$#@:"(!.Q B#A(!.80./-;/),9%'&(%) 9-/8BA* :,"A../),@( ),:,-, "> !k8B&P*B010 % +* :8!71 0#(!-$+7 B"A(B. 0( '(8!$& ,10* :"$&%!Q B% , B8B#,'"(!. -( #3 -0, 8B: "(- !/. !0 !211430 !"657183 0 !:9<;/5 &=n-8!A*U Q&%,'7'":"-/(E*B"),< !:-/8"A-(E"-;8B:# !(%'&(%+) A(B./80./"( ?> 3/. @!BA2CED 8!0"-/(P7)-/(G G 0(*;8!: Q%, #G -8!(*+-Q !@($&):%7)N-34 BN7'-/(G G (B-*B#- B),<":/<

J

9 () * ' ! 6( ' Y&1 .0 # %, +,&h(S&'&!$%> ',&'&Y*^&3( 1c8. Y ' -=

@: & +& ' &2&+*-=!,; QS& 1 1g(c8'B&1 . !$%E ∗ %, +,&

T6$%'& Y&3(( *<(/&3( :1&3(S&$3$%'&e88! ' S /,!$XW5* ' ! 6(% +&#!2&3(, -= b=Z1)%B98B/3( ' K= +11&3( ,%B 3(;(!$ ,PK)!'&!$ !0!$% -&IB ' %+&%BCd=1=e8. W0 .!$ T6$%"(-=4&34;(%9!$,3!$ nW 4p(4n1 & %B&Z=4* &!!$%'&NW 43!$%*! .]W0( $BD! 3(WY&! .25* c* ' ! 6(6BV(/1)'&!,3(/& . QK&!+&2=C ' B2 , ' ('& ' 6( & 1*<(/&S /,!$XWi8BE!$,p(4!$ ,? B2 ' ,%B#F2&3(,%1%BI*^(/&0 .

yx ! +& K%!2&! ' *-=?VS ,%B53(2 [(+*qNT:

T6$%1+&>3 ' $ +11&3( ,%B

3(+O&', %+&%, +,&3!$, ' (+!, %0!$%]&1 .0(+*:VS ,! , (/3 ' $Dd=1=R M

l VS ,#3(!$%%, +,&l 0@ ! Zu I 7VS , 3(/!$% %, +,&I(+*!$%5$:1b= !2&! , *hBZY

' %+&%B 8(4!$%'&2W0 #3(!$%# ∗ %, +,& 0@ ! u@ .x u x Zu I 7VS ,53(C!$%5 ∗ %;Y

, +,& 0@ ! u@ .x u xI uI VS ,F3( !$%F$:1b=/Y !2&! ,

%, +,& * ' $ $B.1X8c(4!$%'&2W0 3(53( !$%+%, +,&(+* S !2&! ,& w,; QS , 11& ' ! 6( 7(&/ %!! ' #$$+]& &%0!$% ' ( ' ,,! 6((+* .B1 ' B 9p(B1X8 BE $+&BE3(2. F .!!,! ' -=

0@ ! u7 u7 H I Zu +&p(44A342=F3(B3W0 .!$(4 .'=1$DR S T1W !$% -& S e8+21. .!! , %!! ' 10(+*:3(p(;Y1&! F .! QS& S q d=1)1 +3(&D # ' |(+*!$% ' (/&2&121g(B2 ,p8\1&! F .! QS& ,3(d=1=e8 B p(/&*. 1 ,!W0$ .131 '

T6$%1,,3((+&/!$% ( 21 5'1+&!,%B Ky=

W0$,VS&'&6 K,; QS& 5!$% ,!2&! QK f(+* 8Bt* .! , 3(2# 21 '

6(,,4#!$% ,!2&! QK 5 K%X8 !$% %, +,&|(+*B!$%?$$ ]BZY' %+&%B d=1= Kg( B 3(PK) 1)'&*%, +,&5(+* !$,U(+*!$% 8 3(5!$, ' K=! * $-= H%B

&2&+*-=.8: *B!$% ,!2&! QK F U1&1+ B<$4 S !$, p(4

6(XWB%B 4 '1+&!,3(/&U*<(/& . !Y8B'&! QS&%B7 :1 S ' $%$Ed=1=1X8char∗

%B4 +11&3( 2 ,! 6(

* ' ( &He8 6(( , 1 !$% ,3( b=Z1) 7%, +,&

l !$%

' $%$i8 B ' (%!2& %' ! ,6 . ! %, +,&PK4%B (l8 B !$% ,;!$

K( B](+*!$%. NB'&! QS,! 6(W0( $BDK)*. -,;$*-= K)!'& wv 7VS ,>3( !$% %, +,&U(+*!$% -& 2%B S 3 * 1&1X8(4!$%'&2W0 H 4

W0 .!$C! :1ZY(b=Z1)h(/&! :1ZY ' (+>$$b=Z1)1 u u I 9 VS ,#3(

char∗

T6$%1B %!2& %' ! 6(%$S& B7 ,!2&! QK S $:1%, T t8Q*^&3( W0$ ' $c83(/,&!$%'&IW0 .!$ !$% ' (+ p(Be8) 3(,3( ' (%!2& %' %B !$, $4 4? . %, +,&6 1)'&(+* !$% 1](+* !$%#$$+!$,!$% %2& %' ! 6( = ' (%!2& %'

-&!X8!$% T |1+&%B 3( # ' e1, · · · , en

(+* S ,!$ i1&1! 6(% !$%!NW= 4 B1 ' &! QK=%B ' ! 6( W

* ' ! 6( /S.( ' ,! 6(Ci1&1! 6( (e1, · · · , en)

' (%!2& %' %B98/B 3(,3(aname

' (%2& %' %B 4f*<(/&!$% / %!2& %' ! 6( T6$%!* hB(%h*^(/&9!$% T anamespace

t8 B/!$%#dW[(( 3(,! +&#!$%c8(AK='= ,!$% ' ( % ' U&13( ! 6( B p( Y1& 121 ' H$! ' #21) ' 8%BV*^(/&>!$% ' * !$%

%!2& %' ! 6(c8 '&2,&%B/3(5*^(/&* & 3(,3( W0$p(;%, +,&# R

′′.L(anamespace).′′.L(aname)

*L(anamespace) 6= ε

L(aname)(4!$%'&2W0

W0$ ' $/ B!$% %+& p(4!,! 6( (+* 1B%B # . 8%B 10i1= ' %B Ky= ]` ' $%$,3(Z(

+& $4UK=1 ! 3(D! (3B;S !+,& !$,!$% S /,!$XWV* ' ! 6(% 8 B ' K)*VS ,%BC!!,! ' -= K= ' + ' (+9d=1=* S, % KRYT6$%O,&%'&! ' $B+! .d=E2&!% *<(/&*I!$ IB2 $B p(4$S&y=I1& ' ! 6(1&3(AK$]W0 .!$,y=E ' $%$42&! %B

!

$:1%,ZY( <S.( , %!2& %' ! 6( & %!2& %' ! 6( !$, H$ ' # ' (+* p(B1X82B!$%c8*<(/& 3 ' $ p(B5 7!$% # ' e8\14H1 ' (+2&3(63(&/$:1%, , ' $ ,<!$% p(B

" # #$ % s D %2& %' ! 6( $4 S /,!$XW<1&1H! 6(s*<(/&H$ ' ! ,G3(

p(BF # ' e8cW0$ ' $7 #21) ' 8%B< '& ( 3( K=F'&2&3(%( * *A . ' @$ ' Z=+!$ , $ !$p(B1

T6$% (4!$%'&DbW[( $:1%,ZY( /S.( , %!2& %' ! 6(% t* & * '&D!b= 1$%1 ! :1. ' ,! 6(c8

# B 8"-W X= $ ' !$%! , 3(7H # ' :(+*6!$% ' (2 p(Be8B +&2&3,%B *^(/&*7-=W0 .!$@!$% % %!2& %' ! 6( Ky=63B,B2 , *)) 4)$ ' ! 6(Ci1&1! 6(

-&!X8 ,&&! $B(+* !$p(; " # # %!2& %' ! 6(%!$,]WA'& 3B#3(F$ ' ) + ,.- /!d= 1!$%1! :1. ' ,! 6(

T6$%'=|&1 .B #"*^&!+, ( 21 !! ,

C$$+]W0 .!$,Z= , 8%p( ,;$/3(?( 63('W0$,13 ,/* '&2&3(/&11 +,& S . $B ,! 6(

" ' $<$:1%,ZY( /S.( ,E %!2& %' ! 6(< 2&!%*%,%BD 3( ? 7+&2=,e&!+1$V*w&!+, +

T6$%* $B3

*3( ' (:1(;H!$%5*^&!+, 24 K%!2&! ' VS ,! 6(!(+*0!$%?$ ' ! 6(7i1&1! 6(!(+*B!$%? ;Y!2& %' ! 6(c8*^&3( ' $, (+*' '" %/ ' $t8(+*\W0$ ' $V(%* ' (%!2& %' %B*^(/&3 ' $D3 ' $#6( ' ,! 6(!'1V(+*!$%$ ' ! 6( 1&1H! 6(

`d*

s O( !$%:*<(/&*

p1 intersect p2(/&

p1 except p28rWA(QB$A$ ' ! 6( (+*3( p(QW

K%H # ' n1i* W0$,p1

X=?$ ' X8+2&!%*%,! ,:(-=:*^(/&p1

B !! ,!$%]&1 .3K) Mp(Bh(S&'&!$%2&!%*%,! 6(,B#D$:1d= Zz :M

'1$*w&!+, + +& ' (%2& %' %B2B2 '&*-=.8IB'1=B2 ,( !$%& 2 |(+*#!$% 3( & ' D!'1

`

Z= ' 4e8!$% ' (%!2& %' ! 6( !!+&!",; QS& HΩi

(+* ' (2 d=1=110 !$% p&! !'1 C$ ' Y! 6( 1&1 6( ' (%!2& %' %B ,; QS& !$% ' (+ p(QB

q*<(/&!$%/ 7+&2=,e&!+1$ *^&!+,

' (%!2& %' ! 6(32Ω0 = q

W -

74 TEXTurn:XSLTValidator:7:3

"Bravo"

23 CHOICEcardinal−?:0:0

22 SEQUENCEepsilon:0:0

24 SEQUENCEcardinal:3:5

1 2 3 4 5

:AA ;.+/% :?&(*'/:<&T*X B=0E1) A.!* 7

T6$%U&1 .](+* VS ,! , K%!2&! ' *-= !$%# , !'1/ ' (%!2& %' %B R

Ωi+1S(a :: t,Ω) = Sstepa::t (Ωi)

p(/& .! ,Y !'1@$ ' ! 6(%X8 5 7+&2=V,e&!+1$*w&!+, + ' (%2& %' %B *^(/&>3 ' $q NT Ωi+1

8B*!$%_&1 .! ,]*w&!+, + +& ' ( ' ,,%B"(+3(!$%\*^&!+, ' (%!2& %' %BO*w&3( !$%_1&VS 6( !'1

T6$%f*^&!+, ' (%!2& %' ! 6( B'1)B(/!$% 2 (+* 3 ' $ !'1c8 BE!$% ' (+b=Z1)R

fT6$% ' (+ (QB$(+*%!$%0q nT (QB$%B 2]& ' &! QS&JB1 ' + ,3 7+&2=O,e&!+1$1&! F .! QS&1R u@ u +& (QB$%B 4 M t O1% ' $p($B'&X8_W0$%'&

t !$% %;Y

, +,&5(+*Dd(t)

*!$%'& 529b=Z1)∈ Ωi+1

8g(4!$%'&2W0 4@$:1d= yz 9I Mp(QB

u x H u@ yx I2 Zu I ! "`* !$%'& F29b=Z1)∈ Ωi+1

8=!$%"&1 .9 p(QBe8yW0 .!$ h1% ' $p($B'&K*<(/& M (char∗)

4[(% ' $ $B98 B?!$%1(B$(+*!$% d=1= f(4!$%'& ' (+ 4p(4!$%'& ' $ $B

!$%'&2W0 e8)!$%E&1 .N*^(/&3!$%!

' (:1Ed=1=e8;K p(;YF %B98% k& &%%B

ru x H u7 .x 2 Zu +&2(B$%B 4!$%2(B$_(+*A!$% -&O( '&*(;' (:1(; .3(/&

u@ +&(QB$%B,4)yz 9I M p(QBe8i& ' & ,|(S&'& ' $ $Bi&

u@ +& (B$%B#4)F M p(Be8& ' &! ,|(S&'& ' $ $Bi&

u@ +&(B$%B#4) p(QBe8i& ' & ,|(S&'& ' $ $Bi&

Zu I @ , q ∈ Ωi+1

+& (QB$%B&4)E1% ' $p($B'&*<(/&q

! : +& (QB$%BO1& ' $-=.8 ! ,!$% yz 9I M8, M B #" B 7+&2=j,e&!+1$p(B>d=1=1

Zu I @ , p(4

∈ Ωi+1+&(B$%B#4)/$:1b= Zz :M

W

& ! +& (B$%B 42 ' (S&'&Y y=<Y ' 4 ' (%!2& %' E&'1&1! ,<!$% " &h(+*2&!% *<(/&*F ,/!$%5W0 $B ' +&B 0 ( 21 !! ,,Z=G$$X8 ,!2&! QK 1O(/&2 y=(/&B'&X8W0 .!$ !$% ' (%2& %' 3 .H$ * 49!$% ' ( (B$(+* $$+ B&Z=E 4!$% (QB$r(+* ,!2&! QK 1BEp(QB1

u u 9 * ∈ Ωi+18'+&((QB$%B 4 1% ' $p($B'&:*<(/&!$%E u u q NT

B4(%f*<(/&0!$%# q NT -=.8 ' 3 1D Y1)'& *^(/&*%B R 8 4 v (+* yz 9I M80 M8 + B 9 " ! !$,/B( p(4

$HS&(&3 ' $ KI1% ' $p($B'& +&7&$(S&%B%' $ K,e&!+1$%+= +&! 5 *!$%

Ωi+1B(1 p(4 ' (!, /VS&'&2=jqNT (+* !$% ' (+)(B$

T6$ 6 k&'1=3,%B +! p(

B33B/ K,e&!+1$%+& t*

yz 9I M8% M7(/& + p(B1)+&U&'1% ' %BDKZ=5!$% -& ' (

B *^&!+, ' (%!2& %' %Bh(S&'&0 M p(Be8K&! ' $ ,3(3 ' $O(+*q′ ∈ parent(q)|q′ ∈

Ωi+1 wv Zz :M p(BG2m U& &%%B98 W0 .!$7!$%2(QB$K(+*03 ' $ ,!2&! QK e8 B ,Y

2&! QK UW0 $B ' +&B (+* !$% ' (2b=Z1) 4 ' $ $Bi& R wv @ Ωi+1

+& (QB$%B 47V1% ' $p($B'& p(B +11 ,7!$%(,!2&! QK q nT

`d*0!$% ' +&B2 . .d= (+*6!$% ,!2&! QK HF "F : 8/ (/1! 6( ' (%2& %'

! ,? M? 3B,B%B

& B +&(B$%BE!$%# UW X=#4 !$%U&!,! 6(K= ,?!$,,!2&! QK 1X8 3((8 X= ' /S.( ' ,! 6( (+*6$:1%,1#!$,O( 21 $$ 0 . !$%>2&!% *<(/&* K) , (B$%B

ix *^&!+, # ' (%!2& %' %B(S&'&+ Mp(QBe8 K&! ' $ ,C3( j1% ' $p($B'&

*^(/&A3 ' $IqNT Ωi+1 B.F .!%B.-=.8?K . (/&1& ' 6( ' ( $B K= ' $ VS&%B Ky= ! , !$%

TB2 -& ' ! 6(%R p(/&* :1e8 (G!$% M ( Q8 . p(XW@!$, %3+& ' 13(/&' (1 K)t*^(/&E&$(4 ' 1!3(/& 0 1!$% ' 1!3(/&b=Z1)1)+& -=j& ' & QS&

,&%'&!+11&3(5 ' $ ' ( $B K= ! ,!$% (4$&! ,Y 9%B'&!$p(+* -,.(/&! .!$ 3( +11&3( 2 ,EB( ' Y ](/&B'&X8i,; QS&& ' $%$

@>$S&#1(% ' 43 E!$% & W ( 1! ' (/&21 $ ' ! 6(%

K=',; ,jW0 .!$ )) !$, ' ( $BMK=% %n*^&3( !$, 0(E!$%h(4!$%'&$B98%!$%#1&1H! 6(% ' ( $B,4WA$ 3(,! ' -= $HS&K=1 &'WY&! .!3(F3(!$ ,5$+&21='&

` !$% Kg(S&:B1 ' &! -1! 6(c8+WB $HS&:B1 ' &! QK=%B ' (+3(XW4:$,! ,IB2 -& ' *-=N*w&3( $:1%,ZY <S.( , %!2& %' ! 6(%X8.B:, 6(;%B|(S&'& 6(5$ ' ! 6( 1&1 6(% ' (:1$-=

6(5i1&1Y

! 6(% C$ ' ! 6(%+&$B.%BDKZ= ' (%! $B'&! ,53 ' $C$:1%,ZY( /S.( ,jW0 .!$& 6(CH$ ' ! 6( " ](!^"7'-/(B7''%8 "A( ( "A$&%B'$&'(G10"-/( G !N7)A'(8!% $+2 N*B-/(BN-/( ! G*B8B,"(B.Q7'-(!:,8!7 "A-(^~ ::," !8B)0,8!(!-0,1*B),'* B:-+ B#-,1*),@-034 !0::," B8B'-/(P B'J FIJBK DJ (B-*B *B-G)@(!-0$+0:),< KML)JH

b Ja J&7'-/8B * 2O\ ')(P8!:*MQ!8B">"7'-/"),9% ),:3 -0,$+(!7)_6"A:<

WW

</when>

<template match="b">

<choose>

<when test="...">

<apply−templates select="x"/>

<otherwise>

<attribute.../>

</otherwise>

</choose>

</template>

sequence

element

choice

attribute

choice

sequence

entry

a

1

b c d

1

1

a −>

b

<element name="a">

<complexType>

<sequence>

<element ref="b"/>

<choice>

<element ref="d"/>

<element ref="c"/>

</choice>

</sequence>

</complexType>

</element>

<apply−templates select="*"/>

<template match="a">

<element.../>

</template>

hAB ;-*<:/&(Z+<+/% Z+'?'=) 7 4 /<)-' .,-/%,HZ+* %,H=% !"# /J/&T *' 7 4 =&( 3 G," /%** &* )' *A+% * U% 6 /+$= G<*J*' *' * L'(G* *'/% 3 /J/&(* 74 P /+ &( '=) J)%)+M%)+ H'=) &*/J/&(* = 9 %*H!-)'=) G!.'G&*Z&T)+ ///*H!'$ *'* !") = 3)%L3 '*Z+U!"#=

a: )+U*+ 6 / ,9U)+/*H! *5*+ :A

b*= %*H!-) 7

W

i1&1! 6( /h(+*B$:1%,ZY( <S.( , %!2& %' ! 6(%X83 ' $ W0 .!$ ! , 3( 1,!$7$ ' ! 6(7 Y1&1 6(

$% ' (%!2& %' ! ,# 7+&2=O,e&!+1$E*^&!+, *<(/& 6(F$ ' ! 6($:1%,ZY( <S.( ,

%!2& %' ! 6(%Q8 ' +&7 !K)! p(4#3(/ 2&3(B %' y= %'W(/&B'&! , R n(B1+&H$ ' %BG B( ' N(/&B'&X8%VS&DKy= 6(CH$ ' ! 6(C1&1H! 6(

' (%H'&TS,! QS&7+11&3(5 ' $ W[( $BMK= 3(|&'1&1# %' $ ,e&3( 1 Ky= " 9 " 9 p(B ' (;Y!, ,( M p(Bh(S&'&9!$% B2 QS $B %!2& %' ! 6(% 7+&2=I,e&!+1$4*w&!+, +"2 ' :!$ !$% $'&2,& ' = 6(&13( ! 6( T6$ ' '&!!, -= B(1p(4 4 y=D'&2&3(/&3!$%'&+= K= (/&B'&! ,!(+*N( 21 :*^&3( !$%j*w&!+, +"2 K !$% M p(QB ' H1 &!,!$%'& K3B 6(;:(+*1& ' ! 6(c8 != , K4! ' -= !$, 9*^&!+, K ](%> p(QW (-= # <S.( %B

(;! 6( $ ' ! 6( 1&1 6(% +&V(!$%*^(/&* )) )) 80H$ ' ! ,(/&3!$I(%e8<K [* 'WA'&6!$( ' $ $B $$+Y(+*:!$% ' (+)p(B

T6$ A 6! :1-=:&12& %' Y

&%B53( )) a, b, · · · 8ZW0$%'& a8b '

+& ' 10(+* $$Yq NT:A!$,A$S&!$% 8 8 ' n(QWh8!$% 6(E$ ' ! 6( i1&1! 6( $43K= ' ( * , ]1,!$ 1&1H! 6(c8$+! ' Y1&1'&TS&%B

T6$ $ ' $. F ,%B 21 &! 6( 6'&2&3(/&6 !$% '( !#"$ 1! ' 4

T6$%

!# ' $ # %B4( 6(%(+* Yd(-= 2 (%ZY !'11,!$Ci1&1! 6(%

p(/& 6( 1&1 6(%KW0 .!$=B2 )'&+p&!Y !'1 21X8 (+11&3( ,! 6( K)!'&A!$ $'&2,& ' = 6(V&13( ! 6(W 4 %B R

!$%(+*\1,!$Ci1&1! 6(%(+* !$% 6(

P = p1 · · · pn W

Pbefore

K)!$%9[(+* &$%,! QS&p ∈ P

W0 .!$ 33B2 , :(/& 2 A!'1c8*^( 6(QWA%B Ky="'&3((/&1(/& j(/& ( !'1%

Pself

K)>!$%(+* p ∈ P

W0 .!$,! , 2 !'1

Pattr

K=>!$%*(+* p ∈ P

W0 .!$,! , F!'1 Pafter

K)!$%6\(+* i&$%,! QS&p ∈ P

W0 .!$ (/& #!'1%X8p(4r*^( 6(QWA%BKy= y= j(/& 5!'1%

c`*|Pbefore | + |Pself | + |Pattr | + |Pafter | 6= n

8!$% ,; QS& 1 B $'&2,& ' = 6(&13( ! 6( (

P " !$%'&2W0 e8 . !U(+*

Pbefore , Pself , Pattr , PafterW0 .!$@$'&2,& ' = 6( &13( ! 6(

+11. %B 3( 3 ' $c8 ' '16$:1d=I(%1X8W0$ ' $ +&N&$(S&%B98(/&B! , 3(%Q8iW0$ ' $ +&3B,B%B3(!$%. !NB2 -& ' *-=

T6$%U&1 .0 ) yz 9I M p(QBh(S&'&!$%. !

T6$ B$% &! !! '3' (%'&TS ,! QS&$-=7&ZYd(/&B'&B!$%]1,!$ i1&1! 6(%0(+* !$% 6( 3(*!$%B( ' Y(/&YB'&_(+*gW0$, !$%'= H$ ' X8K .),; QS&1 1F !$%0* ' Y(+* K%3( i1&1! 6(%X8 (/& p&*!'1%h(/&U1,!$7i1&1! 6(%O(+* F %B *^(/&2W+&B B &VS&'&H:(/&B'&!'1%

W

` ' 4H0(%k(/& (/& # %!2& %' ! 6(% +& %1!%B % %!2& %' ! 6(2(B$%B98,U& +! e8:!$% p(BF ' $ ' %BW0 "K)5&ZYd(/&B'&%BOK=bWA1 $ ' ! 6(7VS ,! 6( B$:1%,E& ' &! 6(c8 B y=/ i*<(/&*,! 6( K( f(/&B'&! ,4(+*Kq nT (XW3!$,>!$% ' (%2& %' %B 7+&2= ,e&!+1$ *^&!+, ' (+!, = K) ' ( /S . $B

T6$ X= ' ;( B %15(+*!$%

-=2! 4 4 ,,7 ', 0(/&B'&! , (+*( 21 X8 ' %B Ky= &(/&B'&! , # *)p(4KB3.W0 .!$

T6$% 3( ! 6( %B W 4 3(V&'1% ' yz 9I M p(B1NKZ= p(B1X8\1&1'&TS , ' +&B2 ,Y. .b= K K&3 ,7(/&B'&! ,p8XK ]W0 .!$V(%U&1!2&! ' ! 6( RQ ]` ' $%$,3(( ' (-= $B. 40!$%TB2 -& ' ' (+f(+*& Zu p(B1X83( * * .0 p(4 p(QW4*^(/& &>!$,!$%Zz : p(QBNW0 )$HS&3!$,k1g(;! .! 6(c8 #" !(S&'&1 M p(B3 %B? %33B98! ' &! ' ,|1& ' ' +&B2 . .b= K Y&!, ,53( B %1

%f(+* %B|1&%B2 ' ,3 B!$% +',&'& . .'&!i 8 2&3(B %' %B ' ! 6( ` [W0 .'&Y(

K A!$%i !$ p(QB9 '

`* %B5 ?!$% %4!6!'1|(+* $ ' ! 6( 1&1 6(c8+ .B '

*!$,+, (;!"(% p(BF #$ ' %B !$%i !$c8(/&X8: *6!$%'& +&p(4

ip(B1# @!$%5 ' e8

p(% $ ' ! 6( 1&1 6(%OW0 .!$ !$ ' (B2 .! 6( ' $HS&5!$% -& 7+&2=,e&!+1$ *^&!+,

' (%!2& %' %B (/&N1& ' $-=.8 Ky=5) ' ! QS&$-= . F .! , i1&1! 6(%A3(max = 1

` A JB(%,*^&!+, ' (%!2& %' ! 6(C!

" 7$ ' ! 6(7i1&1! 6(% ' 1(4+! % -= 1& ' B p(B5*^&3( K= ,CH$ ' %B98B !$ ' !$%52&!%2*^(/&* 3( ,& /S . $B989K) ' y=( 21 ' %B Ky= !$,H$ ' ! 6(W4 F ! ,

T6$%G ' (+* !$%1&%B2 ' ,G ((B$%B Ky= &'1% ' , !$%<2&!%*%,! 6( (+*!$%

% %!2& %' ! 6( Ky= M p(Be8 ' $p(Z(; , .!$%'&B!$%92&!%*%,! 6((/&1 $:1d=Zz :

* &!!$%'&Y& %$+!$,W4 t* )41/ $B3"*^(/&k* &fW[(/& )EW=4(+*-Kg( B2 ,!$%>d=1)1$ ' ! KUKZ=,

i .'&3i1&1! 6( R (%!2& %' /B'&*F !! ' 3(,3( (S&'&Cm(q)

.9 &', %+&t8 B&$(S& B33BC!!,1

p(/&!$% K)'&

i8%!$%*](+* 2= Kg(!$, =#+11)3+&

,B!$%i !$j1g(;! .! 6(j(+**!2&! ,E,&%'&!,%B KZ=!$% 3(,3( B5!$ K)!$%Nq nT$(+*:!$%

i !$

p(B* 65!2&! , 2)!$% p(B $ ' %B t81='& *<(/&* /B'1!$;Yi2&!HS&'&! +3(5!$%Eq ,e&!+1$ (+*A!$%

3(,3(c8 !!+&!! ,5*w&3( E+2&2= p(B Hk(+* !!,1kW0 K)N&3 ' $%%B

T6$%Hk(+* 2= Kg(

(+* ( Y %Bi,&1[*^&3( !!,1 ?!$%9!!,A !$%HK(+*91(; QKi !$53= NK( ?!$%1%, +,&e8

BE .)F -,;$ +&2&3(QW B(XWΩi+1

G*

7+&2=:,e&!+1$(4$K-= !$%!!+,&(+* S . $B ,! 6(7W0$%'&!$%!(XW ,e&!+1$(BF!$% ' (%2& %' %B 7+&2= ,e&!+1$V*^&!+, -= .R @*$S& ' (%2& %' %B (% ' (:1g(;! . k*^&!+, N*<(/&3 ' $$:1%,e8kW0 .!$ @7(+*U1% ' $p($B'&|*^(/&3 ' $ 6( K=i1&1! 6( (+*#3 ' $ ' (!, %%B$:1%,ZY( <S.( , %!2& %' ! 6(

0!$,:&$, %3( K)kB(% 4$NK-=!(+*VS&'&2=!$ ,p8 ! ,?!$%#%Bi,&1(+* !$% (XW ,e&!+1$*^(/& %H'&!! ,?%Bi,&1

W

9 ' !$% (XW,e&!+1$G = (F,C) $NK-=5 4! :14R

p(/& m ∈M, q ∈ Σd, i ∈ I, r ∈ R :

p(/& q′ ∈ F (m)(q)(i)(r) :

B,B choice

%Bi,&0*^&3( !$%k1% ' $p($B'&_*^(/&q′

,fi(m, i, q)

3(fr(modeflow (m,mode(i)), r, q′)

T6$ 34! -= :1$%B 4)EW[(/& Y. ! -,.(/&! .!$

> GIHGNMOJQP:R PGIHKJ'LGNMOJQP:R

0 * 9*'=)A=<J*'

B2 , E1&3(/1)'&YW X=53(FVS ,!$%S . $B ,3(/&YW 40$+&B'&!$/i1) ' %B R_` 6 $+&B 3(B W[(/& ,D$:1 -&! ' ' 4H1O(+* S T1W#B +(/& S ' $%$ K4%B@2&!% *^(/&*! #"$%7(+*) 1 ' $%$i8 2&!%2*^(/&* B,( 21 9 ' $%$

' |1='& *<(/&* ' ZY&$%,%B 421) ' ++& (;!*!$%5!:*<(/&"qfTYqLY B S ' $%$ K4%B 1 X8ZWA0$S&! :1-=E&ZY ! . "%B|1&VS+ 6( )W0(/& 0 !$%1& W ( H_(+*=1!2&! -11X8K)$. VS&%BF3($S&K)1 (/&! -,; -=I1&3(S $B%BDKZ= ' $4$`

' $yW +&! HK ' $

&(')& *+,* -.0/

21 35476984 & W ( S T;:96=<6 1 3 S><? 1 B<6 1 (@ 1&3( 94536A<?-&B4C<3Bi=D8 <@:!BE4F(@:962&=<6B4%BG698 <6A:96=<6 1 3 S TS><? 1 B<6 1 (@*<(/&hqfTYqH<B S TJI 1 :f*K4C<@: 1 KE?$45W 1 698L< E1 6B4A<@35354'1E6=< KE?$471&B453 1 : 1 (@c8M<BN: 1 354( &<?-,.(/& 1 698EF 1 F:1&3(SO45: 1g(@G6984I1&B4VS 1 ( :(@4 1 P<??Y&B45:21Q4536B:X8_WR4IW 1 ??Sp(@6454%B63(&B4'1Q4C<6T6984K <@: 1 3 B 1 ,O:R84'&B4

(U :96R63(KQ4: &B4e8V8 1 :R:B46k(+* qNTYqW S TJIX6B45:96R3C<@:B45:0W4'&B4n& Y<+,V< 1 c8i(@I( &S><? 1 B<63(/&

Z S[]\M[_^>\`\a E[Q^

bk(@698 & W ( <BEW4 1 F:1E?$4FT4V6B4%B 1 U <HS>< & W ( I 2yW4I t8V<BE&=<T<??c6B45:B6B:)(@< Jdfeg4V6 1 F 3(@F:1 6B4'&nW 1 698NIhdb(+* 8E<B4& E 1 , i1 ??_6 1 FT45:<+&B4 1 jF 1 ?? 1 :B453(@BE: kWl Ea l \Manmo M[ pEm l o 0[

qSsr5t@vuw>x#y=h&B45: ?6B:0*^(/&S<z:B4?$4536 1 (@(+*6984 & W ( qfTYqLY:K <@:B45|6B45:96~:B46S<+&B4 1 4Tg< KE?$4I p(/&Y(@354e86984'&B4 1 ::3(@FT4698 1 ,4W48 <SO4z? 1 6969?$463(Y:=<X=< K( 6"2Q6984E1Q4'& *^(/&9FA<3545(+*6984:96b=2?$45:B84546: 1 F:1E? 1 4'&X8IW c

T 1 69?$4 6B4FE? <6B45: 4?$4FT4V6X|E453?

H<696 1 K 6B4z|E453?

I c I>I I>I c I I I W I + W IW I ? " I>I I # I I I " I I WW c W I I W- W I WW " IW " " # /c W I>I I c W c

4/% < -*% #:*X "! %)

6984 1 # 6f:B3B84FA<:96 36 B4 1 1 6 1 <? 1 h<6 1%$ wW~8 1 3B87 $ W]8 <@:R $ < 6 $ FA<6=< 6 $ 3 $ :96 36'&E<|6984 $ W < <?)(c: 1 :f<*B4Rrw@%v+&,K<@:96f4 $ #- 8Y6 $ KQ4< KE?$4 6 $ j< 3"( 3?$4X4VSO4"(.,K4'W :B453 $ |E:0W 1 698j<( 1 # 6:B3=84FA<7<| :96/(c?$45:984546 $ ,0#=<@36 1 3C<? : 1 C4

1 o `),69846dW $ ? <* - 45:96W3C<@:B45:& $ W < <?)(c: 1 :J3 $ FE?$46B45:1 < K $ 6 IhcI698 $ ,!& W ( :~6 1 FT4& |E45: 1 6B4K 4696B4"2#B453 1 : 1%$ <| <F 3B8 ? $ W4" FT4F $ (3# $ ?$4

Tf84"B4J:98 $ ?$|6984 KQ4 $ F $ B44B4C<@: $ 5, $ R3 $ 354"9 <@:R6 $ W~846984"6#=<@36 1 3C<?7&B4C<@: $ < KE?)(5#B453 1 :B4S T1W <| S 3=84FA< $ W S@<? 1 |<6 1%$ 1 :8,4C<@: 1 KE?$42 1 6J %

9 :#;7< =;*>@?A7B*CEDGFH ;+IJ<K;7L =M*NOHPN <'Q >SRHPC L F ;7< "HR3H "HOM L6<K; HO3D+C L F*>TA Q; M*CEMU <V N <KL F*CE>EH ; RWH Q U'UKCSMUCEM*DXA ;7Q*L HYMA/=ZA7C < M?@=KMR[A QW; M*CEM*U < M < FA7C L CE\=A7C < M] >ED < ?=^D+C L F*>EHHY_WFH ; C L HOM@A `CA7B*CAaD+HbA7DaD+B < aHOR6A7B*=AcA7B*H ; HCEDd=F < A7HOM@A7CS=K> Ie<;fL =;CSMUgA7BH L =KMhD+HYAi=KR*RCA7C < MG=KM*R ; H L6< '=> < FH ; =ZA7C < M*DCEMjA7BH^=DXA ; =KNYAH K=K> Q =ZA7C < M=>SU <K; CA7B Lk;7Q M=K> L6< DXA`A `CSNYH0=D I =KDXA?*N <'L F*= ; HRhA < A7B*HfN Q;+; HOM@A`B*=KD+BGD+HbA7DO]

TM45:963C<@:B4tload tDin

tflow tsgc tDout tval ttot ml"nnZlopq I c /c /c "rsut ot l"n@vwwtSs l"n " /c n xyz'Pt W I I c W W I " W I " W I c nZ|tSwmp@l v ml"n I W c I W I "~ su p ~ xWyz'Pt c I>I I c I c I " /c yzKt x+p " IW I>I " I Y Y Y Y

4%?" f)&(*$ / 6 *3%)&(Z+ JG* )J3&'JZh*'JG:A,&%X% %&'JZ"!-) *#Z+ 7^b0z&*A*%, ) *L// *?g*'h %1Z:"&'J 7d '%% 6 J%S<&)H *'/+ /*H! <)J*'/<&(L1% %c/1*G*'8% 1/ * =%* 6 J/=U H%,+H *' J%*H! 6 /+$/'+ ( < $ /3)'+ 7

IW "

TM45:963C<@:B4 6 4 : 1%$ : 3 $ FFT426 ml"nnZlopq I 1 ??$4 - <?M4?$4FT4V6 1 $ 6 6Wql *xWyz'Pt I B4 E1 B45| <696 1 K 6B4 F 1 :B: 1 -rsut ot l"n@vwwtSs l"n W F 1 :=: 1 -:S NT & Y<696 1 K 6B4 $ n xyz'Pt l sJtStSs nz W 6bW $ | $ 3 FT426B:4?$4FT4V6B: $ 6 6"2 1 tSsu"nxyz'Pt W | 1 B45369?)( 1 & T| 1 B45369?)( 1 pWzYpws xW*zK " I <696 1 K 6B45: 4FE6 1 < KE?$4& $ 4 T6B45:96:Z 1%$ :p l x+p wplGxWyWzKt I F 1 :=: 1 -:S NT wv myWnZl@p l I I $ 4 :B6B4" 'Y 1 1 6B4 3C<*B| 1 <? 1 6/(j45:B6 1 FA<6B4W: 1%$ :4" $ n@tSs l"nxWyzKt I>I W 3 $ FE? 1 3C<6B45||E4"E698;Y B453 B: 1 SO4 4" $ &

$ :B: 1 KE?$4 $ W < <?)( : 1 : K #-4" $ B:X<*B4JF 1 :B: 1 - <696 1 K 6B45:

nZ|tSwmp@l v ml"n c <696 1 K 6B45: $ &E4FE6 1 < KE?$4 #&T3 $ V6B426nz Wzs t n"s n I B4 E1 B45| <696 1 K 6B4 F 1 :B: 1 -~ su p ~ xWyz'Pt I 6B4 6 KQ4', $ B4W| $ 3 FT4V6 4?$4FT4V6yzKt x+p Y Y : FFA<*( - =<*E8 S@<? 1 |<6 1%$ j $ 66B4"9F 1 <6B45|Pt n@wl@ ^qfTYq Y Y : FFA<*( - =<*E8 S@<? 1 |<6 1%$ j $ 66B4"9F 1 <6B45|

4/% / 4X /+$ *'/.*' *"* :G0 4"0 <+N*' R0)JG&'JZ 7

FFA<*( - =<*E8 S><? 1 |<6 1%$ `&28 $ 4VSO4"& 8 <@: KQ453 $ FT4J%"tv 1 6984S? <* - 4"f3C<@:B45:& <| 1 6984yWzKt x+pS3C<@:B4&@| $ 45: $ 66B4"9F 1 <6B4~<6M<?? ~1 698 1 B4C<@: $ < KE?$46 1 FT4 8 $ B:

$ 698 1 :M3 $ ?$|K 4| 4

6 $ b? 3B84FA<6 $$ ?$::96 1 ??=<6984" 1 FFA<6 B4& $ 1 6 3 $ ?$| K 4 698 <6 4 - 44"=<6B4K <@| : FFA<*(- =<*E8:

E 1 - < 3B84FA<6 $$ ?$: 3=8453 $ ,6984 - 44"=<6B45| : FFA<*( - =<*E8:4B4VSO4C<?$45|N $ 698 1 - &

698 $#- 8`&c<|< 1 :Q4536 1%$ , $ C4" $ Y $ 6Y)|E4 - B454 "!$#%&J $ |E45: 0 <3C<@:B4 4 4"B4S<@|;S 1 :B45|< - < 1 :B60 , $ |7 $ 4

N4J8 $ Q4X698 <6S698 1 : 1 : $ E?)(7< 1 V6B4"9F 1 696B426X: 1 6 <6 1%$ ~1 698b? 3=84FA<6 $$ ?$: $ ~698 <6 1 6 1 :S<K #-T1 $ S: FFA<*( - =<*E83 $ :96 36 1%$ `&, $ ~698 <6SFA<696B4"'& <| KQ4? 1 4VSO4J698 <6 1 6S3C<DKQ4J: $ ?QSO45|

6T?$4C<@:B6&& W ( 8 <@:A:98 $ 45|]698 <6,K<@:B6T: FFA<*( - =<*E8 S><? 1 |<6 1%$ 1 : $ :B: 1 KE?$4 0 8 1 : n xyWzKt: FFA<*( - =<*E8 S><? 1 |<6B45| 1 ?$45:B:698 <P< F 1 6B4

<@( K 47: $ FT4j< 6 $ FA<6 $ :B45: 1 Pb '(

3=84FA<6 $$ ?$:X3C<DKQ44B4"E? <@3545|DK(Y: $ FT4698 1 - , <@:96B4"&, $ ?? $~1 - 6984 1 |E4C< $ , $ ! $ < <?)( : 1 :

)+* [ 0an^>a m o

qRB9ys%Kt@x-,.( %C"&6984 4/SO4? $ Q4 $ ,0:B6=<6 1 3 < <?)(c: 1 : <@: $ 354 < - < 1 DKQ4 1 - :9845|

/f84X|<6=<J84"B4 | $ 45: $ 63 $ F <*B4X| 1 B45369?)( ~1 698 698 <6 $ ,& W ( &KQ453C< :B4 $ ,| 110 4"B43545: 1 B4" $ 96 1 -3 $ 26B: $ ,6984 :<FT4 4" $ B: 1 6984 | 110 4"B4V6~: FFA<*( - =<*E8 S><? 1 |<6 1%$ : $ , 6 <*B4 :B45|324 $ 4VSO4"&K $ 698 1 Y6984 $ (Y<|3#=<@36 1 354& 4W<*B4F $ B44#B453 1 :B4R # $ KE?$4F ~1 698j<696 1 K 6B4W|<6=<6b(Q45: KQ4 1 -<*## $ 1 FA<6B45| 6 $

char∗3C< :B45| & W ( < FKQ4" $ ,i: 1%$ :4" $ B: 0 48 <HSO4X<?F $ :96Y)4E<@36|<6=<

6b(Q45:2

IW

:0, $ R69845:B4 / Y:K <@:=45| 6b( 1 3C<?i3C<@:=45: $ ,g:B3B84FA<O:96b(2?$45:B84546~6 1 E?$45:& 6984"B4GB4FA< 1 : $ E?)(A6 $ :=<@(698 <64#B453 1 : 1%$ 1 : 4E354??$4V6&i<|698 <6 $ j# $ $ :B45| $ 8# 1 X45|E4"98 $ ,| $ 3 FT4V6 $ B|E4"W<*## $ 1FA<6 1%$ `&Q<| : $ FT4 1 | $ ,^#B45| 1 3C<6B4z4><? <6 1%$ ? 1 4 $ | $ /$ 0 |E453 $ =<6 $ B::B454F 6 $ 4 6984$ E?)(Y698 1 - :SF 1 :=: 1 - , $ 6Q4"O,K4536 1%$ 0 ~1 698j698 1 :S6B45:B6S:B46& 698 <6 1 :2

0l ^O[ \[_^>\ l ^>[_^

(F 1 1 3C<?Q6B45:96 1 - ~1 698c3=84FA< <@:=45:6 1 E?$45: <@:f<JF $ |E4"=<6B4X: 353545:B:&# 1 FA<* 1 ?)( 453C< :B4<@< 1 ? < ?$4 $ 6 6 : 1 |E4S:B3B84FA<@: 0$ ?$| $ 6(? $ <@| 1 26 $ b '(c3B84FA<6 $$ ?$:<6(6984f6 1 FT4 $ , 1 6 1 - &<|j3 $ ?$|j $ 6 4J3 $ O4"96B45| B4? 1 < ?)(Y6 $ : $ FT4698 1 - 698 <6 0$ ?$|32 E1 6B4 ? <6B4 1 j6984# $ 3545:B:& 44, $ |<: $ ? 6 1%$ `& 6 (Y6984j6984"B4 <@:S $ 6 1 FT4, $ S4><? <6 1%$ $ , <? <* - 4"&#B4C<? 8$ 9?$|j6B45:96:=462/f8 1 :6B4FA< 1 :&6984`&? <* - 4?)(Y<6 $! | $ 2

" [ o[ *l$#%#&

4F $ :96=<6 1 - <(c698 1 - 4F 1 1 3C<??)( < a$ 6 6984<@|E4 <@3"( $ , $ F $ |E4? 1 -5$ ,'() /+* : 453 1, 33 $ :96 36B: <@:A $ 65 $ :=: 1- ?$4&~<@: 1 6 1 :T $ 6Y4O4 < 453 $ FFT4|<6 1%$ (O46&S<|P6984"B4 1 :3 B4269?)( $ E?)(k,K4 <|]4/. 4: 1 O4:B3=84FA< < <*B4N:96/(c?$45:9845465# $ 3545:=: $ B:7<0>< 1 ? < ?$42 N4 8 <O41 :96B4C<@| B45: $ 96B45| 6 $ :B4?e, FA<@|E4 1 6 6B45:96 3C<@:B45:W& $ 6984<@: 4536B:698 <6 4 4? 1 4O45| 4"B4 6984 F $ :961 F $ 96=<V61

•e^ $ 4"h, 36 1%$ 1 - $ ,06984W:96b(2?$45:B84546: 1 FE? 1, 4""2E $ FA<@:32 1 -.$ ,(4" $ B:

•e^ $ 4" 48 < 1%$ 6, $ ~F $ |E45:<| "

•e^ $ 4" 48 < 1%$ 6, $ ~F $ |E45: 1 : FFA<*( - =<*E83 $ :96 36 1%$

•n|E426 1 6/(Y6=<:O, $ 9FA<6 1%$ 4" $ ,XB454 ~1 698 3 $ ( 1 -T$ , <(Y: 1 FE?$4W|<6=<6b(Q4

•n|E426 1 6/(Y6=<:O, $ 9FA<6 1%$ 4" $ ,XB454 ~1 698 :=<FT4 <FT4&#| 110 4"B426 6/( 4z4?$4FT4V6B: 1 :B3B84FA<

•n|E426 1 6/(Y6=<:O, $ 9FA<6 1%$ 4" $ ,XB454 ~1 698 : % :96 1 6 6 1%$ - $ : 1 :B3=84FA<

•n|E426 1 6/(Y6=<:O, $ 9FA<6 1%$ 4" $ ,XB454 ~1 698 : % 6b( 1 -4 (74/.c6B4: 1%$ 1 j:B3B84FA<

•4 :B4 $ ,(4/.Q4" 1 435451 |E4V6 1 ,X(3 $ B4536 1%$ :2, $ &6* ( : 1%$ :S4" $ B:

/f846B45:96B:<*B4 $ 6J< 6 $ FA<6 1 3 B4 - B45:B: 1%$ 6B45:96B:37982 6984"( 4"B4 FA< <??)(&M<| 6984B45: ?6B:K<:L| F $ , <3 $ V6 $ ?3 $ - =<*E8`& $ <: FFA<*( - =<*E8; 4"B4 1 :Z 4536B45|YFA< <??)(2<>=9? <; =F ;7< R Q NYA7C < M4@ACBED A <@< >)? =D+HYA <KI; HOU ; HOD+D+C < M.A7HODXA7DGF <KQ >SRHHG=IGJKMLONP ;+;7<K; D8N=KM.N <KL HG=> < MUQFa=9RA7B ;7<KQ U'B4R*=A/=0DXA ;7Q NYA QW; HODO?=MRH*=KNOS L =F*FCSMUgA7BHOC ;<K; CEU'CEM N=KMHHUT"H ; RhA7C L HWVmN < MD Q*L CEM*UW] ? <K; A7B*CEDF ;7<3X HONbA?!F`B*CEN/BL H ; HO>YR2CEMET'HODXA7CEU"=A7HYD I H=KD+C6H*CE>ECAZR@?=0A7HODXA`D Q CA7H^CEDdA <@< HY_WFHOM*D+C6T"HK]

I*

kWlG# a l \Manmo

n:96B4C<@|d& 4 8 <O4, $ 3 :=45| $ , | 1 - <( # $ ?$4FT: 1 6984 6=<: 1 6 1%$ ,X $ F () / 4"B: 1%$ LI 6 $ 4"B: 1%$ *&(<| , $ F /;6 $ c3B84FA< 2 - $ 1 - 1 :B: 45:B4? <6B45|D6 $ () /+* <*=<FT46B4"B:<| ><* 1 < ?$45: K< , ?? 1 FE?$4FT4V6=<6 1%$ $ , $ < <?)( : 1 : $ L6B4F $ =<*(D6B4545: $ ,6B4F $ =<*( 6B4545:J| $ 45:X $ 6(O464/. 1 :96'& 6984 # 1 FA<*( : $ B354 $ ,4 : 1%$ :J4" $ B: 1 :X6984 1 3"B4C<@:=45|4/.#B45:B: 1 O445:B:v:96 1 36945:B: $ ,: c3=84FA<6b(Q45:24 $ FA<(: 1%$ :4" $ B:3C< 48, $ |A|E4" 4|E::96 $ - ?)( $ T6984 w@" t r Xt M%y uw %52 /f8# $#- 8 $ 66984 # $ 4536&## $ Q4"4><? <6 1%$ <@: :B4" 1%$ :9?)(8 <F 4"B45| ( 1

•c3C<*B3 1 6/( $ ,04F 1 1 3C<?M6B45:96S3C<@:B45:Q 6 1 E?$45: $ ,g6=<:, $ 9FT:X<| 1 # 6& $ 6 6:B3=84FA<@:

•c3C<*B3 1 6/( $ ,g8 1)- 8 <? 1 6b( $ 6 6 :B3B84FA<@:

(F 1 1 3C<?~6B45:B6z3C<@:B45: 4"B4cw@ 6 $ , | $ L6984 N4 1,<( 4"B4A $ 6 # $ 4" : 6 $ 6=<:O, $ 9FT:&f<|GFA<(? <@3 2O45|]< 0$ 92 1 - 1 # 6 :B3B84FA< 2 /f8 1 :A: 1 6 <6 1%$ ]| $ 45: $ 6&R8 $ 4O4"&FT4C<698 <66984 8 $ ?$4 1 |E4C< $ ,:96=<6 1 3 ) / @<? 1 |<6 1%$ 1 1 :R:96 1 ?? M a$ 9 , $ gB4C<? 8$ 9?$|Y<*#E? 1 3C<6 1%$ 1 :S: $$ <@:~6984() / 4"B: 1%$ :*6=<: 1 6 1%$ 1 :~3 $ FE?$46B4&#:96/(c?$45:984546 < 698 $ B: ~1 ?? 453 $ FT4z< <*B4$ ,69843 $ E? 1 - 46 454N:B3=84FA<@:<| :96b(2?$45:984546B:K<?? ~1 ?? 4 4545|E45|,<6X6984z:=<FT4z6 1 FT4E'&_<|6984"( ~1 ?? 453 $ FT4JF $ B4? 1 2O4?)(Y6 $ 4J| 1 :96 1- 6B45|76 $- 46984"2/f84 <? 1 6/(T# $ ?$4F $ , $ 6 6S:B3B84FA<@:f8 <@|j<z: 1 FE?$4J3C< :B451/f8# $#- 876984G <*96 $ ,6984G# $ 4536 84"B4Yb '(c3=84FA<6 $$ ?$: <@:<0>< 1 ? < ?$407& 1 6 8$ ?$| $ E?)( 3 $ :96 36: FFA<*( - =<*E8:,X $ F$ 4X:B3B84FA< ? < - < - 451 B45:96 1 36B45|: % :B46 $ , 4? <C.d+2 $ 6f<W: 1 - ?$44? <C.d :B3=84FA<, $ |$ T6984 N4 <@: $ T69846# $ Q4"&B45:96 1 36B45|., $ 9F &c<|6984 $ E?)(3 $ O4"96B4"g, $ |6 $ 3 $ O4"96 c3=84FA< 6 $ 4? <C.Jd M : /q@p@r5 8$ ?$|D4 1 6984"3"=<@:98 , $ <?? : c3=84FA< O4"B: 1%$ : $ , 4/ I :B3B84FA<@:, $ | '& $ 3 $ O4"966 $ : $ FT4698 1 - 698 <6 <@:z $ 6 $ L6984.# $ Q4"&iB45:B6 1 36B45|, $ 9F 2 $ O4"B: 1%$ , $ F / :96 1 ?? ~1 698 7q@p@r <@:W&26984`& :=45|<@:~<z? <@:968B45: $ 96&B45: ?6 1 -1 $ 6 6X:B3B84FA<@:698 <6| 1 |Y $ 64/.E354545| / 1 4/.#B45:B: 1 O445:B:2 <?F $ :96 $ 1%$ : : $ ? 6 1%$ <@:., $ | 1 ]6984 , <?8 $ 37 1 / $ :B4 <@:T6984 $ 6 6Y:B3=84FA<: FFA<*( - =<*E8A6984 9w@xE%sr5t@vu : FFA<*( - =<*E8 3 $ :B6 36B45|,X $ F <jVvx 6=<:O, $ 9F & : 1 -6984 $ 1)->1 <?t T:B3=84FA< $ ]6984N x@ : 1 |E42 /f8 1 : 1 : E1 6B4 ,4C<@: 1- ?$4 453C< :B4&S<@: &6* ( 8 <@:<?)B4C<@|(T|E4F $ :96=<6B45|d& : FFA<*( - =<*E83 $ :96 36 1%$ ,X $ F < - 44" 1 3 1 |E4V6 1 6b(T6=<:O, $ 9F 3C< 4FA<@|E4W3 $ FE?$46B4?)( ~1 698 $ 6? $ :B: $ , 1 , $ 9FA<6 1%$ 2

E?)(j6 0$5-$$ | 6B45:96 3C<@:B45: 4"B4, $ |32b $ 698 :B4W6984 :B3=84FA< $ 6984 1 # 6J: 1 |E4&Q<| A3',(2 T<@: $ 6 62 $ 6A69847?$4 - <@3"( / M <@:=45| O4"B: 1%$ $ , Pt n@wl@& &6* ( $ 6B476984"( 1 6T8 <@|G6 $$ FA<( 4" $ B:, $ 4#=<@36 1 3C<?04><? <6 1%$ 2 N4? <* - 4?)( < - B45451)6 1 :J< $ ?$|:96b(2?$45:B84546&Q8 <0 1 - 8 <@| , $ J| 110 4"B42645| 1 6 $ B:X<|7 FT4" $ :X3B8 < - 45: 1 1 6B:S:Q453 1, 45| 1 # 6? < - < - 42< "! M I =NYA?*M < TK=K>ECSR*=A7C < MH=N S0VmHOMRhHY_WCEDXA7HR IJ<K; A7B*H ; DXA$#%& <I A7B*HfF ;7<3X HONYA' DfR Q; =ZA7C < M<"(YB*HYM*NOHfA7BH^R' < B)

I

f<6B4 -$ ( 3 $ V6 7- <*B|E45|<696 1- 6B4 3 $ ( 1 - * I 8 1 6B45: <@354W $ 9FA<? 1 h<6 1%$ #- ) #& ) e0<*=<FT46B4"B:X6=<!2 1 - |E4', < ?64FE6/( ><? 4 I*n ><? 1 |j3B8 1 ?$| I 4 E1 B45| <696 1- 6B4 F 1 :B: 1 - In ><? 1 |4FE6/( ~3 $ 26B4V6B: *

"!# "!%$&(')* "!% +$,-. (./01* (2!345+*6(7-8-9:;<=95'9 "!=6 (>.?1'1+.@ ($AB+!C (5DE:GFH=F (1D(: "!IJ+!8,:** (:IK91L+*@-J+!8,:* "*M!09K-8191;1NOP(!87*1(Q:* "*R*:S$& "T*:5U*29/URJU'912VEW?(!DX:*Y96"96(9*1DX<K+*!!6"hB!AZ=OP[c<=91! ":=! (91@*:5U*\+*'9:N@9 -]6".+DE1D>U-* .E*\'; (8!6C5Y>^(_ J!-*.')* "!7!DEX^`__': (8!6a- "CU-* .E*1Lbc- "(W$d! (Z+Q +$e ".Y:** (L$& "f*9UZ(2DZ!18X.* ".:Ng-h 91"';H! (*J+iU (!.6UjZ(H-. (.k:* "*@':(.-D8J05!60<=9-"';Z! (*J+iU (!J ($ ( U(.d$&* (l!.E@bm918a+*\^(_(n?^:!+DC "! 0C'; (!/+!1W+!D7U$o*:*<L(*Dd89 "Y!"*:*!+<=9-/(';"W<=95'9>*9\ (..ER*'91DE K! +Y('1';1E1NK9 g ++::k*!6DE;$B(.A U(.;jH':+16( (*8K'1+.1D 89 U<p!/-1!- (Z1+,(*(:1*1 (.E (!MK971 U+!21+-1:J\* q+<L8E ?7'1+Dr<=A*9#s! "!:E8r(*(;11W .EC9DE:$B+. U+.HL*9,:E8>-*!6WE':(.-!6C9\1* (NtK9,-8-9:;K5=+! RE[E,H (!"uE! R[E EW9'1+! /2 " (5DE1DQN

n6, < 1 ?$45| @<? 1 |<6 1%$ ~1 698L< 1 F#B45:B: 1 O44v 74" $ B:& 8 1 3B8 4"B4 <*96 1 6 1%$ 45| $#- 8E?)( 1 /g< ?$4I(w#2# $#- 8E?)( $ 4J698 1 B|<*B4J: 1%$ :"2E6984B45:B6<*B4B4C<? 7)x 1%$ :J4" $ B: 84"B4<*#Q4C<*X? <* - 4?)(j6 $4 4 | 4z6 $ :B6/(c?$45:984546< 698 $ B: 8 <0 1 - ? $ :96 3 $ 26 $ ?7&i<| : 1 - #B45| 1 3C<6B45:4, $ 3 $ V6 $ ?? 1 -zy $ <64E? <@3545: 84"B4:B4?$4536 1%$ :B4FA<26 1 35:J8 <@| 454,F $ B4<* # $ # 1 <6B42 N4X: : 4536R698 <6~FA<( $ ,69845:B4G#B45| 1 3C<6B45: 4"B4W<@|E|E45|7| 1 - ,X=<V6 1 3J4 0d$ 96B:f6 $ - 466984J6=<:, $ 9FA<6 1%$ B45: ?6B: $ ,(: 1 - ?$4 1 # 6 1 :96=<3545:6 $ :B3B84FA< ><? 1 |<6B4E/f8 1 96b(4" $ B: 4"B4J| 4X6 $ M|/L~ /<|3M|/@~ ME<696 1- 6B45: ~1 698 1 # 6 :Q453 1, 45|Y6/( 45: 4 1 -M|E=~:E 245|j6 $ 6984 4 / $ 6 6& 84"B4J6984"( 4"B4 |E453? <*B45|32/f84J:B3=84FA<8 <@:S<8 1 :96 $ (|<6 1 - <@3326 $ I& ~1 6987 FT4" $ :hB4 1 : 1%$ :<|7<@|E| 1 6 1%$ : : 1 354&1 3? | 1 - 6984W698 1 B| <*96b(:Q453 1, 3C<6 1%$ : 1 3? |E45|d&_<| ~1 698 <45| 1 6 $ <@332c? $-5$ ,, $ 2Q4 $ E?$42/f8 1 :8 <@:~?$4C<@|76 $ 6B4FE? <6B45: ? 1 2O4698 1 : $ 451Y: E / /Q| | ? |M| TR3| Y* | T |Id Y |l | l H Q|EY~ ?I M? R \ G # ? / I I I X M /

<; M*H=MRh=gB*=K> I R*= RWD;FaH ; HfD+FHOM@AdRWH H Q U'UKCSMU^A7B*H T'=>SCSR=A <K; = I A7H ; U'HYA+A7CEMUgA7BCSD ; HOD Q >A?> <@< SCEM*U Ie<; A7B*H H Q U A7B*=AN= Q D+HR2=gD+HYA <KI<1 NYCu=>E¡ #¢ ; HY>SHO=KD+HODaA < H ;+; A7B*=A H='RW>YR@] DaB*Hi>SHYD+D < M2>SHO= ; M*HORFa=KDaA7B*=AK£%=U"=CSM¤ A7B*H ; HR¥t¦KM < H Q UCN! A A7B*H+HHOUKCEM*M*CEMU <KI A7B*HTK=K>ECSR*=ZA <K; ' Dg>SC I HG=D ;7Q M*M*CEMU4N < RHK? L =9REHH\§1¨© <KI DXA ; =M*UKHWVm> <@< SCSMU ; HOD Q >A7D'FaH ; H2R Q H[A <H Q U'DfCEMA7B*H'TK=K>ECSR*=ZA <K; ]UB=A7H ; ?= I A7H ; N < RH L =A QW; CAZR@? L6< DXAfD QW; F ; CED+CEM*U ; HOD Q >A7D FaH ; H2ª«¦¬5¬ TK=K>ECSR*=A7C < MPH ;+;7<K; D N DHODXAN=KD+HYDk®*MRCEMUGH Q U'D`CEMGF ;7< U ; = L A7B*HF ;7< U ; = L N < RH B*='R HHYN <'L HF ;7< U ; = L N < RWHK®MRWCEM*UGH Q UKDCEMGA7HYDXA`N=KD+HODO]E]E]

I+¯ I

/f8 1 : , B:964/.Q4" 1 4354 ~1 698><? 1 |<6 1 - <T? <* - 4:B3B84FA<O 6=<:, $ 9F :B3=84FA<Y6 1 E?$4 1 | 1 3C<6B45:X698 <66984z F 4" $ ,4" $ B: - $ : $ 6 $ , # $ $ 96 1%$ ~1 6986984:B3=84FA<O:96/(c?$45:984546J: 1 4&Q<| 698 <6X6984: 1 4 $ ,i6984 8 $ ?$4 :B3=84FA<3C< - $ 6 $ <*B|E:f? $ :B: $ , $ O4"9 1 4 <| 3 $ 26 $ ?'n: < - 84696 1 ~1 698 $ 6# $ Q4"h $ 4" 6 $$ ? 1 - 2

Z [ ^ l$# [_^ * [gm * \`[ l # [

45: 1 6B4W<z F 4" $ ,M3B8 <??$4 - 45:6 $ < ><? 1 |<6 $ Q 8 FA< $ S< 6 $ FA<6 1 3E'& $ S4/.<FE?$46=<:O, $ 9F w>" Ow>)% 1 6<? <@( :j# $ | 3545:><? 1 | 4/ & ->1 O4 ><? 1 |j:=<?$45:hB4" $ 96B:2 $ FT4W3=8 <??$4 - 45:& ~1 698 B4 E1 B4FT426B:h, $ <><? 1 |<6 $ S $ 6S6 $ : 1%$ :9?)(74"&<*B451

•/f84"B4 <*B46 8$ |/| FA<6B3B8 1 - 6B4FE? <6B45:& $ 4W< : $ ? 6B4 <| $ 4J $ 62 b $ 69878 <@|j3 $ B4536# 1%$ 1 6/(73 $ F 6B45| $ 6984 $ 6984"S8 <|d& a$ 698 4"B4 <?$: $ :B45|32

•U@<? <6 1%$ $ ,(6984PEMT, 36 1%$ 1

r3& $ O4"J<4 FT4"=<6B45| : 1 FE?$4W6/(Q4 <|<A:96 1 -

? 1 6B4"=<? 0$ 92O45| , 4

•/f84X/?| 1 :96 36 1%$ 1

t3B46=< 1 45| #B453 1 : 1%$

•/f84"B4<*B4S6 0$ | 110 4"B4V66B4FE? <6B45:

r5<|

r6FA<6B3=8 1 - 4?$4FT426B: <FT45|Q#& ~1 698<4 1 :92

698 <6 < #-- ( @<? 1 |<6 $ 3 $ , :B45: y $ 6 $ 69846 0$ 2 /f8 <6| 1 |7 $ 6S8 <*#Q4 2

•/f84Xt? "!#$t&%(' / 1 6984? <@:96W6B4FE? <6B4 ?$4T3 $ 1 45|N6 $ < 1 26B4 - 4"<696 1- 6B4, $ F < 1 V6B4 - 4" |<6=<6b(Q42 $ 4" $ B: 4"B4B4" $ 96B45|32

• ) N|<6=<6/( 45:3 $ 1 45|+*-, 2

.Amo0/ #21 ^>anmo

/ $ 6984 |E4 - B454 6B45:96B45|d&~6984 $ E?)( 6 8$ <@: 4536B: 1 $ :96=<6 1 3:() / ><? 1 |<6 1%$ ]698 <67:96 1 ?? 4545|1 F# $ O4FT4V6 , $ <5#=<@36 1 3C<? $ ? 1 4 <*#E? 1 3C<6 1%$ 1 <L< 698 $ 1 - 6 $$ ?<*B451Weg4"O, $ 9FA<354Y<|:B4: 1 6 1 1 6b(6 $ <*B|E:j#B45| 1 3C<6B45:2

) [ * p m *3Yl o0/0[

/f84T< 698 $ $ ,fb c3=84FA<6 $$ ?$:&(%|E4"B: +4@??$4"& 1 , $ 9FT45| :698 <6J6984"B4 1 :J:96 1 ?? $$ F , $ ? <* - 4 4"O, $ 9FA<354 1 F# $ O4FT4V6B: 7,K<@36 $ I 1 ]6984 ><? 1 |<6 1%$ <? -$ 1 698EF 265 1 698 : 3B8 <1 F# $ O4FT4V6& 698 1 - : 8$ ?$| 453 $ FT4WF 3B8F $ B4 :B4', ? 2% $ 6984"3 $ :B: 1- ?$4 1 F# $ O4FT4V6 1 : 6 $ <*#E?)( ><? 1 |<6 1%$ $ E?)( 6 $ 3 $ 26B4V6jF $ |E4?$: $ ,z4?$4FT4V6B:- 44"=<6B45| ( 6984W6=<:O, $ 9F : FFA<*( - =<*E8698 <6X8 <0O4B45354V69?)( 3B8 < - 45| 453C< :B4 $ ,45| 1 6B:17%| 110 4"B4354 - =<*E8 46 454 6 0$Py $ - =<*E8: <#B4 1%$ : 7- 44"=<6 1%$ $ 4z<|<4/.c6 7- 44"=<6 1%$

I+¯5*

$ 4 3 $ ?$| 473 $ F 6B45| <@: <]<@|E| /$ P6 $ 6984 y $ < <?)(c: 1 :2 '<? 1 |<6 1%$ ]:B8 $ ?$| 6984 4<*#E? 1 45| $ E?)(6 $ 6984S4?$4FT4V6B: 1 T69843 $ :96 36B45| : FFA<*( - =<*E8 698 <6 8 <@|T6984 1 R3 $ V6B426F $ |E4?3=8 < - 45|7| 1 - 6984 - 44"=<6 1%$ 2 /f8 1 : 1 :f426 1 B4?)( $ :B: 1- ?$4 ~1 698 1 Yb c3B84FA<6 $$ ?$:& 6f $ 6(O46 1 FE?$4FT426B45|32

)+* m3Mm^ l$# )+* [fa / l \[_^ l o * m mp pf[/(m *l \gm * ^

* - 44"=<? 1 F#B45:=: 1%$ $ #B453 1 : 1%$ $ ,6984 y $ < <?)( : 1 : 1 :698 <6 1 zF $ :96iB45:Q4536B:& 1 6 1 :g4/. 354??$4261 t74/.E<FE?$45: 4"B4 , $ | <|, $ 4: 353545:B:O, ??)( 3 $ :96 36B45| 698 <6JFA<@|E44?$4FT4V6B: ~1 6986984 1)- 8V6 x w@uA 6 $ - 453 $ FT4 3 $ 26B4/.c6 6/( 45: $ ,: $ FT476B4FE? <6B4 1 P6984 < <?)(c: 1 :2/f844 <69874/. 6B4: 1%$ 76 1 332Y:B454FT45| $ O4"=<??: 3 1 4V6~6 $ 2O454" y $ :~:B4" <*=<6B4&E4O4 1 73 $ FE?$4/. $ $$ 9?)(Y|E45: 1)- 45|j3C<@:=45:2b8( , <*6984F $ :96W: 1%$ :J4" $ B:&` <*96 1 3 ? <*9?)( 1 ,6984: c3=84FA< 1 # 6 <| $ 6 6W6b(Q45|t n@wl@z6B45:96W3C<@:B4& 4"B4| 46 $ us%=% xz 9>yBwO)A)v%v % 2 /f84Pt n@wl@z3C<@:B4:B454FT45|d& 1 $ 1 3C<??)(&6 $ 4 <*96 1 3 ? <*9?)( <@| 453C< :B4 $ , 1 6B:< 698 $ B:? <@3 2 1 - :96=<6 1 3:@<? 1 |<6 1%$ `&S| 1 1 - 6984F 1 26 $ ? <6B4 1)- 826C. <6B3B8 1 - 1 6 ~1 698 #B45| 1 3C<6B45:&#<66 $@1 V6B: 84"B4J6984 1 @@x#w>uKy><? 1 |<6 1%$ , < 1 ?$45|%72e^B45| 1 3C<6B45:S<*B4 O4"(8 <*B|A6 $ < <?)( 4X:96=<6 1 3C<??)(A<| - 44"=<??)( 1U'O4 1 ? $ 462(<? 2)& 8 $ < 1 FT45|Y<6<X: $ |<|3 $ FE?$46B4f< <?)( : 1 :i, $ 0<X: % ? < - < - 4&>8 <@|z6 $ B45:96 1 36 < <@(z3C<@:=45: 84"B4f|<6=< ><? 45: 4"B4 4 1 - O$@1 45| 3 $ F <*B45| 2G+4@??$4"46 <? 2: #-- 45:96 : 1 - < # 1 F 1 6 1 O4W6984 $ B4F # $ O4" & 6| $ $ 6 -$ $ 6 $ B: 4 1 6X<(3, 96984"275N4 1 - <T: #-- 45:96 1%$ , $ <T: 1 FE?$4 #B45| 1 3C<6B43B845332O4" : $ : 1 FE?$4&Q698 <6 1 6:98 $ ?$| 44C<@:( , $ :B4"B:6 $A1 |E426 1 , ( 69843C<@:B45:X698 <6 1 6 ~1 ??B453 $- 1 4 :26984W3C<@:=45: 1 6 ~1 ?? ->1 O4 $ 7 1 1/f84 2 1 |E: $ ,j#B45| 1 3C<6B45: B453 $- 1 45| ~1 ?? 4698 $ :B4698 <6A<@:B:=4"96T: $ FT4698 1 - ~1 698 1 $ 4 tc&2 $ -/M :B6B4" :S| 1 :96=<354 $ , < $ |E451

• /tW Y~~/ & EMW I=~~b?/E value!

• tR~~b?/"

• "Z~/~/"

• Q(!|E/Z~~ I !# #(G n !

•<( $ ,g6984 < a$ O4& ~1 698< E ! #, 36 1%$ <* $ |76984W4/.#B45:B: 1%$

e^B45| 1 3C<6B4z6B45:96B:S3 $ ?$| $ 4J|E45: 1)- 45| 6 $ 0$ 923=<6984" F 3B8 ? 1 2O4J $ |E4J6B45:96 S···

test(Ω)'&#4/. 354"E6

698 <6 84"B4 $ |E4z6B45:96 $ E?)( B w@ x $ > %5yBw@V /M:&Q<#B45| 1 3C<6B4698 <6FA<(N95 w@sxc& @s%y=w@ $ WBVByBt@9w>)T< / 2<$# DaB*CED^CED^F QW; H8D+FHON Q >S=A7C < M?A7B <'Q UKB]Z¡ H[R < M < AUSM < F F`B < B=KR= Q A7B <K; CAZR A <2L6< RC I R A7B*HgA ; =KMD Ie<K;7L =MRP=A

F`B=ZAfA7C L H']&% Q AiA7B*H^A ; =KMD Ie<;7L R < HYD HH= ; A ; =KNYHOD <I D <KL HYA7B*CEM*U6>EC6S"H A7B=ZA?=KM*R D QW; HO>YR4N <KQ >SR HHOM*H®*AiHOM <;7L6<'Q D+>YRIJ;7<KL DXA/=ZA7CENUT'=>SCSRWCEA R@]<79 DaB*HgF ; HORCEN=A7HgCEM(' Q HODXA7C < M N <KQ >SR =K>ED <$X Q DXAHHgB*CEUKB*>ECEU'B@A7HR CSMA7BHgHORCA <K; ?=KM*R=)CRV < T"H ; A7HY_AiN <'Q >SR Hb_F>S=KCEM

F`B=ZAA7BHUT'=>ECuR=A <;* A7BCSMCSD,+iCA L H=M*D

I+¯E¯

/f84f|E453 $ =<6 $ 1 :0<:96=<|<*B|453 $ =<6 $ |E45: 1)- <696B4"9 1 :96=<354 I+¯Z'&698 <6 ~1 ?? F $ | 1 , (W: $ FT4 $ ,69848, 36 1%$ :(|E4 , 45| 1 c4536 1%$ qv 2 $ 6984 / 2%X:(<X|E453 $ =<6 $ & 1 6 ~1 ??E8 <0O4S<?? 69848# $ 4"96 1 45:$ , < /&h: $ FT4(F $ | 1 , ( 1 - & <| <@|E| 1 6 1%$ <??)( <S: 453 1 <? $ 4"=<6 1%$

accept(q, p)& 8 1 3=8z|E46B4"9F 1 45:

1 ,#: $ FT4$ /q3C< <@:B:g6984g#B45| 1 3C<6B4R6B45:96

p<60<?? 27, |E4 , 1 6B4?)(z4 - <6 1 O4&>6984G / 1 :M| 1 :B3C<*B|E45|

1 j6984 #B45| 1 3C<6B4J6B45:962 * 6984" ~1 :B4&6984( / 1 :6B4"E? <@3545| (7<|E453 $ =<6 $ $ O4" 1 61

U.E<FE?$451p = M I=~/~/?/"-2 /f846#B45| 1 3C<6B4 1 : :(cV6=<@36 1 3C<??)( B453 $- 1 45| <@:<3C<@:B4[, $ <

<696 1- 6B4 #B45:B4V6 |E453 $ =<6 $ &c, $ | 1 <T|E453 $ =<6 $ ? 1- =<*(2/f84accept(q, p)

$ 4"=<6 1%$ <@35354"E6B: < / 1 , 1 6J8 <@:W<Y|E453? <*B45|N<696 1- 6B4 <FT45| ?/2&* 354T<696=<@3B845| 6 $ 6984 /<| $`1 6B:B4?e, 4 1 - <:B4 | $! /& 6984J|E453 $ =<6 $ S|E453? <*B45:~6984?/<696 1- 6B4cl@|vsml 2

U.E<FE?$451p = E ! MER~/~/2# -2 /f84 #B45| 1 3C<6B4 1 :A:(cV6=<@36 1 3C<??)(kB453 $- 1 45| <@: < 3C<@:=4

, $ S< n3 $ 26B4V6 F $ |E4? B45:96 1 36 $ |E453 $ =<6 $ 2 /f84accept(q, p)

$ Q4"=<6 1%$ <@35354"E6B:< /1 , 1 6B:Y3 $ V6B426jF $ |E4?J4/.#B45:B:B45| <@:7< B4 - ? <*Y? < - < - 4&| $ 45: $ 63B45: ?6 1 6984,4FE6/(? < - < - 4 84 1 26B4"B:B4536B45| ~1 698

Ed\(eifoo)

∗ K<Y? < - < - 4 $ ,S<??3 $ 26B4V6F $ |E4?$: ~1 698N $?/N4?$4FT426B: 2 * 354<696=<@3B845|P6 $ 6984 /&(6984 |E453 $ =<6 $ TB4F $ O45:7<??|E453? <*B45| ?3B8 1 ?$|B4 ,X $ F 1 6B:J3 $ V6B4V6 F $ |E4?+

Cd(qdecorated) = Cd(q)\eifoo

1 :J<??g6984 y $ < <?)(c: 1 :4545|E: 2

U.E<FE?$451p = 2 M !|R~~ ? ! ##" n 2"/f84[#B45| 1 3C<6B4 1 :(:(226=<@36 1 3C<??)(B453 $- 1 45|T<@: <X3C<@:B4, $ < n4/. 6=< <FT4 6B45:96 |E453 $ =<6 $ & 1 6B:

accept$ 4"=<6 1%$ :96 4 1 - <j4/. 6=< <FT4J6B45:96&

<|Y6984B45:96 $ , 1 6S $ 6SF $ | 1 , ( 1 - <(3# $ Q4"96 1 45: $ , < / 2

/f84J6B453=8E 1 4 ~1 ??M<?$: $ <*#E?)(5, $ \?| 4/.#B45:B: 1%$ : 1 () / :2 4?$4FT4V6B:2nY6984 y $ < <?)( : 1 :& |E453 $ =<6B45| /: ~1 ?? y $ <* $ | 46 454j6B4FE? <6B45:&F $ |E4? 1 - 6984 y $| 1 - <2B4C<?26=<:, $ 9F F $ B40,K< 1 698, ??)(W698 <4O4"2U $ FT4R3C<*B4RF :96 44/. 4"B3 1 :B45|d&O698 $#- 8`& 84y $ : $ ,~: $ FT4T|E453 $ =<6B45| /HuAv,2Y<6 <6B4FE? <6B4 ~1 698 y $ : $ ,f6984T:=<FT4 / ~1 698 $ 6z<|E453 $ =<6 $ & $ ~1 698 <T| 110 4"B426 |E453 $ =<6 $ 1 $ :B4"9@<6 1 1 6/(j3 $ ?$| 4J4|< - 4"B45|32 * 4 0$ 92>< ?$4: $ ? 6 1%$ 3 $ ?$| 46 $ 3 $ : 1 |E4"

d(q) v q

1 ? <696 1 3545:&Q: 3B8 698 <6J<A< B4 # $ < - <6 1%$ $ ,<T|E453 $ =<6 $ ?$45:B: / ~1 ??g8 <*# 4 < 6 $ FA<6 1 3C<??)( 84 1 6 1 :<@|E|E45| 6 $ <W3 $ V6B4/. 6R:B46&c<|T6 $ 4, $ B35451 5 844O4"6 0$ | 110 4"B426|E453 $ =<6 $ B: $ O4"R6984:=<FT4 /

q<*# 4C<* 1 N6984:<FT4T3 $ V6B4/. 6 :B46& a$ 698L<*B4 B4F $ O45|L<|

q1 :W<@|E|E45| 84354 $

6B4"9F | $ /$ 0 |E453 $ =<6 $ B: 2

!#"%$&'() +*&,-

5N4P, $ ?? $ $ $ X4/. 4" 1 FT426B: ~1 6986984:B4O4"=<?0:9FA<??$4"3 $ |E4 <@:B: 1 :96<? -$ 1 698EFT:: #-- 45:B6B45|32n - 44"=<?7& 4 1 6984" 1 :X:96 1 ?? 1 26B4 - =<6B45| 1 V6 $ 6984 ) $ , 69844/.E? $ =<6 $ ( 45| 1 6 $ j# $- =<F & 6X6984<? -$ 1 698EF 3 $ |E4J4/. 1 :96B:<|d& <| 4J8 <0O4 6B45:96B45|7: 1 FE?)(Y698 <6~4 1 6984" - 44"=<??)(3B46 9:S: $ ? 1 6969?$4|<6=<A698 <6 1 6 8 <*B| ?)(j3 $ V6 1- 6B45: ~1 698 <(c698 1 - 1 26B4"B45:96 1 - &_<|:B6 1 ??M| $ 45:S $ 6GB46 9 : $ F 3B81 , $ 9FA<6 1%$ 698 <6 1 6 8$ ?$| 4 $ ,g $ 84?)76 $ 6984 :B4"2

I+¯

&(')& G- /. D.W/

% <696B4"9 1 :w% .B4? <6 1 O4~6 $ <:B3=84FA<& 1 , 1 6 4O4" FA<6B3=845:< $ |E4 1 <( 1 :96=<354 | $ 3 FT426698 <6 1 :+@<? 1 | ~1 698 B45: 4536~6 $ 6984 :B3B84FA< 2% <698Y4/.#B45:=: 1%$ 1 :w% Bv"w>s@J tw

q1 < :B3B84FA<

d1 ,91 $ ~<( 1 :96=<354 | $ 3 FT4V6

><? 1 | 962g6 $d&26984h <698Y4/.#B45:B: 1%$ <? <(c:f:B4?$4536B:f< 4FE6b(A:B4 4354 84 6984 3 $ 26B4/.c6R $ |E4

, $ S6984 1 6B:S4><? <6 1%$ 1 : $ ,06/(Q4q2

% <698`4/.#B45:=: 1%$ 1 : w%5t@" )v" ]wv% ~1 698 B45: 453676 $ <:=3B84FA<d1 ,91 $ <( 1 :96=<354

| $ 3 FT4V6 @<? 1 | 962 6 $d&, $ <( /

q1

d1(6984 <698j4/.#B45:B: 1%$ 1 :< : B| B4? <6 1 O4W6 $

q2

% : B| <698:X<|j4/.#B45:=: 1%$ :<*B4 1 26B4"B45:96 1 - 6 $ 2c $ < $ 6 1 < ) / < 698 $ 1 - 3 $ V6B4/. 6& 453C< :B451

•/f84"( B4O4C<?_| 1 :B3"B4" <3 1 45: 46 454j6984 <@(: 1 : :B45|Y:96b(2?$45:984546B: :2g6984 <( 1 6 <@:|E4 , 45| 1 :B3=84FA<&%O4"( $ , 6B4 O4"B: 1%$ | 1 :B3"B4" <3 1 45:2

•/f84"( B4O4C<? y $ ?$4C<!2 : 1 V6 $ 3 $ |E4A698 <6 1 : $ 6 1 V6B4|E45|D6 $ 4 :=45|d&? 1 2O4A?$4 - <@3"(N3 $ |E4 $ E1 ?6 1 ?$45:

•/f84 4/.<@36 <@(D698 <6 ] <FT45:Z <@3545:T<*B4 a$ | 1 eg<698G4/.#B45:B: 1%$ 1 :< : $ B354 $ ,F 3=8 3 $ , : 1%$ <| 6 1 FT4 <@:B6 1 - 1 ) 1 V6B4|E45|] <FT45: <@354 :B4 ~1 ?? <?F $ :B6 354"96=< 1 E?)(?$4C<@|D6 $ < : B| <696B4"9: $ 4/.#B45:B: 1%$ :& <|3C<698 : 4 3C< #- 826 ~1 698 $ 66984A4545| $ ,|E4 #-->1 - 2

/f84 y $ < <?)( : 1 :<? -$ 1 698EF <@: 1 :96 FT426B45| ~1 698 < : B|74/.#B45:=: 1%$ |E46B4536 1%$ 3 $ |E451 $ R< : $ ? 6B4< : B| 1 6b( $ , EI"!#(? I?| :B4?$4536 1%$ :R<|6B4FE? <6B4h ?$4 tP <696B4"9: 3C<??6984F a$ 698

p'& 6984J6B45:B6 1 :S: 1 FE?)(

abs(p) =

absurd1 ,

S(p,Σd) = ∅ok

$ 6984" ~1 :B4 $ I"!$#+?II?| 1 :96 36 1%$ ::B4?$4536 1%$ :W&E6984B4? <6 1 O4 < : B| 1 6b(76B45:96 1 :

abs(p, q) =

absurd1 ,

S(p, q) = ∅ok

$ 6984" ~1 :B4 4? <6 1 O4,< : B| 1 6/( 1 <D:B4?$4536 1%$ | $ 45: $ 6 1 FE?)( < : $ ? 6B4,< : B| 1 6/(J6984"B4 FA<@( 4 $ 6984"3 $ 26B4/.c6T6b(Q45:2 %#N4/.#B45:B: 1%$ : 4"B4Y $ 66B45:96B45|d& 66984"(<*B4 8$ 9698(G3C<| 1 |<6B45: , $ : 3=8 < 6B45:96&Q6 $$ 1 4/.E<FE?$45: 4"B4 , $ || 1 - : $ FT4| 110 4"B426 0$ 92 1 69846B45:B6:=46 $ ,R69842 1 | %#S|E/"/G(&E ! #?'& & 84"B4~6984f6/( 40 <@: |E453? <*B45| ~1 698 $ 6 6B4/. 6 3 $ V6B4V62 45: ?6B:[,X $ F;69846B45:96:B46<*B451/f84W:=4O4j6B45:96S3C<@:B45:~ $ 6 :98 $ j8 <O4J $ < : B| <696B4"9: $ S:B4?$4536 1%$ :X<6 <?? 2

I+¯

/M45:963C<@:B4nt na nr

3 $ FFT426 ml"nnZlopq I $ <696 1- 6B45:|E453? <*B45| E1 ?6 1 <696 1- 6B4 ?$4 < : B|n xyz'Pt I I I n3? : 1%$ $ ,(<|7? <6B4"hB4F $ ><? $ ,(:B3=84FA< <*96tSsu"nxyz'Pt * IpWzYpws xW*zK * ¯p l x+p Iwv my nZl@p l v~ su p ~ xWyz'Pt yzKt x+p I *Pt n@wl@ w I* I

# =1+(:8 +!D - ".:8 .D -1') (! E*1*- (!1Nnt

a9!.?:7 +$\*:5U*.1<=A*9 .*D U:*!1N

na

5>*9r!.?:X +$ (.E18 -.*D :1'; (! E*1*- (!>! "': D(N

nr

5=*90!./12B:1'; (!sE*1* "!QW/F R Y+*=$& (R<=9'9X*90F R <K(Ya': (!Y8/2 ($*91+a'; "!*+!!6X+! 2!/*.'; (!9 (5DE!69a:1'; (!E*1*- (!MWQ+!Dq9:1'; (!rE*1*- (!<K(,$& ".!D P(<K8E,-1')C(!1E84"!.1!';"N7t1-C':"-,! +C9 U<=!9(J! *:5U\*.1K<=9s/-.D7U:*!1WE (Y-.*D-1')* "!:N

UO4698 $#- 86984"B4 1 : $ 6f< : 1 - ?$4 < : $ ? 6B4?)(A< : B| :B4?$4536 1%$ `& 4X:96 1 ?? 4? 1 4O4698 <6R: 3=8<W6B45:961 : ><? < ?$4 1 <45| 1 6 1 - 3 $ V6B4/. 6& 453C< :B4 1 6 1 : O4"(L3=84C<*3 $ FE?$4/. 1 6/( ~1 :B4&R<| 1 63C<6B3B845:: 1 FE?$4WF 1 :96/( 1 - : <|7 <FT45:Z <@354W4" $ B:2

.Amo0/ #21 ^>anmo

/f8 1 : 6B45:96 :=454FT: O4"(j: E1 6=< ?$4 , $ - 44"=<6 1 -5$ ? 1 4z8 1)- 8E? 1)- 8V6 1 - <*9 1 - : 698 <6: $ FT4698 1 - 1 :|E4 , 1 6B4?)( $ - ~1 698 <j4/.#B45:B: 1%$ `& <@:S4><? <6B45| 1 j6984J3 $ V6B4/. 6 $ , <:B3=84FA< 2

&('$# * .J/ &% #. /

X4545| ?$45:B:6 $ :<@(&S698 1 :7< <?)( : 1 : 1 : E1 6B4 : 1 FE?$451 :AFT4"B4?)(]? $$ 2 :., $ Y4FE6/( , $ Y<(PF $ |E4E3 $ 26B4/.c6R:B46B:<,6B4" y $ < <?)( : 1 :2 /,;() / :Z|"2: 1 #z<|%/?| 4"B4 <696B4FE6B45|A4><? <6B45|d&6984 1 R:B4 4354 3 $ :96 36 $ B:R3 $ ?$| <?$: $ 4<@|E|E45|A6 $ |E4C<@|A3 $ |E4< <?)( : 1 :& 6R:96/(c?$45:984546< 698 $ B:6b( 1 3C<??)( :B469845:B4 1 :96 36 1%$ : 4/.E<@369?)(6 $ 3 $ :96 36W: $ FT4698 1 - 698 <6 1 :8 <*B|,6 $ <* - 4T< a$ 6:96=<6 1 3C<??)(2 $ FT45# $- =<FFT4"B:T3 $ : 1 |E4" 1 6 <@|D:B6/(c?$4A6 $ :B4 E1 ?6 1 D6B4FE? <6B45:E1&I>I ~3C<??R698 <68 <0 1 - <us%=% x6B4FE? <6B42 $ 698 $ :B4&698 1 : |E4C<@| 3 $ |E4 < <?)( : 1 : 1 : :B4', ?X6 $ O4" 1 , (G698 <6j<?? E1 ?6 1 6B4FE? <6B45:jB4FA< 1 :=45|32

I+¯Ev

/M45:963C<@:B4nu nb

3 $ FFT4V6 ml"nnZlopq I /f84W|E4C<@| E1 ?6 1 ?$4 1 :S6984 /M =~/~ $ 4 ql xWyz'Pt r sut ot l"n@vwwtSs l"n vn xyz'Pt I ¯ /f84 < : B| <696B4"9 ?$45:W& <|j: $ FT4 E1 ?6 1 ?$45:l sJtStSs nz ¯tSsu"nxyz'Pt * *pWzYpws xW*zK * *p l x+p * ¯wplGxWyWzKt wv my nZl@p l n@tSs l"nxWyzKt InZ|tSwmp@lv ml"n vnz zs t n"s n ¯~ su p ~ xWyz'Pt ¯yzKt x+p IPt n@wl@ I

,a@ (.!" +$IDE1"D2*:5U:Nnu

5G9=': (.!e +$DE1"D2*:5Ue!0*9=.:d-8191;G EDE.:unb

5K*92'; ".!K ($DE(D ./p!1+:N

.Amo0/ #21 ^>anmo

4C<@|6B4FE? <6B4 |E46B4536 1%$ 1 :& $ ,_3 $ B:B4&2<GB4C<??)(: 1 FE?$4 < <?)(c: 1 :2"n6 3C< #- 8V6f<?F $ :96 $ |E4C<@|T3 $ |E41 :9FA<?? :B6/(c?$45:984546B:& 8 1 3=8 1 : 8 <*B| ?)(A<W: # 1 :B4: 1 354 69845:B4 4"B4j# $ < ?)( :96 1 696B4`&c6B45:96B45|d&|E4"E? $ (O45| <| $ 6 FA< 1 26=< 1 45|T? <6B4"2/f84f? <* - 48Pt n@wl@f:96b(2?$45:9845468 <@:<GB4 1 : 1%$ T8 1 :96 $ (|<6 1 - <@3 276 $ I & ~1 698<? <* - 4 , =<@36 1%$ $ ,0?$4 - <@3"(73 $ |E46984J4 45:96& ) :Q453 1, 45| O4"B: 1%$ 8 <@|#¯Ev|E4C<@|76B4FE? <6B45:2

&(' #. 9-$J-

5N4 <V66 $ #B45:B4V66 $ 6984Y:96b(2?$45:984546T< 698 $ & ->1 O4 < 6B4FE? <6B4 1 $ 2 1 -L1 :96 36 1%$ P<|G<3 $ 26B4/.c6J6b(Q4& 6984PB4C<@: $ :X698 <6J: $ FT445| - 4 y $ :G,X $ F 6984 1 :96 36 1%$ 84 1 $ 2O45| ~1 698,69843 $ 26B4/.c66b(Q4&| $ x#t>z4/. 1 :B62 *2,X3 $ B:B4& 1 63 $ B:=4& 6=<* - 46B: , $ jvvD< :B4266=<* - 466B4FE? <6B43 $ ?$| 4B4" $ 96B45|d& 6~698 <6 8$ ?$| B45: ?6 1 76 $$ FA<( $ 1%$ :& 1 , $ 9FA<6 1 O4zFT45:B:=< - 45:2 453C<??

Fl : I →M→R→ 2Σu

5N44/. 4536698 <6W<:96/(c?$45:984546W< 698 $ ? $$ 2 1 - <6J< :96b(2?$45:984546G, $ W<T? 1 6969?$4 8 1 ?$4 ~1 ??0 $ 6J4/.Q4536uTt@B y $ :S6 $ 4/. 1 :96~698 < 8 <6

Fl

B46 9: 1 6Js%W< =<6984"2 $#- 8<*## $ . 1 FA<6 1%$ `& <| : $ ? $$ 21 26 $ : 1 - 6984W:=46S| 110 4"B4354

miss(m, q, i, r) = Fl(i)(m)(r)\F (m)(q)(i)(r)

I+¯w

84"B46984\ : Σu × Σd → Σd

$ 4"=<6 $ W4/. <|E:e∗, a∗

$ 1 6B:J?$4',6 8 <| : 1 |E46 $Ed

<|Ad 4', $ B4 | $@1 - $ 9FA<?:B46S| 110 4"B4354 K<|E46=< 1 ? 2

% ,K4 4/.Q4" 1 FT4V6B:g:98 $ 45|W698 1 :miss

6 $ B46 9z6 $$ FA<( y $ :i6 $+ 4 1 , $ 9FA<6 1 O4& 84select(i) <@: $ $ 4 $ , 6984 , $ 9FT:

a~~ ! # $

a~~, $ X<(<C. 1 :

a&#: $ 6984

\:B4FA<26 1 35: <@:3B8 < - 45|

6 $ 4 0 4536 1 O4?)(74/. <|e∗, a∗

$ 1 6B:~?$4', 6 8 <| : 1 |E4J6 $∅& 1)- $ 1 - <( 6b(Q4 :B3=84FA<?$45:B: y $ :2

5 1 698: $ FT4 3 $ |E4 1 :B6 FT4V6=<6 1%$ <@|E|E45| 1 6984J< :96=<@36f4><? <6 1%$ 7<| 6B4FE? <6B4J3 $ FQ46 1 6 1%$ < <?)( 45:&E6984Ay=w %C $ ,(< y $ 4 1 - B4F $ O45|3C< 4 4" 1 45| 1

I2/f84 y $G1 : 1 ,K4C<@: 1- ?$4 |E4" 1 # 6 :B3=84FA<@<? 1 | 1 6b( 1 3? | 1 - <698T4/.#B45:B: 1%$ A< : B| 1 6/( * 2/f84 y $ 1 : $ O4" 1 |E|E4 (j<6B4FE? <6B4 ~1 698<8 1)- 84" 1 F $ 96h#B453545|E4354¯ 2/f84 y $ 1 : $ O4" 1 |E|E4 (j<6B4FE? <6B4 ~1 698<8 1)- 84"2# 1%$ 1 6/(

96984"&_|E4C<698 B4" $ 96 1 -3$ , y $ :X6 $4 E1 ?6 1 ,6B4FE? <6B45: <@:2O4"E6X:=4" <*=<6B4P,X $ F 698 <6 $ , y $ :6 $ :B4"~6B4FE? <6B4P ?$45:W&E6 $ 4 < ?$4 , ?6B4" 1 - 6984F < <@(2f<??0<:B46 $ , 45| - 4 y $ :2, $ : $ FT4 , .E45|i, r

1

⋃

m∈M,q∈Σdmiss(m, q, i, r)

< x "P, $ S6984 1 :96 36 1%$ i<|j6B4FE? <6B4

r 69845:B4 <*B4WF 1 :=: 1 -Py $ :698 <6X3C< 4P#B45:B4V6B45|

6 $- 46984" 1 < ) 2

$ FT4 6B45:96 3C<@:B45:<*# 4C<*z6 $ 8 <O4A|E4C<@|D3 $ |E4& 6 $ry $ :6 $ |E4C<@| 3 $ |E4T8 <O4 454 B4F $ O45|32nk, <@36A: 3B8 y $ : 8 <0O4 454 B4F $ O45|d& (G6984j6B4FE? <6B43 $ FQ46 1 6 1%$ < <?)( : 1 :T:B6=< - 4 $ ,J6984:B3=84FA<?$45:B: y $ < <?)( 4"& <|j| $ 45:~ $ 6<*#Q4C<* 1 j69846=< ?$42 $ W4C<@3=8 | ?$44/. 354"E6GPt n@wl@& 6984 F 4" $ , | ?$45: 1 : E1 6B4F $ |E4"=<6B43 $ F <*B45|,6 $ 6984:96b(2?$45:B84546S? 1 4W3 $ V6& FT4C< 1 - 698 <6S698 1 : < :B4V6 y $ 1 , $ 9FA<6 1%$ 3 $ ?$|j4C<@: 1 ?)( 4J| 1 :E? <@(O45| 1 < ) '& <|j698 <6 1 6 1 :~ $ 6S6 $$ O4" $ :=4J6 $ 4 1 , $ 9FA<6 1 O42

.Amo0/ #21 ^>anmo

% ? 1 6969?$4 E1 6 $ , 1 :Q4536 1%$ $ , 6984|<6=< 1 | 1 3C<6B45| 698 <6 1 6 1 :- E1 6B4 -$$ | F $ :96GB4" $ 96 1 - :B3=84FA<1 3 $ F <6 1- E1 ? 1 6b(,<| 1 3 $ F <6 1- ?$4 1 26B4"9FT45| 1 <6B4:96B4":0 E1 6B4 :B8 <*E?)(2/f84 ?6 1 FA<6B44><? <6 1%$ $ , 1 6B: 6 1 ? 1 6/( ~1 ??~ $ 6A3 $ FT4 4', $ B4j< #B45:B426=<6 1%$ $ , 1 6 1 : 1 FE?$4FT4V6B45| 1 P< ) '& 6 1 68 <@: 454|E4F $ :B6=<6B45|A698 <6R6984 <F $ 26 $ ,i|<6=< 6 $( 4h#B45:B426B45| 1 : E1 6B4 <*## $ # 1 <6B4 6984"B4<*B4:B4O4"=<?? 1 45: $ ,(: <@354G, $ S4C<@3=8 2

I+¯

/M45:963C<@:B4nbp nbep nbi nbei nui nuei l

ml"nnZlopq * * wv ql I I ¯ r sut ot l"n@vwwtSs l"n *n xyz'Pt I I I+¯ ¯l sJtStSs nz I+v I+v I I * wtSsu"nxyz'Pt I* * ¯ ¯ I* pWzYpws xW*zK * * I p l x+p v v I I I I I>I*wplGxWyWzKt w ¯ wv my nZl@p l I>I*n@tSs l"nxWyzKt I>I *Ev v v I>InZ|tSwmp@lv ml"n I I * nz zs t n"s n * ¯ * * w w *Ev5*~ su p ~ xWyz'Pt I ¯ I+¯ I+¯ w IyzKt x+p *w ¯ ¯ I+vwPt n@wl@ ¯ I ¯E¯ I+v I(w v v I * *

2nbp

Y./1Y +$G! "!:E8 .!DE11W<=91H*9,*(6";K1+\5 .Ab]!QNkK92':+./-, +$ U< 1 U(<K(K/ "-Y*1':1DE1!';H (1*5DE(Nnbep

Y.?:J +$,:!J1D6( U<YC ./p!31+:N K9P'1+.7 ($ U<S1 (K<L"C/ "-*1':1DE1!';, ":*5DE(Nnbi

R.?:L +$ .!/DE:W<=91Y9R*+*6(:e1+R5 ./p!QNeK9Z'1+.Y +$ U< *: U+<K(k'91J!'; "U*A8"Nnbei

Y./1J +$,:!1DE6"/ U<Y0* .Ab]!3:5U*11N3K9P':+./- +$ U<*: U+K<L"'91J!'; "U*A8"Nnui

d[Q(nbi

W .Y*(6";!6.:K1+:NdK9\'1+., +$ U< *: U+<K(K'9:J!': (+8(Nnuei

e[Q(nbei

W.L+*6(:!60.:L*:5U:NeK9\'1+.R ($ U< *: U+?<L"@*'910!/'; (+8(Nl Y.?:Y ($!1K!7*92-8191;1N

I+¯

&(' g/ ..

/f8 1 :S: 1 FE?$4< <?)( : 1 :~3C< , |j<?? /M:f698 <6~4O4" 453 $ FT4J3 $ 26B4/.c6~6b(Q45:~| 1 - <z6=<:O, $ 9F &<| 4O4"S<*B4:B4?$4536B45| 1 < / %# 1 :96 36 1%$ `&E<|., $ R<??Q|E453? <*B45|Y3B8 1 ?$|B4j<|<696 1- 6B45:$ , 8 1 3B8 6984:=<FT4:96=<6B4FT4V6J8 $ ?$|E:2 ) |E4": $ FT4<@:=: FE6 1%$ :&i<T#B4 6=<:O, $ 9F3C< 6984 4- 44"=<6B45| 698 <6z:96 1 :W: % 6B4545: $$ 6B45| 1 <( $ ,f69845:B44 /M:,X $ F 1 # 6& 4', $ B4 4 1 -,K45| 6 $ 6984FA< 1 6=<:O, $ 9F 2 nN3C<@:B45: 84"B4? <* - 4<F $ V6B: $ ,f|<6=< 1 : 1)- $ B45| 4" 1 45:'&M698 1 :3 $ ?$|j: % :96=<V6 1 <??)(j:=<O4J6 1 FT4 <|YFT4F $ (2/f84 :< - 4 $ ,f< - 44"=<6B45| #B4 6=<:O, $ 9F 1 : $ 6 <? <@( : :=<,K4&_4O4 1 , 1 6W| $ 45: $ 6B4F $ O4A|<6=<<@36 <??)(j<@353545:B:B45| 1 U :963 $ : 1 |E4"X<j4?$4FT4V6 |E453? <*=<6 1%$ ei

x

~1 698j6984J3 $ 26B4V6XF $ |E4? l@|

(r, s, t)

<| < e0<698 4/.#B45:=: 1%$ j:B4?$4536 1 - < |3B8 1 ?$|<eix

3 $ V6B4/. 6S $ |E4W<@:aMEZ~~ 2n6S:98 $ ?$| 4A4 1 |E4V6698 <6 1 ,( 3B8 1 ?$|B4P<*B4.B4F $ O45| 1 < #B4 6=<:O, $ 9F & 6984A:B4?$4536 1%$ ~1 ?? $ :B4?$4536: $ FT4698 1 - | 110 4"B426S698 < 4', $ B42/f84 < <?)( : 1 : 8$ 92c: : 1 FE?)( (7:=<0 1 -1 V6 $ <:B46

s11

•%?? /:~698 <6 <*B4, $ |Y6 $ 4J3 $ V6B4/. 6S6b(Q45: $ ,(: $ FT4J6B4FE? <6B4

•%?? /698 <6<*B4 1 T6984[B45: ?6 $ ,_< :96=<@369?)(4><? <6 1 - <(r|E/"z4/.#B45:B: 1%$ $ 4() /1 :96 36 1%$ : 1 ,? 1 O43 $ |E42 $ %# 1 :96 36 1%$ :W698 <64><? <6B45|,6 $ pcdata

&_6984:B46 $ ,g4?$4FT4V6+ /:f698 <6~6984:B4F 1, <?i:96B4" 1 Y6984 1 :96 36 1%$ :|I(A4/.#B45:B: 1%$ <@::=<0O45| 1 :B6B4C<@|d& $ & 1 ,X6984?$4 - 698 $ , 6984 <698;4/.#B45:B: 1%$ <@:7I&698473 $ V6B4/. 66/( 4T, $ 69844@<? <6 1%$ <@:z:=<0O45|32 /f8 1 : <@:J6 $ <0 $@1 | :<0 1 - 1 6B:B4?e,& 8 1 3=8 0$ ?$|N? <6B4"#B4O4V6w@xA|E453? <*B45| <3545:96 $ $ , 3,X $ F 4 1 -4, ?6B4"B45| < <@(2

<|76984

•4F $ 1 - ! & <|PMh,X $ F

s12 /f84S:=<,K46/( $ , 698 1 :F $ O4 1 : |E4" 6984 B4C<@: $ < ?$4E

<@:B: FE6 1%$ j698 <669846=<:O, $ 9F | $ 45:~ $ 6 :B4 <*B| :96B4":[,X $ F <( $ ,069845:B46b(Q45:2

•3 $ F 6 1 - < :B453 $ |Y:B46

s23 $ 26=< 1 1 - t|""##|E/ /M: $ ,g<?? /: 1 6984:B46&

6=<!2 1 - 3C<*B4f $ 6(6 $ 3 $ : 1 |E4" $ E?)( /M:(698 <6 4"B4 :B45|<@:(3 $ V6B4/. 6 6/( 45: <||<6=<3C<* 1 45:W& 6<?$: $ 6984W<3545:96 $ 6/( 45:S698 <6S3 $ V6=< 1 6984F 2

• 1 <??)(3 $ F 6 1 -

u = Ed\s2&c698 1 : 4 1 - 6984J:B46 $ ,g4?$4FT426S6/( 45:f698 <64 1 6984"<*B4 :B45|

| 1 B45369?)(Y6984FT:B4?-O45:& $ ~8 <O4 |E453? <*B45|j|E45:B354|<26B:698 <6X<*B4 :B45|32

%f696 1- 6B45: 4"B4 1)- $ B45|d& <@:~6984"(7<*B4J8 <*B| ?)( 0$ 9698 B4F $ 1 - 2

I

/M45:963C<@:B4|u| nt d f

ml"nnZlopq I>I * ql xWyz'Pt I v ¯ r sut ot l"n@vwwtSs l"n * I *n xyz'Pt /wv5*l sJtStSs nz I * * tSsu"nxyz'Pt * I* I pWzYpws xW*zK I>I I *E¯p l x+p I I I>IwplGxWyWzKt w wv my nZl@p l v *5* n@tSs l"nxWyzKt I+¯ I+¯nZ|tSwmp@lv ml"n I I nz zs t n"s n *5* ¯~ su p ~ xWyz'Pt ¯w ¯ IyzKt x+p w E Pt n@wl@ * I(w *

2E" Y./1Y +$.!.-D!.EY:::!RDE';5+U* "!K+!D-.J(8a6"*(97$&*(6(:!='; (.!":N|u|

*9J!.?:\ ($L.!.1D4::1!"2DE';5+U* "!:u

nt

5H9* +*(e!.?:\ ($@::1!"0D1';5+U* "!Z!r1"'9!.EH'91JNeK9\5+*6(\'; ".!L$& "^)@%5 ?1':(.H ($G(!.*D:1')* "!>*9UY51=92.E*1* +D7+=9(`E_C111!=D1';5+U* "!QNd5t9K!.?:G ($/-.J(8,6(+9\$&*(6(:!t6":!1*+D\<=95'909"k! H('9k (.E*.E-*!6Z$&+6":!1W

(!Df5K9H* +*(Q!.?:= ($t$&+6":!*1N

II

.Amo0/ #21 ^>anmo

/f8 1 :f<? -$ 1 698EF 1 :: $ 1 4/.Q4: 1 O4 1 3 $ F 6 1 - B45: $ B3545:698 <6R6984"B4 <@:R $ 4545| $ ,iFT4C<@: 1 -698 <62 n62, $ |,<., < 1 X F 4" $ , :B45|,4?$4FT4V6W|E453? <*=<6 1%$ :& 8 1 3=8N3 $ ?$| 4 :B45| 1 <T#B4 , ?6B4" - 44"=<6 $ & $ <@:< 1 , $ 9FA<6 1%$ j6 $ :B6/(c?$45:98454645| 1 6 $ B:S698 <6~6984"B4 1 :~:96 1 ??: $ FT4 1 # 6 |<6=<698 <6S8 <@: 4547F 1 :=:B45| 84"B4 3 $ FE?$46B445:B: 1 :6B4 E1 B45| 2

&(' " "M..-$ ..

/f8 1 :<? -$ 1 698EF 6B45:B6, $ (: % #- =<*E8: $ ,#6984~3 $ :96 36B45|T: FFA<*( - =<*E8698 <6 4O4" - 4 4"=<6B4 $ 6 62n6 <@: $ :B4"9O45|698 <6: $ FT4:96/(c?$45:984546B:^# $ 3545:B:B45|T: $ FT4~: % 6B4545: $ ,Q6984 1 1 6 B453 B: 1 O4?)(& 6:=454FT45| 4O4"S6 $.$ 6 6 < (2698 1#- 1 69845:B4J6=<O4"B:=<?$:2/f84: FFA<*( - =<*E8 ,X=< - FT4 6 - 4 4"=<6B45| , $ 4C<@3B8

(m ∈ M, q ∈ Σd, r ∈ R) <@:TFA<*92O45|d&

|E4"Q4 | 1#- $ 846984" $ $ 6r8 <@| < (/ M & EtW &ME! $ # 1 :96 36 1%$ :2

/f84 &0: FFA<*( - =<*E8D45| - 45: 46 454 <??6B4FE? <6B4.,X=< - FT4 6B: 4"B43 $ 354"E6 <??)( B4O4"B:=45|d&< |76984 3? $ : B4 $ ,<??a, =< - FT4 6B: ~1 698 < B4C<@3B8 < ?$4 $ 6 6 1 :96 36 1%$ <@:S3 $ F 6B45|32 1 <??)(&6984W45| - 45: 4"B4B4O4"B:=45| <@332Y6 $$ 9FA<? 2

.Amo0/ #21 ^>anmo

/f8 1 :< <?)(c: 1 :z3 $ ?$|D<@36 <??)(N3C<6B3B8: $ FT4A3C<@:B45: $ ,~6 1 FT4 <@:96 1#- 6=<O4"B:=<? $ , :B45|L: % 6B4545:$ ,6984 1 6&a# $ 1 |E45|,698 <6 $ 4 # 4" <*## $ . 1 FA<6B4E y $ < <?)( : 1 :3 $ ?$| # $ O4698 <6 $4y $8$ ?$| -$ 6 $ 6B4FE? <6B45: ~1 698 $ 6 6 1 :B6 36 1%$ :2 4 $ 4O4"&R698 1 : <@:8 <*B| ?)(D4O4"A698473C<@:B4FA<( 4 453C< :B4 $ ,06984 E1 ?6 1 ?$44, $ d&E698 <6 $ 6 6B: 3 $ 1 45: $ ,g6B4/. 6 $ |E45:2

"!

# $ , ' &%"

5N4J8 <O4 :9845|76984 4 O4? $ Q4 $ ,(:96=<6 1 3W< <?)(c: 1 :6(O46 <? 1 6969?$4 E1 66, 96984"1

•% FT4698 $ | , $ G,K<@:B6J< | E1 6B4 #B453 1 :B4() /+* y $ < <?)(c: 1 : |E4" ) c3=84FA<@<? 1 | 1 6b($ , 1 68 <@: 454 , $ |32

•/f84 6 1 FT4< |FT4F $ ( Q4"O, $ 9FA< 354 $ , - 4 4"=<?() / y $ < <?)( : 1 :X8 <@: 454 1 F# $ O45|4 $ 9F $ :9?)(J698 1 : $ ,z3 $ B:B4,4/.c6B4 |E:6 $ () /JIN< | 6 $ $ 6984"5# $- =<FT: 84"B4:e0<698

I *

<696B4" FA<6B3B8 1#- 1 : :B45|32

•26=<6 1 3 ) / ><? 1 |<6 1%$ 8 <@| 454 4/. 6B4 |E45|76 $ 3 $ O4" ) /+*A< | : c3B84FA< 2

•)68 <@: 454 |E4F $ :96=<6B45|P698 <64 ) / y $ < <?)(c: 1 : 1 : $ ,K<@:B64 $#- 8 , $ B4C<? 6 1 FT43 $ |E4 <@:=: 1 :96 :B4&E4O4 , $ ~? <* - 4W:96b(2?$45:B84546B: < |Y? <* - 4W:B3=84FA< 2

•/f84J3? < 1 FT: < a$ O4J8 <O4 454 O4" 1, 45| : 1#- < 4/. 1 :96 1#- 6B45:96 :B462

• ) /+* ~1 698 1 6B:[ <*96 1 <??)(6/( 45|Y6=< :O, $ 9FT: 1 :~:96 1 ?? $ 6< 5 ¯ 453 $ FFT4 |<6 1%$ & < | 1 61 :~6 $$ : $$ , $ [, ?? :B3C<?$4W4F 1 1 3C<?i6B45:96B:2

•4 $ 4O4"&E6B45:96S3C<@:=45: 4"B4W3 $ :96 36B45| , $ fF $ :96<*# <*B4 69?)(Y| 1 3 ?6 3C<@:B45:&< | $ FA< $ # $ ?$4FT: 4"B44, $ |32

% Q4"O, $ 9FA< 354 $ 6969?$4 453 2 1 6984 45:96Z2 $ 4/. 1 :B6 1#- #=<@36 1 3C<?U() / y $ <? -$ 1 698EF 698 <6# $ 8 1- E1 6B45| $ ? 1 4: ) / y $ < <?)(c: 1 : , $ A? <* - 4 1 :B6=< 3545:& <@:Y4? 1 F 1 <6B45| ~1 698 $ 6Y? $ :B: $ ,#B453 1 : 1%$ 2 4 $ 4O4"& 1 6~6 45| $ 6~698 <6+><? 1 |<6 1%$ <@:~6 $$ :9? $ , $ S? <* - 4 1 :96=< 3545:(/f8 1 : 4545|E: $ 6 4|E4 , E1 6 1 O451/f84: FFA<*( - =<*E8 @<? 1 |<6 1%$1 b '(4c3B84FA<6 $$ ?$:f3 $ ?$| 4<?6B4"B45| 6 $ ><? 1 |<6B4 $ ?)( <:B4?$4536B45| :B46 $ , $ |E45:&i< |N< <? -$ 1 698EF 3 $ ?$|,6984 4FA<@|E4698 <63 $ F 6B45:R6984| 110 4"B4 354 46 454 5- 4 4"=<6 1%$ <? y $ - =<*E8:2/f8 1 : 1 : # $ < ?)(A6984 , B:960# $ ?$4F6 $ 4: $ ?-O45|d& 4', $ B4 $ ? 1 4:96=<6 1 3 w@" OwOt@x $ 6 :96 y $ < <?)(c: 1 :/ 453 $ FT45:[#=<@36 1 3C<? , $ ~<??B4C<? 1 :96 1 3 1 :96=< 354 : 1 45:2% ??6# $ $ :=45| 3 $ |E4 <@:=: 1 :96T<? -$ 1 698EFT: 4"B4 1 FE?$4FT4 6B45| < | 4><? <6B45| , $ :=< E1 ? 1 6b( $ B4C<?:96b(2?$45:B84546B:&< |<??_:B454FH6 $ 4< ?$4X6 $ # $ 1 |E4X: $ FT4jB4C<?7&#=<@36 1 3C<?_84?) 2 /f8 1 : ~1 ?? ?6 1 FA<6B4?)(:98 $ 84 6984"(j<*B4 1 6B4 - =<6B45| 1 6 $ 6984W45| 1 6 $ ~1 698 # $ Q4" ) ' 1 : <? 1 <6 1%$ 2/f84 , <?6B45:96 ~1 698j6984 : c3B84FA< 1 6 |E4 , 45| Pt n@wl@X:B6/(c?$45:984546:98 $ 45|7698 <6h#B453 1 : 1%$:96 1 ??M:98 $ ?$| 4 1 F# $ O45| , $ 6#=<@36 1 3C<? :B451 e^B45| 1 3C<6B4z4@<? <6 1%$ < | <3 $ 6B4/. 6 :B4 : 1 6 1 O4 6B4F E? <6B4 <*=<FT46B4"B45: $ ? 6 1%$ <*B4 453545:B:=<*(j6 $T- 46 69844" $ J3 $ 6G, $ 698 1 :3C<@:B4| $ 6 $ 84"B4: $ FT4 3 $ , |E4 354A3C< 445:96=< ? 1 :B845| , $ W6984 :B4"W698 <6z848 <@: B4C<?R4" $ B: 84 69846 $$ ?6B4??$:8 1 F 84Y8 <@:T4" $ B:2 % ?6B4" <6 1 O4?)(&f: $ FT4 <(D:98 $ ?$| 4T, $ |6 $,1 |E4 6 1 , (D6984 y $ 698# $#- 8< :B6/(c?$45:984546 46 454 6984 <@| 3 $ :B6 36: 1 ,J6984"B4 1 : $ 4E< |P6984j4?$4FT4 6 698 <6A3 $ 6=< 1 : 1 6 ? 1 2O4W|E453 $ =<6 1#- : FFA<*( - =<*E845| - 45: ~1 698 $ 1)->11 , $ 9FA<6 1%$ & $ S698# $#- 8 < $! :B4FA< 6 1 35:1 , $ 9FA<6 1%$ $ |E4J6/(Q42

,- +'( ' " + +

% ) /`45| 1 6 $ <*#E? 1 3C<6 1%$ <@:fFA<@|E42 )6B: <@3 2 4 |73 $ |E43C< 4X8 $$ 2O45| ~1 698 :96S< a$ 6< (T,X $ 6 4 |d& 698 $#- 8 ? 1 2O4J6984 $ 4z<6\/H Z %&M|E &M|E /Q

I¯

RQ|/|L2I EMEZ 2I E"2Istylesheet input−schema output−

schemainput− namespace

input− root

stylesheetinput − schema M bg output − schema

j M a $d (a M m M bm e k ao? ca e Mlk d (a ,be a M joa m '? M m ) m 2

input−namespace M bg inputroot M ca k _ba M joa m M iUa ?$ /( M bg k _bac' k a e a\joa k M joa: ?Q / M bg 'ic_ba\j M ? d k 2 /`_ba d k m ir_ba\j M e M J M a dhmM k g a k aUi k a g k /? 'ir_ba\j M k Je ca g iUa g a e M . m ic_ba\j M m i M i ca k e k dfe k _ba '('ic_ba\j Mlk ' ehm 'ic_ba\j M 3c k a bgFdhm , Jdhm _ba g a bm a g M m k k m ir_ba\j Me M J M a2

input− namespacej M a ?j d kk a g d k _ Mlk i M m a k _ba( M efdhg Mlk ? g a M Je k m k M joa m M iUa2

input− rootj M a ?j d kk a g k _ba( M efdhg Mlk ? dfefe M k a mcmd k _ Mlk i M m a$ M bg d k k _ba a mcm

_ d ir_ m _b Jehg a(a\ d, a g 2

/`_ba M M i e M mrm Mlk _ dhm M mcm joa g k aoiU ,b ca g 3a(a\ 'k _ dJ aUa g a g dhm d i e bg a g u? iU?joa m d k _'ir_ba\j Mlk @ ehm /1

• k _ba />1 #3, g<d caUi k ?

•"!?L?4 ! & / 9 & 4 L J9 d M /21 #., g<d caUi k ? l k _ba , # / ; "!$L g<d caUi k ?

• J9l*&@9%4 L J9 d , # / ; J9l*&%9

• k _ba />1 #3, g<d caUi k ? l! 'ic_ba\j Mlk ' ehm

• M efe L J9 m d k _ba , # /7g<d caUi k ? l" 'ir_ba\j Mlk @ ehm

•* "& !3!-,.*$4 L J9 m d k _ba #.* g<d caUi k ? l! 'ir_ba\j Mlk @ ehm

n|G#J |C~8 # | / $#W~

/`_ dhm _ M m k _ba M g M krM a k _ Mlk k _ba i e M mcm Mlk _ dhm% ca iU ,b ca g 2

&/ I #"]Q|!/?|E/stylesheet

#:]t/'$#E|? input−schema

#:]I'/'/#E|?I output−

schema #:]M '#Q?|IE

input− namespace #"]M '/I?

inputroot

/`_ba joa M JdJ l k _ba M M joa k a\ m M bg k _ba ca m(Je k m M ca k _ba m M joa M m ?iU?jj M bgFefd a M efdhg Mlk d 2

( * #J*)-O#J,+

/8 m( ? k bg<efdJ l m k- e a m _baUa k d k _ m ic_ba\j M ca m ciUa m M bg iU k a/. k M e M joa m M iUa$2c' ka e a\joa k M joaE d ?j Mlk d Mk a m k k d.Je a : 3?j Mlk M m g a mdf a g 2 /`_ban ?j Mlk dhm c k k- a51

M"/ 2 MEname

Ienabled

'l!/inputlanguage

7]%]Q?|IlX'ZPinputnamespace input−

root

input−schema & ' '/'/l!IEG

output−language

output−schema &'/'

M|EE stylesheet

& Q|EE 4 &M"

input − language M bg output − languagej M a m M a e df ?ca g 2/`_ba k _ba\ M M joa k a\ m M ca

M m a/. Je M d a g M (a2

1` ~ * #J*)O#J,+ # | / &#0 ~

' t(I #:]/M"/Etriple

#:]'Q|E # ' E$#/ ?"M"I'M|E%#'/ I#?t( #"]I"!$# M /?I"!$# M #:] !#E| !#| #"]"!$#+I?|"$# M| !#(?|# Q/?| #:]' # ' Q|#I?

n

C2I($#I$#+t(IE2I(#I#(t(/

tripledhm k _ba M k d.Je a ,be a M joa2 k _ba ,be a dhm M g<d caUi k ? M efexd k m g<d caUi k ? d a m M ca m a M cic_ba g 3?

:9# ,%&b4 5 7, ,be a m M bg M efexm ic_ k d.Je a m M ca d ua M Je a g 2

'M|E%# |"#?t( g<dhm M Je a m k _ba+iU k a/. k m a bmcd k d (a M iUa m k ? e M J M a M M e mdhm Z"!$# t k a\j d Mlk a m k _baU M efdhg Mlk d c@iUa mrm _ba k _bauiU k c ey M _n_ M m aUa iU bm k i k a g !#(?|# Q/?|k a\j d Mlk a m k _ba c@iUa mcm _ba M efe,be a m ca 3a\ca g k d k _ba k d.Je a_ M (a aUa e M g a g ' # 'M| # m aUi d, a m k _ba j a\ l k d joa m k F a M ir_ k d.Je a M bg 2"# #(M"/ M d k m ?2(a M g aUa g M i32 M k a\a M ic_0 2

#b &` ~ ~ *| / ~8 ` |$#J |~8 *

/`_ dhm dhm M md i M efe M g a dbm krM efefdJ /8?joi Mlk M bg a g<d k dJ k _baXEZ MJGQ2H 2 Qb Y 2 "Z* IQ|? M bg IZ;E||"2 c a\ k d a md /21 #3, 465 7, 2 /`_ba_ M bg<e a\ a/. k a md dhm aUa g a g k j M 2(a k _ba ) qca m e k d d k a\ M efe d k _ba M efdhg Mlk ? bm a k _ba a Om a\9 d iUad k a\ M i k d (a e 3? ca m e dJ ca m ciUa m bmdJ M i bm k ?j c k @iU exd ) m "!A 8A 2

>=24 / 9#%(*$4 #.*J4 1 aUa gJm k a M e k a\ca g k e M g M k ?j MlkrM (a\ k _baWi e M mcmpe M g a\ lk _ba'I 0i e M mcm k _ba m m k a\j i e M mcm e M g a\2 * k _ba\ dhm a$ M k ?j MlkrM dfefe k e M gbg a\/8?joi Mlk m jo g<d, a g i e M mcm e M g a\ m 2 ?E ! dfefe iU a(a\ 'k _ dJ aUa g a g k k _ba m a\9 e a k iU krM d a\ M bg M ehm M i bm k ?j c k 'iU e_ M bg<e a\ k k _ba! %5 g<d caUi k ? l k _ba' 2"8a\j dhmcmcd bm c M Je aUa g k a m a k a 3?ca k _ dhm dfefe?92 2

/`_baU?ca k d i M efe k _ba a M Jefd i Mlk d m _b Jehg ?92 k _ba 2 /?joi MlkWM bgYd k m ' aUa gJm k aca m krM k a g d k _ k _ba"' M M joa k a\ #"] YII/= ?/Z- I| ? RM|EE/?|K |E/"$2# k M m Je a(a\ k a m k a g a e 'i Mlk d m g a Je joa k i M aHa/. aUi k a g k krM 2(a M efd kk e aa/. a\ d joa krMlk d : a ?ca m iUiUa mcm 2

v

1` ~ q~8| / ~ q ~8

fM(" #:]M"triple

/`_ba\ca dhm i ca k e m M (an? e M g i M M Jdfefd k- d k _bana g<d k ? d k dfefe Je m krM k 3c?j M k d.Je a2 # kiU Jehg a k d d M efe +M gJg a g k 3? k _ba ca m a k 3a M md- Jdfefd k- m k bg d k dhm k aUiUa mcm M M bg k _ba ) #k _Jca M gHm krM m JdJ a(a d k _ba M efdhg Mlk ? k _Jca M g i\ M m _ba m e a M dJ k _ba bm a\ M ic_ M iUa k M _ dhm jo bm a$ M bg iU k _ dhm g MlkrM 2

sut w #%-!(v #(yJ!b#%

'?joaniU ,b Mlk d M M joa k a\ m M ca M M dfe M Je a$ M efe dJ iU k c e l 1

• k c edy M ef ? d k _Jj m!bm a g

• MlkrM e $$dJ M bg0g j JdJ

• M Jd k +k a m k m bm a g

,b Mlk d Fdhm k g M j d i$ d 2 a2 d k ca Jd ca m jo g<d, i Mlk d l M M M m ciUa ,be a$ M bg M ca Jdfehg 1

, J*:* 8A A4 5x*", -,.*$4 :9 -, 4 :9 C, , 2A 1 9

•/ lME Q I?|I"! ! !#1 a k JdJ :9 1 k _ba 2 2 2 k a m k m dfefe kM i k M efe 2 dfefe i M bg<dhg Mlk a a g< a m M mg<dhm i bmcm a god 2 2 2 k dfefe Je j M 92 k _ba\j M m k a k d M efe ca\jo(a g 2 ) m a g ? m M Jd k- ir_baUi32 m 2

•/ &'Q|//"/ !I?| !# 1 M Je a m ? g<dhm M Je a m iU e ?ca g iU k a/. kk- a m M mg<dhm i bmcm a g+d 2 2 2

•/ &'Q|//"?/'NE t 1' M Je a m ? g<dhm M Je a m ca c M Mlk d luiU k a/. ky ?a M ic_ iU e ? l M iU k a/. k k a2 # g<dhm M Je a g y c M Mlk d dfefe Je +krM 2(a Je M iUak _ba , m k k d joa M iU k a/. k k a dhm M gJg a g k a M ic_ k a\j Je Mlk a Je aFiU k a/. k m a k 2 # a M Je a g iU k a/. k y m dfefe aFca c M Mlk a g ?a M ic_ a l a M ic_ iU k a/. kk- a l a M ir_k a\j Je Mlk a Je a2

•/ &'Q|/M'NbPlN E t;1 M Je a m ? g<dhm M Je a mx a a\ Mlk d l m jj M M _. M joa k m ? M bg -iU k a/. kuk a m 2? m k e a m _baUa k m2d _ d ic_ m ?joa a\j k k a\j Je Mlk a m k _ Mlk j Mlk ir_ a d k _ba\ l k _b m a k a m k _ dhm c a\ k m _b Jehg a :9 1 $2 4 a(a\:m ic_ m k e a m _baUa k m M ca (a\ M ca$ M bg ? M efe k _ba\ m k e a m _baUa k m "! m jj M M _3 M joa k m dfefe' aa\j k- M bg dfefe bm k i e kk a\ k _ba m jj M M _ 2 'a kk dJk _ dhm% c a\ k +k b,.* dfefe a efd j d Mlk a k _ba\j 2

•

/w

, J*:* 8A A4 5x*", -,.*$4 :9 -, 4 @, >A 1 9

/`_ba efe dJ k M efdhg Mlk d a Mlk ca m ?92 ca ca m a krMlk d bm l m k e a m _baUa k jo g Je a m? m ic_ba\j M M mcm a g k k _ba m krMlk d i M M e mdhm M ef ? d k _Jj 2 /`_ba 7M ca k ca e Mlk a g k _ Mlk a k a\j m krMlk d iE O() M efdhg Mlk d k md j Je m a\9(a k a ?ciUapiU bmcdhm k a i d k _ba g MlkrM M mcm a g k 0 M ef ? d k _Jj m ca(a k dJFm ?joa 2 dbgJm l m d bm a\c? m 2

•/ T|/ 2 E 't ! # 1 5q_ba k _ba\ k M efdhg Mlk a k _ba () /+* m k- e a m _baUa kjo g Je a m bmdJ M :'ic_ba\j M ?() /+* 2 2

•/ T|/ 2 E I !#15q_ba k _ba\ k + M efdhg Mlk aU 'ic_ba\j M d k m ic_ba\j M m bmdJ k _ba 5 ¯ 'ic_ba\j M 3? 'ir_ba\j M m 2

•/ M 'I" 'N M|E 2I EME I ! # 15 _ba k _ba\ k _baU M efdhg Mlk ? m _b Jehgdf ?ca M m an? M efdhg Mlk d a\c? m d0d k m k e a m _baUa k ! m ir_ba\j M M m a _ M m a$ M bgk k iU k d a2

, J*:* 8A A4 5x*", -,.*$4f* , 4 , @9 2A 1 9

•/ T| I' ?t' !I?|/@NI?|/|/ I !/"M/" "Q|! # 1 5q_ba k _ba\k _ba' M efdhg Mlk ? m _b Jehg df ?ca m a\j M k d ia\c? m a iU k a\ca g g dJ md j Jefd, i Mlk d _ M m a$ M bgk k iU k d a2

•/ QI2MI?]IE2tM|! # 15 _ba k _ba\ k _ba md j Jefd, a\ m _b Jehg ca\jo(aG M dM Je a g aUi e M Mlk d bm 3c?j k _ba m k- e a m _baUa k 2

•/ QI/t ' E%]I EMEQ| !#1 5 _ba k _ba\ k _ba md j Jefd, a\ m _b Jehg ca\jo(aMlkk d- k a m a k g aUi e M Mlk d bm .c?j k _ba m k e a m _baUa k 2

•/ QI$NQE@]I"EMQ| !# 1 5q_ba k _ba\ k _ba md j Jefd, a\ m _b Jehg ca\jo(a M M joa k a\ g aUi e M Mlk d bm .c?j k _ba m k e a m _baUa k 2

•/ '?P IMMI?ZI?| 'IM| I ? ! # 15 _ba k _ba\ k _ba md j Jefd, a\ m _b Jehgnm M (aM iU Wk _ba m k e a m _baUa k d j M jo g Je a d ? k M bg m k a\ d ? k Fa M ic_ m krM a l k _ba md j Jefd, i Mlk d d k _ba g<d caUi k ? M joa g Wk _ba M TIQME?]'@N E"!# joa k _b g 2) m a Je ? g<d M m k d i m k M 0 aUi k m a\ ?j M iUa2

• M"|"II ME' t(I?|"2E?2t' ! # 15 _ba k _ba\ k _ba md j Jefd, a\ m _b Jehg ca m a\9(a ?ca\joE(a _ d k a m M iUa Je k a/. k g a m k mdhg a l Q|=~-/ g a mxd k _ba m k- e a m _baUa k 2

m ir_ba\j M M k 1 "u d joa\ m aUiU bg a g<d k d *-26* m ir_ba\j M M k 1 k i k ca m m aUiU bg a g<d k d *-2

¯ m ir_ba\j M M k * 1U MlkrMlk a m m aUiU bg a g<d k d *-2 ' % m aUi d, i Mlk d ;* 2 . k a bmcd- Je a( M 92 e M J M a Z 2 `_ d g g<d k d *-2 v " Mlk _ M J M a Z " Mlk _; 2Aw # 3?j Mlk d 'a k M'aUiU bg g<d k d ;*-2 - a\ 2 M bg . Mlk _ * 2 g MlkrM jo g a e . g j * 2 aUa\ k M à/.;'a M m k d M M a k _x M bg J M 2 a(a 2 % 3?j M e jo g a e ? M a/. ca mrmd (a

. M joa k l () 2 *w /16* ¯ *5* aUa\ k M à/.5 d j M k a bm J M 2 a(a M bg `_b?j M m 'ir_a k d i32 U. ca mcmcd (a a mcm l

m 183c?j M i k d iUa k k _baU? k _ba\ca M bg M i32 M M d # M a m w * w * * $ a J M bg M joa m M dfe a krMlk d i M M e mdhm l . me k c M j m # " "!$# &%'%(

) * %,+- %'% % '% &% /. 1020 ) 0 304010 %\ M a m - v<5 M efdJ _ m k % bm k M efd M 2% bm k M efd M *- % bm k M efd M ?j k a\''i d a k # i

* % bg a\ m à\ $ebg a k M e 687 Mlk _ e M J M a 9 . Mlk _$: *_ kk 1 !! %%; 0¯ ? !< !E. Mlk _ *!' *

¯ >=u d ic_ M jj M d ic_ M g@? a e j0 M e. _ (?_ bm M bg (?_ ' efdhmcmdhg a m % ) 0 % #A B%DCE% * % 0 B%GFIH% (F ) % %J * KL01%""% gJg<dhm 5a me a -7 M cic_

, m _ J a , M M ic_ d 5l¯?i8687NM m ir_ba\j M j M g a md j Je a$ O >7 d ir_ M a e , M 36QPM k M bm ?j Mlk d bm 9I6QPM:SR(a\ mcd O(_ kk T !! %%; 0¯ ? !< !VU me k O!'

O v EP k a _ M , a bm a\ % md j Je a c@l3? k _ba k dJXW iU?j Je a k a a mcm lL6;PM M bg 6ZY a\ #

A\['%]C^%`_N0a bNc 0 0 3% $O- w % m _bXdJ7 M e _b k M d je7 a e k M bg ?j M 5 M ehm _L6 a\ M bg U Mlk _NO i k d bm

M bg a\ Mlk ? m 93i\: fO 5 d jg7 M k a bm J M d aDR(a M bg `_b?j M m P'ic_a k d i&df 5 _ d ic_h6i7NMjP'ir_ba\j M m % g j d k

W " M mcm "ucaU? g a\i JdJ k >lM P9¯E¯EvE¯m: T v O<O >R M 7 dfe Jl M P i d M bg ' d i k ? ' d M \ aUic_baUi'd dJ ?n6i7NM k M bm ?joa\ m # o X(

&%'% ) 1 l% ) f% %'% ^. _p<q_rF (4<qL. s(<qL. / XC b ) C ) ) b B% * 0 4010 %Q$ %]C M a m $ OO % 77$O

tO % bg a\ m 7+4 efe a\:7 M gJm,u m k a\1v * e a m a M bg 7 d ic_ M a e #]P'ir_ M k v M ic_LP krMlk d iiR M efdhg Mlk d l6QPMw` M bm 3?j Mlk d bm xaUir_ Jd i M e a ? k 8P W yW ¯O< # PC2* i k Xva\ZO

tO >7z7 MlkrM >SMxaUa$ M bg 7@7 M Jd M UJ ?j l6i7NM m ic_ba\j M e M J M a m bmdJ ?j M ee M J M a k _baU? # A\['%]C^%_N0a Vb|c 0 0 3% 7 k ca M e M M g M $O

tOO J M d aDR(a % k ?j MlkrM k _baU? 3?L6i7NM0ca m a M cir_ba\ m s<q_rF % Vh¯ 9¯m: T ¯ V v<OO

tOE¯ >7 M gJmxu m k a\1v * e a m a SP krMlk d i ' M efdhg Mlk d l6QPMQ7 M m k a\ m k _ba mdhm ) Jd R(a\ mcd k l% M _ bm O-

tO >7 d ir_ M a e # P'ir_ M k v M ic_nMxaUi k ca k a m 0m krMlk d i M M e mdhm ) Jd R(a\ md k l"% M _ bm O tO %d d _ d d(J M M > M gJm m krMlk d i k- aic_baUi&d dJ ?86QPMQ # &A m# &%'% )

* % m J. _ $<C b ) C C^% ;% ) f%'% ) $ M a m Ow' a ?1dC ) P % -O % 7 "uca mcm

tOEv "s25 M g<e a\3%^ ?j M em a\j M k d i m l Mlkk a\ bmd 6;PM tOw M e krM m M `x M iU 5 dhg a\j M 7 M 1d bm Mxa a\: M bg M iUXv 5 d a e M bg % k ?j Mlk d i iU W

m k i k d lZ687|M W v M m a g k @ ehmm aUa M m joa krM W c M jj dJ h. XCE0%w * KL0'%^A ) (f%'% ) $ l9 : T OE¯ ¯ <$OE¯

Practical type-safe XSLT 2.0 stylesheet authoring S0ren Kuula ...

Documents

Transcript of Practical type-safe XSLT 2.0 stylesheet authoring S0ren Kuula ...