Testing Communicating Systems: a Model, a Methodology, and a Tool

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v SPQfew[Te1J1NdZ={~e p [�qsJUP�V�[lqs[�RTJrN\J1qUer}v SVQfeD[TerJ1NdZ�{�e p [lqsJUPT��[�q|Q�[j�1mnJre1}v SV0Qfew[ue1J1N+Z�{�N p JAQSH�QSN�Q�[lm��[�m�WzJre�{rZ�qA��[�q|Q�[3�rmnJre�Z�{ SV

}v Top = (G, {Ii}1≤i≤n, T r)

Qfew[ NOZUV�ZlmnZ � �j}v Mi = (Si, Li, Ci, Pi, Vi, V0i, P redi, Assi, s0i,→i)

Qfe�[lHD_A`.a�b�G eUWz� p N p [�N Ii ⊆Li�∀i ∈ [1, n]

}

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SV: vSP: p

?av>1/!b/v1:=p

Shared resources

Entity 1 Entity 2Topology

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∀i ∈ [1, n]ßIi ⊆ Li

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S =(SP, SV, SV0, (Mi)1≤i≤n, T op)

� o QSN p Mi = (Si, Li, Ci, Pi, Vi, V0i, P redi, Assi, s0i,

→i)[lH.P

Top = (G, I, (Str , Ltr, s0tr,→tr))�wQfe PjJ�x�H.JUP � � N p J _A`.a�b�G ζ(S) =

(S, L, C, P, V, V0, P red, Ass, s0,→)e|Wz� p N p [�N�t

v S = {s = (str, s1, ..., sn) | str ∈ Str, ∀i ∈ [1, n], si ∈ Si}v s0 = (sotr, s01, ..., s0n)}

v L = G�C = C1 ∪ ... ∪ Cn

�P = SP ∪ P1 ∪ ... ∪ Pn

}v V = V P ∪ V1 ∪ ... ∪ Vn

�V0 = V P0 ∪ V01 ∪ ... ∪ V0n

}v Pred = Pred1 ∪ ... ∪ Predn

�Ass = Ass1 ∪ ... ∪ Assn

}� e+�oZ=t2r|{S��ZtLZk¡.r>w2r>t2u¥Zkm�{SpkZ=t2nXZ � �Xr>u¢�GZkm�Zk�o��rGZ=t!nqm�w2�@r�{+r>£�m@nqw2nqzkm�z � Z-wvtLZ=mouvnxw2nqz]m%z � Z=mrGmPw2nxw9¤P�

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v →= {(str, s1, ..., sn)a,pred,ass−−−−−−−→ (s′tr, s

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ai,predi,assi

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�� Ê�� ÌHÑLÐ � Í�Îy��GÍ�Ì��@Ë�Ñ4Êy 0vMÖK4FACE1%1L;]D|K>CÅÒ@MÖç$;ñÓA<4;]1L;kMoK�K4FH;ã;W�ÓA<>;k1>14CÅØ�CÅK2ái5+MH?ùK4FH;ãà+;kMA;=<>CED¼DGFH57<G5+DK4;k<SÒ7Ü�I¥ê�1Ü°Ò+<!?�;]14D=<4CVåACVMAà�5+MH?�K4;k1LK4CVMAàºÓA<>Ò7K>Ò�D=Ò+8E1=Ú�ëJÒ�?�;k8ÅCVMAàº1LÓ¦;kD=CXÔ¦D=5PK>CÅÒ@MH1¥CE1¥ÓA<4;]1L;kMoK4;k?�CÅM'!HÚ �@ÚÛ�;]12K>CÅMAàºç�CÅK4FJ?�CÅé¦;k<4;kMoK�K2áoÓ¦;k1�5+MH?%57ÓAÓH<4Òo5+DGFA;]1`CE1�ÓA<>;k14;=MoK4;]?SCVM'!AÚ ��Ú

0vMJK4FA;ö<4;k3�57CVMH?�;=<§Ò7ÜOK>FACV1�14;kDK4CVÒ+M ß[ç$;öç�CÅ8V8UD=Ò+MH14CE?�;=<¢K2ç$Ò�1LÓ¦;kD=CXÔ[Dk5PK>CÅÒ@MH1SA

5+MH?SB

ß�14FH5+<4CVMAà�K4FA;�1L;=K-Ò7Ü¥ÓH57<G573º;K>;=<G1SP

ß�57M[?ãK>FA;�14;K-Ò+Ü�ØP57<>CE57åA8V;k1SV

ß�1LÕ[DGFñK>FH5PKSV0

CV1§5ºÔHMACÅK4;�1L;=K¢Ò7ÜOK>FA;�CVMACÅK4CE578�Øs5+8ÅÕH;k1�Ü°Ò@<¢ØP57<>CE57åA8V;k1�Ò+ÜSV

Ú �ñ;�3�Ò�?�;k8SA

Ý¾<4;]1LÓ ÚSB

Þ«å�áJK>FA;�í`Û¥04ï¢ðA = (SA, LA, CA, PA, VA, V0, P redA, AssA, s0,→A)

Ý°<>;k14Ó ÚB =

(SB , LB , CB, PB , VB , V ′0 , P redB, AssB, s′0,→B)

ÞÚLAB

Ý¾<4;]1LÓ ÚLBA

Þ-ç�CV8Å8¥?�;kMAÒ7K>;SK4FH;1L;=KSÒ7Ü�;=Ø+;kMoK>1ºÒ7Ü

LAÝ°<>;k14Ó

LBÞ�ç�FACEDGFÖ1Lá�MHDGFA<>Ò+MHC �k;�ç�CÅK4FÖ57Mù;kØ+;=MoK�Ò7Ü

LBÝ¾<4;]1LÓ Ú

LAÞ|Ú¦RAÒ+<§;WA573ºÓA8V;+ßHCXÜ

LA = {?a1, ?a2, !a3}57MH?

LB = {!a2, ?a3, !a4}K>FA;=M

LAB ={?a2, !a3}

ßLBA = {!a2, ?a3}

ßO57MH??a2

Ý¾<4;]1LÓ Ú!a3

Þ�1Lá�MHDGFH<4Ò@MAC �k;k1�ç�CXK>F!a2

Ý¾<4;]1LÓ Ú?a3

Þ|Ú�Û�Ò-14CÅ3ºÓA8VCÅÜ°á+ßoç$;�ç�CV8Å8¦5+1>1LÕH3�;¥K>FH5PK∀a ∈ LAB

ß7K>FA;=<>;�CV1$5.ÕAMACEæoÕA;b ∈ LBA

14ÕHDGFK4FH57K

a1Lá�MHDGFH<4Ò@MAC �k;k1�ç�CXK>F

bÚ

�(�� % � !�$T! � ��'3� 68'j!#/*��&. ��;&(,"�7�

(a) Topology TopS

��LAB

�LBA �

�GA

�LA\LAB

� � �! " � �GB

� � �! "#�LB\LBA �

(b) Topology TopS’

�τ�LAB

�LBA �

�GA

�LA\LAB

� � �$ " � �GB

� � �! "#�LB\LBA �

�� $%H�'& n)(Ar>t2rGmPwOw2z]��zk�qz]»]nqrGuB+*8$0�7�-,�!.*8��K�/,.�7 2/*$j� ê�ÕAÓAÓ¦Ò@14;§K4FH57K

SCE1$K4FA;«1LÓ¦;kD=CXÔ[Dk5PK>CÅÒ@MS3�5+?�;§ÕAÓ�Ò+Ü�1LÓ¦;kD=CXÔAô

D=5PK>CÅÒ@MH1SA

5+MH?SB

Ú�ð I¥ê�3ºÒ�?�;k8ÅCVMAà-Ò+ÜSCV1 �

CS1 = (SP, SV, SV0, (A, B), T opS)ß

ç�CXK>FTopS

K4FA;ã5+Õ�K4Ò@3�5PK4Ò@M×Ò+Ü�RUCVàHÚ !ÖÝ¾5@ÞÚTopS

CE1S5Ä12KG5PK>CVD�K>Ò+Ó¦Ò+8VÒ+à+á@Ú10O;kDK4Ò@<<

G, LAB , LBA >?�;kMAÒ7K>;k1-K4FA;SØ@;kDK4Ò+<G1

< gab, a, b >14ÕHDGFóK4FH57K

a ∈ LAB14áoM[DGFA<4Ò+ô

MAC �k;k1�ç�CXK>Fb ∈ LBA

ß¥57MH?ÙK4FA;kCÅ<%14áoM[DGFA<4Ò@MAC��k5PK>CÅÒ@MÖà+CVØ+;]1SÓA8E5+D=;ãK>Ò×57M Ò+åH14;=<>ØP57åA8V;

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Ú¢ð¢M ;WA573ºÓA8V;�Ò7Ügab

D=5+M å¦;aÝ¾<4;]1LÓ Ú

bÞ�CÅÜ

aÝ°<>;k14Ó Ú

bÞ�CE1J57M ;=3ºCV1Lô

1LCVÒ+MÙÝ°K4FA;SØ�CE1LCVåA8V;�5+DK4CVÒ+MÄÒ+Ü�5+MÄ;=3ºCE1414CÅÒ@MÄ57MH?Ä5%<>;kD=;=Ó�K>CÅÒ@MÄCV1ö57MÄ;=3ºCE1414CVÒ+M[ÞÚ 0vMÄK4FH;145+3�;öç�5sá@ß

< GA, LA\LAB, idle >?�;=MHÒ7K4;]1!K>FA;�Ø@;kDK4Ò+<G1

< ga, a, idle >14ÕHDGFJK>FH5PK

a ∈ LA\LABÚO0vM

< ga, a, idle >ßUK>FA;%í`Û¥04ï!ð

AÓ[;k<LÜ°Ò@<43�1�K4FA;J5@D|K4CVÒ+M

aà+CVØoCVMAà

ÓA8V5@D;�K>ÒºK4FA;-Ò@åH14;=<>Øs5+åA8V;�5@D|K>CÅÒ@Mgaß¦57MH?�K4FH;-í`Û¥04ï¢ð

B<4;k3�57CVMH1¥CÅM%K>FA;-1>573º;-12KG5PK>;

Ýidle

ÞÚ Û¥FA;S14;KGA

DÒ+<><>;k14Ó[Ò@MH?A1kß¦CVMóà+;=MH;=<G5789ß�K4Ò�K4FA;S14;KLA\LAB

Ú�RUCÅMH5+8Å8Vá+ßTopS578V8ÅÒPç!1$K4FH;-57ÓAÓA8VCED=5PK>CÅÒ@M�Ò+ÜU;]5+DGF�Ø+;kDK4Ò@<-Ý°CÅÜUCÅK!CV1¥Ó¦Ò@1>14CÅåA8V;]Þ�CVMJ5�à+8VÒ+åH5+8�1LK>57K4;.Ò+ÜSÚ

� &� ��M& *"$*�7�-,�!.*"�� ,.�� 2/0$3� �¢ÒPç.ß 1LÕAÓHÓ[Òo1L;öK4FH57K�K4FA;�14áoM[DGFA<4Ò@MAC��k5PK>CÅÒ@MH1§Ò7ÜLAB;=Ø+;kMoK>1cç�CÅK4F

LBA;=Ø@;=MoK>1c5+<4;�MAÒ+MAô9Ò@åH1L;k<4ØP5+åA8Å;�Ý¾5@1cCXK�CE1UK4FH;!D=5+14;�Ò7ÜHK>FA;�åA8E5+DGQoô�å[ÒsW.K>;k1LK

57<GDGFACXK>;kDK4ÕA<>;]Þß�K>FA;=Mi3ºÒ�?A;=8VCÅMAàSCVMÖI¥êìCV1��

CS2 = (SP, SV, SV0, (A, B), T opS′)ß

ç�CXK>FTopS′ K>FA;J57Õ�K>Ò+3�5PK>Ò+MiÒ7Ü«RUCVàHÚ !iÝ¾å[Þ|Ú`0vM

< τ, a, b >Ò7Ü

< τ, LAB, LBA >ß

K4FA;�14á�MHDGFA<>Ò+MAC��k57K4CVÒ+MñÒ7Üaç�CÅK4F

bà+CVØ+;]1�ÓA8V5@D;ºK>Ò¼57M�CÅMoK>;=<>MH578`5@D|K>CÅÒ@M

τÚ �«;=MA;k<>5+8Å8Vá+ß

ç$;SDk57MÄ?�;k1>D<>CVå[;ºK>FA;�14áoM[DGFA<4Ò@MAC��k5PK>CÅÒ@MãÒ@MóCVMoK4;k<4MH5+8`5+DK4CVÒ+MH1-Ò+MA8Vá¼Ü°Ò@<-5%ÓH57<4K-Ò7Ü¥K4FH;1Lá�MHDGFA<>Ò+MHC �]5PK4CVÒ+M�;=Ø@;=MoK>1¥5+1¥CÅK!CE1¥K4FA;-Dk5+14;§Ò+Üc5öK>;k1LK¢57<GDGFACXK>;kDK4ÕA<>;+Ú

Û¥FoÕ[1=ß�Ü°<>Ò+3 5�K>;k1LK4CVMAàJ12KG57MH?�Ó¦Ò+CVMoKkß�K>FA;�I¥ê¼3ºÒ�?�;k8�CV1�MHÒ7K.Ò+MA8Váã5�Ü°Ò+<>3�578O3ºÒ�?�;=8578V8ÅÒPç�CVMAàSK>FA;º?�;k1>D<>CÅÓAK4CVÒ+MãÒ+Ü`CVM@K>;=<4ô�D=Ò+3ºÓ¦Ò+MA;kM@K�DÒ@3�3öÕAMACED=57K4CVÒ+MH1kß[åHÕ�K-578E1LÒ�5�3ºÒ�?�;=8K4FH57K!CV1�5+åA8Å;�K>ÒºCÅMHD=Ò+<>Ó[Ò@<>57K4;§K4FA;�K>;k1LK¢57<GDGFACÅK4;kDK4ÕA<>;k1kÚ�(�S� % � !�$T! >��$0/ �F�� "�7��!�/0��&. ��;&(,"��Û�ç�Ò¢3�5P÷2Ò@<U5+ÓAÓA<>Ò@5@DGFA;k1�ç$;k<4;$ÕH1L;]?.Ü°Ò@<�ÓA<>Ò7K>Ò�DÒ+8@K4;]12K>CÅMHà � G��1N�QS��J�`zJre|N�QSH�� 5+MH?�� [�eUe|QS��J`zJre|N�QSH�� Ú70vM�5@D|K4CVØ+;�K>;k1LK4CVMAàHßPK>FA;¢?�;k<4CVØP5PK>CÅÒ@MöCE1O3�5+?�;�Ü°<>Ò+3 1LÓ¦;kD=CXÔ[Dk5PK>CÅÒ@MH1=Ú7Û¥FH;!?�;=<>CÅØP57ôK4CVÒ+MÄD=5+M�D=Ò+MH14CE?�;=<-Ò@MA8Váñ5%ÓH5+<LK-Ò+Ü$K>FA;�14Ó[;]DCÅÔ[D=57K4CVÒ+M�ç�CXK>F�K4FA;S5+CÅ3 Ò7Ü¥8VCÅ3ºCÅK4CVMAàJK4FH;12KG5PK4;�14ÓH5+D=;¢;W�ÓA8VÒ@14CVÒ+MSç�FACEDGF�Ò�DkDÕA<G1�?�ÕA<>CÅMAà�K4FA;.14á�12K>;=3 DÒ@3ºÓ[Òo1LCÅK4CVÒ+M�5+MH?�5+MH578Vá�1LCE1kÚÛ¥FACV1�5+ÓAÓA<>Ò@5+DGFJCE1«Q�MAÒPç�Mñ5@1!K>FA;�K4;k1LK�ÓAÕA<>Ó[Òo1L;öK4;]DGFAMACEæ@ÕH;+Ú�ð�D|K>CÅØ@;�K>;k1LK4CVMAà�Dk57Mã?A;k578ç�CXK>FóÒ@MA;ºÒ+<.14;=Ø+;k<>5+8ODÒ+3º3öÕAMACED=5PK>CÅMHà�;kM@K>CXK>CÅ;]1 �� Ú�ï§MóK>FA;ºÒ7K4FH;=<.FH5+MH?�ß�ÓH5@1414CÅØ@;K4;k1LK4CVMAàSD=Ò+MH14CV?A;=<G1$;=W�;kDÕAK4CVÒ+M�K4<G5+D=;k1�Ò7ÜO57M%CV3�ÓH8Å;k3�;kMoK>5PK>CÅÒ@M ß�ç�FACEDGFJD=57M%DÒ@MoK>57CVM%ØP578ÅôÕA;k1¢Ò7ÜOØP57<>CV5+åA8Å;]1!57M[?JD8VÒ�DGQ�1kßH57M[?JDGFA;kDGQ�1¥K>FA;�ØP578VCE?�CXK2á�Ò7ÜcK>FA;k14;.K4<G5+D=;k1¢ç�CXK>FJ<4;]1LÓ¦;kDKK4ÒñK4FA;J14Ó[;]DCÅÔ[D=57K4CVÒ+M ÚU0vMÇK>FA;�ç$Ò@<4Q�1-<>;=8E5PK>CÅMHàãK>ÒñÓH5@1414CVØ+;�K>;k1LK4CVMAà � � � 9ßUK>FA;�5+Õ�K4FHÒ+<G1DÒ+M[1LCE?�;=<�Ò@MA8VáSÒ+MA;�ÕAMoK>CÅ3º;k?%14Ó[;]DCÅÔ[D=57K4CVÒ+M Ú

Û�Òó1LCV3ºÓA8ÅCÅÜ°á+ßO8V;K�ÕH1ºDk578V8 ZlH.J1k��MZlRyVzZ�H2JrH�NAN\J|e|N�QSH#� K4FA;�K4;]12K�Ò+Ü¢Ò+MA;�1LÓ¦;kD=CXÔ¦D=5PK>CÅÒ@MÝ¾DÒ@M�Ü°Ò+<>3�57MHD=;�K4;k1LK4CVMAà�Þ�57MH? e1J1��J1qs[�mYk��MZlRyVzZ�H2JrH�NDN\JreUN�QSH#� K4FA;%K>;k1LK�Ò7Ü.1L;kØ+;k<>5+8¥14Ó¦;kD|ôCXÔ[Dk5PK>CÅÒ@MH1JÝ°CVMoK4;=<>Ò+Ó¦;=<G57åHCÅ8VCXK2á@ßO;=3öå[;]?A?�;k? ß`DÒ@3�Ó¦Ò+MH;=MoK�K4;]12K>CÅMAà�Þ|Ú�0vMiK>FA;J<4;]12K�Ò+Ü§K>FACV11L;]D|K4CVÒ+M�ßoç�;�DÒ+M[1LCE?�;=<�K>FH5PK

ggaCV1�5��ð-ÚAÛ¥FHCV1�14;kDK4CVÒ+M�14FAÒPç!1`K4FH57K¥K4FA;«K4;]12K!5@D|K4CVØ�CXô

K4CV;k1�573ºÒ+ÕAMoK$K4Òö5�I¥êº3ºÒ�?A;=8VCÅMAà[ß@å�á�?�;=Ü°;=<><4CVMAà.K>FA;§?�CÅé�;=<>;=MoK�DGFH5+<>5@D|K>;=<>CV1LK4CED=1OÒ+Ü�5.K>;k1LKK4Ò�K>FA;-K>Ò+Ó¦Ò+8VÒ+à+á�Ò7Ü�DÒ@3º3�ÕAMACED=57K4CVÒ+M ß[57MH?%K>FA;�5+ÓAÓA8VCVDk5PK4CVÒ+MJÒ+ÜcK4FA;�578Và+Ò+<>CÅK4FA3

ggaK4Ò

Øs5+8ÅCE?A57K4;.5öK4<G5+D;�Ý¾ÓH5+1>1LCVØ+;«K>;k1LK4CVMAàoÞ$Ò+<¥K>Ò�à+;kMA;=<G5PK>;¢K><>5@D;k1�Ý 5+D|K>CÅØ@;«K4;k1LK4CVMAà�Þ|Ú��!�$*$0� ,�� /0��$1/*�� ê�ÕAÓHÓ[Òo1L;�K>FH5PK

ICE1!5+M�CV3ºÓA8V;=3º;=MoK>57K4CVÒ+M%Ò7ÜUK4FH;-1LÓ¦;kD=CXÔ[Dk5PK>CÅÒ@M

SAß

57MH?óK>FA;SK><>5@D;S3ºÒ�?�;=8V;k?ìåoáñK4FH;�í`Û¥04ï¢ð Ò+Ü�RUCVàHÚ #ÇÝ¾5oÞ.CE1�5%K><>5@D;SÒ+ÜIÚUÛ¥FACV1�K4<G5+D=;

<4;kÓ[Ò@<LKG1�K>FH5PKIF[5+1º;W�;]DÕ�K>;k?

a ∈ LAÝ°ç�;J<4;]D=5+8Å8�K4F[5PK

ACV1�K>FA;Jí`Û¥04ï¢ð Ò7Ü

SAÞ

5PK�3ºÒ+3º;kM@K !Aß Ü°Ò@8Å8VÒPç�;k?óå�áb ∈ LA

5PKö3�Ò@3º;=MoK $J14ÕHDGF�K4F[5PK-K>FA;�14FH57<>;k?óØP57<>CE57åA8V;v ∈ SV

CV1¢;kæoÕH578�K4Ò #[Ú¦I$FA;]DGQoCVMAàºK>FA;�ØP578VCE?�CXK2á�Ò7ÜcK>FACV1!K4<G5+D=;-DÒ+M[1LCE12KG1�CVM¼3ºÒ�?A;=8VCÅMAàS5I¥ê

CS3 = (SP, SV, SV0, (A, PTrace), PTop)ßPç�CÅK4F

PTraceK>FA;!í`Û¥04ï¢ðÖÒ+Ü�RUCVàHÚ #

Ý¾5@Þ¥5+MH?PTop

K>FA;-57ÕAK4Ò+3�57K4Ò+M�Ò7ÜORUCÅà[Ú #JÝ°å[ÞÚÛ¥FA;�K4Ò@Ó[Ò@8ÅÒ@à+á

PtopCE1OÓH5+<LK>CV5+8 ß7C9Ú ;+ß7CÅK$?�;=ÔHMA;k1`Ò+MA8Vá-K>FA;¢14á�MHDGFA<>Ò+MAC��k57K4CVÒ+MH1UÒ+M

PTrace

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�� "<a,a,a> <b,b,b>

��

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< a, a, a >Ý¾<4;]1LÓ Ú

< b, b, b >Þ!D=Ò+MH14CE?�;=<G1¥K4F[5PK

A57MH?

PTrace1Lá�MHDGFA<>Ò+MHC �k;

Ò+MaÝ°<>;k14Ó Ú

bÞ|ß75+MH?�K4FA;�Ø�CE1LCVåA8V;�5@D|K4CVÒ+M�ç�CV8Å8�å¦;

aÝ°<>;k14Ó Ú

bÞÚ �ñ;�FH5sØ@;$8E57å¦;=8V;k?�K4FH;¥1LK>57K4;

<4;]5+DGFA;]?ºåoá�K>FA;§5@D|K4CVÒ+MbCÅM

PTraceå�á

ACCEPTCVMSÒ+<G?�;=<`K4Òö3º5+Q+;

CS35�I¥êAò¢Û

57MH?�K>ÒSå[;ö57åA8V;�K4Ò�5+ÓAÓA8Vágga

Ú¦I$Ò@MH14;kæoÕA;=MoK>8Åá@ßgga

578V8VÒPç!1�K4Ò�?�;]DCE?�;-CÅÜPTrace

CE1!5Øs5+8ÅCE?JK><>5@D;öÒ7Ü

A�¦CÅÜ

gga<4;=K4ÕA<>MH1�57Mã;=3ºÓ�K2á¼14;K�Ý

PATH(CS3) = ∅Þ�K4FA;kM

PTraceCV1�MAÒ+K¥5öØP578VCV?�K4<G5+D=;¢Ò7ÜAÝ¾ç$;«<>;kD=5+8Å8[K4F[5PK

ggaCE1¥57ÓAÓH8ÅCV;k?�K4ÒöK4FA;�14;=3�57MoK4CED=1�Ò+Ü

CS3Þ|Ú

� J1Ru[lqs� � } ô �«;=MA;k<>5+8Å8Vá+ß¦K4FH;ºD=Ò+MH1LK4<>ÕHDK4CVÒ+MãÒ+ÜPTop

?�;=Ó¦;=MH?H1.12K><4Ò@MAà+8Vá%Ò+MPTrace

Ú0�K¥14FAÒ+ÕH8V?�?�;ÔHMH;§Ò@MA8Åá�14á�MHDGFA<>Ò+MAC��k57K4CVÒ+MH1`Ò+M

PTrace;=Ø+;kMoK>1�57MH?�CÅM�K4FA;�145+3º;¢Ò+<G?�;k<kÚ

ô�Û¥FA;�K4<G5+D=;PTrace

CE1�DÒ+M[1LCE?�;=<>;k?Ç5+1�57Mì;kM@K>CXK2á�Ò+ÜCS3

ç�CÅK4FAÒ@Õ�Kº5+M�á�?ACV1LK4CVMHD|K>CÅÒ@MDÒ+3ºÓH5+<4;]?öK4Ò�K4FH;!Ò7K>FA;=<$;=MoK4CÅK4CV;k1kÚ@Û¥FACE1�5+8Å8VÒPç!1cK4Ò.;kMA8E57<>à+;¥K4FH;�Ü°Ò+<>3�Ò+Ü¦K>FA;¢D=Ò+MH14CV?A;=<>;k?K4<G5+D;]1�K4Ò�57M�á�K><>5@D;]1$3ºÒ�?�;k8Å;]?�å�á�5+M�í$Û¥04ï!ð ?�;=ÔHMACVMAàS14Ò+3º;.5+D=D=;=Ó�K>CÅMHà�1LK>57K4;k1kÚô�Û¥FA;�;WA5+3�ÓH8Å;�Ò7Ü!K>FA;�Ó[5+1>1LCVØ+;�K>;k1LK4CVMAàóÒ7Ü!K>FA;�14Ó¦;kDCÅÔ[Dk5PK4CVÒ+M

SACV1�Ò@MA;ôvDÒ@3�Ó¦Ò+MH;=MoK

K4;k1LK4CVMAà[ßUåHÕ�KºK4FA;%57ÓAÓH<4Òo5+DGFÄ<>;=3�57CVMH1öK4FA;%1>573º;�CVMìK>FA;%D=5+14;�Ò7Ü§14;=Ø@;=<G578Åô�D=Ò+3ºÓ[Ò@MA;=MoKK4;k1LK4CVMAà[Úk0vM.K>FACE1�14;K4K4CVMAàHßkK4FA;¥?�C��SDÕA8ÅK2á�CV1�K4Ò§<4;kÒ+<G?�;=< ØP5+<4CVÒ+ÕH1�K4<G5+D;]1�Ü°<>Ò+3 K4FH;$?�CÅé¦;k<4;kMoKDÒ+3ºÓ¦Ò+MA;kMoK>1�K4ÒSD=Ò+MH1LK4<>ÕHDK!Ò+MA8VáSÒ+MH;�K4<G5+D;@Ú �ñ;�K>FACVMAQSK>FH5PK!K>FA;-1LK>573ºÓ%3º;kDGFH5+MACE1L3�1kß57MH?%;]1LÓ¦;kD=CV5+8Å8Vá�K>FA;�1LK>5+3�ÓJÓH<4Ò�D;]141!ÓA<4;]1L;kMoK4;k?�CVM � � #��ßHD=Ò+ÕA8E?%å[;öÕH14;k?�Ú¦Û¥FACV1§1LÕHå�÷2;kDKà+Ò�;k1¥å¦;=á@Ò+MH?�K4FA;�Ü°<G573º;kç$Ò@<4QºÒ7ÜUK4FHCV1�Ó[57Ó¦;=<!57M[?�MA;k;k?A1!3�Ò@<4;«CVMoØ@;k1LK4CVà@57K4CVÒ+M ÚC�'j/0� ,��^/*��$1/*�� RAÒ@<!5SI¥ê�ò¢Û

Sß�K>FA;.ÓH5PK>FH1

PATH(ζ(S))à@;=MA;k<>57K4;]?�å�á

ggaDk57M

å[;-Õ[1L;]?�K4ÒS?�;k<4CVØ+;�K>;k1LK§D=5@1L;]1¥K4FH57K§DÒPØ@;=<]ß�Ü°Ò+<!;=WA573ºÓA8V;+ßH5+8Å8S1LK>57K4;]1=ÚHÛ¥FHCV1§573ºÒ+ÕAMoKG1

K4Ò%?�;ÔHMH;�5+8Å8S1LK>57K4;]1«5@1¢å¦;=CVMAàJ5+DkD;kÓ�K4CVMAà�1LK>57K4;]1�Ý

ggaDÒ+ÕH8V?ãå[;�57Mó5+?A5+Ó�K>57K4CVÒ+M¼Ò+Ü

K4FA;�Û�Û¢ä7ò!04ï.ä �ñÓ�3º;K>FAÒ�?A1-Ü°Ò@<-ÕAMoK4CV3º;k?Ä14á�12K>;=3�1>ÞÚ�Û¥F�ÕH1kß�ç�;SDÒ@MH1LCE?�;k<-FA;=<>;�Ò+MH8ÅáK4FA;�K>;k1LK!ÓAÕA<>Ó[Òo1L;«K4;]DGFAMACEæoÕA;+Ú5 �768 -��/0��&. ��(�AG N\JreUN3V2W#q�V�Z�erJ?]1` � c�Qfe�[lH~_w`�alb8G

(S, L, C, P, V, V0, P red, Ass, s0,

→) p [��*QSH#��N o Z�e1J1N�eyZ={+e|N\[�N\J|e ACCEPT[�H2P

REJECT� p [�qs[3�rN\Jrq|Q��1QSH��N p JI�UJ p [��*kQ�Z�qUeAN\Z �UJAN\J|e|N\JUPj}

ð Û¥N CE1.5�ÓA<>Ò+Ó¦;=<4K2á%K4FH57K-Ò+MA;ºç�Ò+ÕA8E?¼8VCÅQ@;�K4Ò¼DGFA;]DGQJÒ+MóCÅ3ºÓA8V;=3º;=MoKG5PK4CVÒ+Móå¦;=FH5sØ�CVÒ+<]ÚTP1

Ò7Ü`RUCVàHÚ $¼Ý¾5@Þ¢CV8Å8VÕH1LK4<G5PK4;]1¢5+M¼;WA573ºÓA8V;�Ò+Ü`5�Û¥N Ü°Ò+<§K4FA;�1LÓ¦;kD=CXÔ[Dk5PK>CÅÒ@MSA

ÚTP1K4;k1LK>1!K4FH57K¢57M%CV3�ÓH8Å;k3�;kMoK>5PK>CÅÒ@M

IÒ7Ü

SAD=5+M�;=W�;kDÕAK4;

aÜ°Ò+8V8ÅÒPç�;k?�åoá

b5PK¢5+M�CVMH1LK>5+M@K

å[;=K2ç$;k;=M[2, Sig]

5@D=D=Ò+<G?�CÅMHà¥K4Ò!K>FA;$D=8ÅÒ�DGQhÝSig ∈ SP

CE1�5§1LF[57<>;k?�ÓH5+<>5+3�;=K4;k<�Ò7ÜSA

Þ|ÚÛ¥FA;.8V5+å[;k8��H?�;kMAÒ7K>;k1�K4FH;-578VÓAFH57å¦;K

LAÒ7Ü

AÚ��ó;-5+1>14ÕA3º;«FH;=<>;§K>FH5PK

a, b, c ∈ LAÚ

bdH2Jrk��UZlRyVzZ�H2JrH�N�NOJre|N�QSH��3}ê�ÕAÓAÓ¦Ò@14;!K>FH5PKTP1

CV1�5-Û¥NÄÜ°Ò@<�14Ó[;]DCÅÔ[D=57K4CVÒ+MSA

Ú�ðÙ3ºÒ�?�;k8ÅCVMAà-Ò+Ü�K4FACE1�K>;k1LK$CVM�I¥êºCE1 �CS4 = (SP, SV, SV0, (A, TP1), TPop1)

ßoç�CÅK4FTPop1

K4FA;.K>Ò+Ó¦Ò+8VÒ+à@áSÒ7Ü�RUCÅà[Ú $%Ý¾å[Þ|ÚÛ¥FA;$Ø@;kDK4Ò+<G1

< LA\{a, b}, LA\{a, b}, idle >?�;=MAÒ+K4;$Ü°<4;k;$;kØ+Ò@8ÅÕ�K>CÅÒ@MH1�Ò7ÜH14Ó[;]DCÅÔ[D=57K4CVÒ+M

AÒ+M�;=Ø+;kMoK>1cÒ7K>FA;=<cK>FH57M

a5+MH?

bÚCS4

CE1�5-I¥ê�ò§Û×5+MH?-K>F�ÕH1gga

ç�CV8Å8Hà+;=MH;=<G5PK4;�ÓH57K4FH1DGFA;kDGQ�CVMAà

TP1Ú

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ACCEPT

��

<a,a,a><b,b,b>

(b) Topology PTop1

�LA\{a, b} � LA\{a, b} � � ��

* *

n�� !�"�# �� $

�� %H� ¿ �>w2nqpsr�w2r>u�w2nXm@»@Âoz]mor4a �>z]¡.��z]m@rGmPwcw2rGu�w2nqmo» ¸ �¹4��!Ò7K>;�K>FH5PKºÜ°Ò@<öK>FA;%145+3�;%Û¥Ncß�1L;kØ+;k<>5+8¥I¥êÇ3�Ò�?�;k8ÅCVMAào1�Dk57M×å[;�Ü°Ò+<>3�ÕA8E5PK>;k?�ßOD=Ò+MH14CV?�ô;=<>CÅMAàÖ?�CÅé�;=<>;=MoKJK4Ò@Ó[Ò@8ÅÒ@à+CV;k1kÚ�0vM Ü¾5@D|K]ß�K4FA;ì?A;ÔHMACÅK4CVÒ+M Ò+ÜöK>FA;ÄK4Ò@Ó[Ò@8ÅÒ@à+áÖà@CÅØ@;k1%3ºÒ+<>;;W�ÓA<>;k1>1LCVØ�CXK2áóK4ÒñK4FH;�å¦;=FH5sØ�CVÒ+<G1ö5sç¥57CÅK4;]?Äå�áì5ãÛ¥NcÚ�ð K2á�ÓACVDk578�;WA573ºÓA8V;�Ò7Ü!K>FACV1º;=W�ôÓA<4;]1414CVØoCÅK2áãCE1-5@1.Ü°Ò+8V8VÒPç!1 � 14CÅM[D;SÓH57K4FH1�à+;kMA;=<G5PK>;k?ñåoá

ggaÜ°Ò@<

CS457<>;ºÒ7Ü!57<>åACÅK4<G57<>á

8Å;kMAà7K>FH1ñÝ°K4FA;óM�ÕA3�å¦;=<�Ò7Ü�K4<G57MH14CXK>CÅÒ@MH1GÞ|ß`Ò@MA;ñDk57MÙç�CE14FÙK4Ò×à+;kMA;=<G5PK>;¼Ò+MA8VáùÓH5PK>FH1�Ò7Ü8Å;kMAà7K>FH1�8V;k1>1�K>FH57M

n ∈ INÚ�Û¥FHCV1�ç�CV14F Dk57MAMAÒ+K�å¦;ã;W�ÓA<>;k1>14;k?ùå�áÖ5ÇÛ¥N Ý°K4FA;k<4;ñCV1

MAÒì3º;kDGFH5+MACE1L3 K4ÒÇD=Ò+ÕAMoK�K4FH;ã;=Ø@;=MoKSÒ�D=D=ÕA<4<>;=M[D;k1GÞ|Ú��¢ÒPç.ß`8V;K�Õ[1�DÒ@MH14CV?�;k<�K4FH;óI¥êCS5 = (SP, SV, SV0, (A, TP1), TPop1′)

ß�ç�CÅK4FTPop1′

K4FA;óK4Ò@Ó[Ò@8ÅÒ@à+áùÒ7Ü�R�CVàHÚ�$Ý¾DkÞÚ�Û¥FH;¼8V5+å[;k8 � � ��CVM

TPop1′?�;kMAÒ7K>;k1�Ø+;kDK4Ò@<>1

< a, a, a >ß< b, b, b >

ß�57MH?<

LA\{a, b}, LA\{a, b}, idle >Ý¾5óK><>5+MH14CXK>CÅÒ@M � � �OCE1ºK4FH;=MiK4FA;¼14;KSÒ+Ü§K><>5+MH14CXK>CÅÒ@MH1�Ò+M

K4FA;]1L;«Ø+;]D|K4Ò@<>1GÞ|Ú �ÖCÅK4FTPop1′

K>FA;«14;=3�5+M@K>CVDk1`Ò+ÜCS5

CE1�5�K4<>;=;«Ò7ÜU?�;=Ó�K>F�8V;k1>1$K4FH5+Mn57MH?�K4F�ÕH1¥K>FA;.8V;=MAà+K4FH1¥Ò+ÜUÓH57K4FH1¥à@;=MA;k<>57K4;]?�å�á

gga5+<4;«8V;k1>1�K4FH5+M

nÚ

ACCEPTREJECT

REJECT

other

other

h[2,Sig]/b/−

−/a/−−/c/−

−/c/−

�&��'�(�)�� *�"�,+

<b,b,b>

<a,a,a>

<c,c,c>

(b) Topology PTop2

�LA\{a, b, c} � LA\{a, b, c} � � �)� ��

�� -H� ¿ �>w2nqpsr�w2r>u�w2nXm@»@Âoz]mor4a �>z]¡.��z]m@rGmPwcw2rGu�w2nqmo» ¸ Á]¹4�Û�ÒãD=8ÅÒo1L;ºK>FA;�Ó[57<4K-Ò7Ü!Ò+MH;ôvDÒ+3ºÓ¦Ò+MA;kMoK.K4;k1LK4CVMAà[ß�8V;K�ÕH1-K>5+Q+;�K>FA;�Û¥N

TP2Ò+Ü�RUCVàHÚ &

Ý¾5@ÞÚTP2

K>;k1LK>1�K4FA;�1>573º;�Ü°ÕHMHD|K>CÅÒ@MH578VCXK>CÅ;]1ö5@1TP1

ß�åAÕ�KöÓH<4Ò@FACÅåHCXKG1.K4FH;�57ÓHÓ[;]57<G57MHD=;Ò7Ü

cCÅM%K>FA;.K2ç�ÒöÔ[<>1LK§1LK>5PK>;k1�Ò+Ü

TP2ÚAÛ¥FA;-8E57å¦;=8/. ZlN p Jrq .sCVM TP2

?�;=MHÒ7K4;]1¥K4FH;-;=Ø@;=MoK>1LA\{c}

Ú �¢Ò7K>;öK>FH5PK�K>FA;S?�;Ô[MACXK>CÅÒ@MñÒ+ÜREJECT

1LK>57K4;]1�CV1�Ò@MA8Åá¼5�3�57MHMA;=<�Ò7Ü�ÓA<>Ò7ôFACÅåHCXK>CÅMAà�14á�MHDGFA<>Ò+MAC��k57K4CVÒ+MH1`Ò+M�5ö1L;=K�Ò7Ü�;kØ+;=MoKG1=Ú�Û¥FACE1¥ÓA<4Ò@FACVåACXK>CÅÒ@M�D=5+M�å¦;«Ü°Ò+<>3�ÕA8E5PK>;k?CÅMºK>FA;!K>Ò+Ó¦Ò+8VÒ+à+á�CÅMH1LK4;]5+?ºÒ+Ü¦K>FA;�K>;k1LK`ÓAÕA<>Ó[Òo1L;@Ú+0vMºK>FACV1$D=5@1L;@ß7ç$;§D=57MºÕH14;

TP1CVMH12K>;k5@?

Ò7ÜTP2

Úo0vMH?�;k;k?�ß@K4FH;«5@D|K4CVØ+;¢K4;]12K>CÅMAàöÒ7ÜSA

ç�CXK>FSK4;]12K¥ÓAÕA<>Ó¦Ò@14;TP2

Dk57MSå¦;§3ºÒ�?�;k8Å;]?åoá�K4FA;öI¥ê

CS6 = (SP, SV, SV0, (A, TP1), TPop2)ß�ç�CXK>F

TPop2K4FA;�K>Ò+Ó¦Ò+8VÒ+à+á�Ò7Ü

R�CVàHÚ &�Ý°å[ÞÚ�0vMTPop2

ß�ç�FH;=MÄ5%1Lá�MHDGFA<>Ò+MHC �]5PK4CVÒ+MñÒ+McÒ�D=DÕH<>1kß�K4FA;SD=Ò+3º3�ÕHMACVDk5PK>CÅMAà

1Lá�1LK4;=3 ;=Ø@Ò+8VØ+;]1GäP3�ÒPØ@;k1�K4Ò�5�åA8ÅÒ�DGQ�CVMAà�ä7?�;k5@?�8ÅÒ�DGQ�1LK>57K4;¢5+MH?�K4F�ÕH1�?�ÕA<>CVMAà�K4FA;«57ÓAÓH8ÅCED=57ôK4CVÒ+M%Ò7Ü

ggaK>Ò

CS6ßgga

CE1¥Ü°Ò+<GD;]?�K4ÒS?�;]æ@ÕH;=ÕA;�K>FACV1¢1Lá�MHDGFA<>Ò+MHC �]5PK4CVÒ+M�ÚAR�CVMH5+8Å8Vá+ßAMHÒ7K4;K4FH57K�ç�;ºFH5sØ+;�ÕH14;k?

TP1CVM

CS6K4Ò�K>;k1LK

TP2ß�57MH?ãK4FA;k<4;=Ü°Ò+<>;�5SK>;k1LK-ÓAÕA<>Ó[Òo1L;ºD=5+M

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DÒ+MoKG57CVM�Ò@MA8ÅáACCEPT

1LK>57K4;]1=Ú2J1��J1qs[�mYk��MZlRyVzZ�H2JrH�N�N\J|e|N�QSH#�7}ê�ÕAÓAÓ¦Ò@14;ºK4FH57K

SCE1«K4FH;S1LÓ¦;kD=CXÔ[Dk5PK>CÅÒ@Mó3�5@?�;ºÕAÓ�Ò7Ü�14Ó¦;kDCÅÔ[Dk5PK4CVÒ+M[1

SA5+MH?

SBß�5+MH?

TP1Ý¾RUCVàHÚ��Ý¾5oÞLÞ�CV1U5«Û¥N¼Ü°Ò+<

SÚPÛ�Ò§14CÅ3ºÓA8VCXÜ°á@ßPç$;�5+1>1LÕH3�;$FA;=<>;�K>FH5PK

a ∈ LAßa 6∈ LABÝ

aCE1cMAÒ7K�5�14áoM[DGFA<4Ò@MAC��k5PK>CÅÒ@M-;=Ø@;=MoKGÞßs5+MH?

b ∈ LAB∩LBAÚ7ðù3�Ò�?�;k8ÅCVMAà«Ò7Ü[K4FACE1cK4;]12KOCVM

I¥ê�CE1�5@1�Ü°Ò@8Å8VÒPç!1��CS7 = (SP, SV, SV0, (A, B, TP1), T op)

ß+ç�CÅK4FTop

K>FA;¢K>Ò+Ó¦Ò+8VÒ+à@áÒ7ÜOR�CVàHÚ��Ý°å[ÞÚ[Û¥FA;.Ø@;kD|K>Ò+<

< b, b, b, b >D=Ò+MH14CV?A;=<G1�K4FH57K

AßB57M[?

TP114á�MHDGFA<>Ò+MAC��=;

Ò+MbÚoÛ¥FA;«Ø+;]D|K>Ò+<

< a, a, idle, a >DÒ@MH1LCE?�;k<>1�K4FH57K¥Ò@MA8Vá

A57M[?

TP114á�MHDGFA<>Ò+MAC��=;!Ò@M

aÚ[ð!à@5+CÅM�ß�K4FA;-5+ÓAÓA8VCVDk5PK4CVÒ+M�Ò7Ü

gga578V8ÅÒPç!1�à@;=MA;k<>57K4CVMAàöÓ[5PK4F[1�DGFA;kDGQ�CVMAà

TP1Ú

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ACCEPT

��'�� (b) Topology Top

� � �LAB\{b}

�LBA\{b}

� � �! " �

�GB

� � �$ "#�LB\LBA

� � �$ " �

� � � � �� ! "#� � �

�GA

�LA\{LAB ∪ {a}}

� � �$ "#� � �$ " �

�� ¿ �>w2nqpsr�w2rGu�w2nqm@»@Â�uvr>psr>tLZk�xa¾�Gzk¡.��z]mor>m7wOw2r>u�w2nXm@»@�Û�Òã14ÕA3º3�57<>C �k;ºK4FACE1�1L;]D|K4CVÒ+M�ß�RUCÅà[Ús4%ÓA<>;k14;=MoKG1�K4FA;�K4;]12Kº5+D|K>CÅØ�CÅK4CV;k1�Ý°ç�CÅK4FAÒ@Õ�K-K4FH;�CV3öôÓA8Å;k3º;=MoK>57K4CVÒ+MH1GÞ|Ú�Û¥FA<>;=;%3�57CVMÖ12K>;=ÓH1�5+<4;%CE?�;=MoK>CXÔH;]?�Ú`RUCV<>1LK48Vá+ßcÜ°<>Ò+3 Ý¾CEÞº5+MùCÅM�Ü°Ò@<43�5+81LÓ¦;kD=CXÔ[Dk5PK>CÅÒ@M�Ý¾1GÞ|ß�Ý¾CÅC�Þ«5�K>;k1LK-57ÓAÓA<>Ò@5@DGFÇÝ°Ó[5+1>1LCVØ+;�Ò+<.5+DK4CVØ+;öK4;]12K>CÅMAà�Þ|ß 5+MH?×Ý¾CÅCVC�Þ§5�K>;k1LK57<GDGFACXK>;kDK4ÕA<>;+ß�5J?�;]14D=<4CVÓ�K4CVÒ+M

SCÅMóK4FH;�I¥êã3ºÒ�?�;k8�CV1�;k8V5+å[Ò@<>57K4;]?�Ú�ê�;kD=Ò+MH?A8Åá@ß 5 ��ð

578Và+Ò+<>CÅK4FA3 Ý°ç�CÅK4F�5öD=ÒPØ+;k<>5+à+;!D<>CÅK4;=<>CVÒ+M[Þ�CV1�57ÓAÓH8ÅCV;k?SK4Òζ(S)

K4Ò�à+;kMA;=<G5PK>;§5ö1L;=K�Ò+Ü�;W�;ôDÕ�KG57åA8V;¢ÓH57K4FH1

PATH(ζ(S))ÚoRUCVMH578V8Åá@ß+K>FACE1$14;K�CV1$CÅMoK>;=<>ÓA<4;=K4;]?�5+D=D=Ò+<G?�CVMAà.K4Ò-K4FA;§K4;]12K

57ÓAÓA<>Ò@5@DGF �¦Ü°Ò+<.ÓH5@1414CVØ+;öK4;k1LK4CVMAà[ß�CXÜPATH(ζ(S)) = ∅

K4FA;kMñK>FA;�CV3�ÓH8Å;k3�;kMoK>5PK>CÅÒ@M�Ý¾1GÞCV1SÝ 57<>;]Þ§CVMHDÒ@<4<>;kDKkÚ RAÒ@<-5+DK4CVØ+;�K4;]12K>CÅMAà[ß�K4;]12K�Dk5+14;k1�57<>;ºà+;kMA;=<G5PK>;k?ãÜ°<4Ò@3 K4FACE1-14;K]Ú 0vMK4FA;§Ò+ÓAÓ¦Ò@14CXK>;+ß+K4FA;«D8E5+1>1LCED=5+8�K4;]12K¥5+D|K>CÅØ�CÅK4CV;k1`CÅM�Ø+Ò@8ÅØ@;¥K4FA;«1LÓ¦;kD=CXÔ¦D=5PK>CÅÒ@M ß7K>FA;¢à@;=MA;k<>57K4CVÒ+M578Và+Ò+<>CÅK4FA3õ57MH?¼K4FA;�K4;]12K.57<GDGFACÅK4;kDK4ÕA<>;-CVM¼K>FA<4;k;ö14;=ÓH5+<>57K4;�1LK4;kÓH1�57MH?JK4F�ÕH1§8ÅÒ�Ò@14;k1¢K4FH;à+;=MH;=<>CVD�DGFH5+<>5@D|K4;k<$Ò+ÜUÒ@ÕA<�Ü°<>5+3º;=ç�Ò+<>Q¦Ú

Û¥FoÕ[1=ß�K4FA;k<4;�CV1�MAÒñ<4;]5+14Ò+M�K>Òã3�57Q@;�?�CE12K>CÅM[D|K4CVÒ+M×å[;=K2ç$;k;=MÄK>FA;k14;�K2áoÓ¦;k1�57M[?Ç57ÓAôÓA<4Òo5+DGFA;]1�Ò7Ü�ÓH<4Ò+K4Ò�DÒ@8�K4;k1LK4CVMAà[Ú

Specification(s)

Test Architecture

Generation(GAG)

Interpretation

Modeling (CS)

Test Approach

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Û¥FA;%CÅMAÓHÕ�KSÒ7Ü�Û��.ê�í CV1�K>FA;¼?�;]14D=<4CVÓ�K4CVÒ+M×Ò7Ü.5ìI¥êÄÜ°Ò@8Å8VÒPç�CÅMHàó5�14CÅ3ºÓA8V;¼1Lá�MoK>57W�Úí`5+DGF�í`Û¥04ï¢ð Ò7Ü!5ãI¥êóCE1-?�;=ÔHMA;k?�CVMì5J14;=ÓH5+<>57K4;ºÔH8V;+Ú�ð 1Lá�1LK4;=3 ÔH8V;�?�;]14D=<4CVå[;]1�K4FH;5+D=D=;k1>1�ÓH5PK>FH1�K4Òº;k5@DGF�D=Ò+3ºÓ[Ò@MA;=MoK]ßA5+1¥ç�;=8V8 5+1$K4FA;-14FH5+<4;]?�?A57K>5º57MH?�K4FH;§K>Ò+Ó¦Ò+8VÒ+à@á�Ò7ÜDÒ+3º3öÕAMACED=5PK>CÅÒ@M ÚPÛ¥FA;¥Ò+Õ�K>ÓAÕ�KOÒ7Ü�Û��.ê�íóCV1O5+M��§ëãîóÝ¾;�¢K4;=M[1LCVåA8V;!ë¼57<>Q�ÕAÓöî�57MAà@ÕH57à@;]ÞÔH8Å;-5@D=D=Ò+<G?�CÅMHà�K>Òº5SI�5+8ÅCÅÜ°;-è§Û�è�?�;ÔHMHCÅMAàS5öK>;k1LK¢1L;]æ@ÕH;=MHD=;+Ú

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SymbolicT race()CV1�K4FA;kM%Dk578V8Å;]?�Ú

�N\JOV � t ��RT�UZ�m�Q��T`�qs[j�UJ*}SymbolicT race()

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Idle

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y>=Sig/!busy/−

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TransmitFinish

−/!begin/x:=0

x<=2*Sig/!begin/x:=0

x<Sig/?CD/x:=0

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−/?busy/x:=0

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Init

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∅ ;� � �<�� Ã �qrG¡.rGmPw�Â :Öe7¤+mo�L�@t2zkmon��|Zw2nXzkm�ú�moÃ�psr>m7w2u ¸ ePwLZ=w2rGuL¹ ;hP� _ �O¸ Ã �Xr>¡.rGmPw 6= d�f¥Y[Y�¹�w2�@rGm�7� �@}ouv� ¸ Ã �qrG¡.rGmPw|� � Z=w2��¹ ;�P� eP¤@¡ � z]�qnq�|�[tLZ=�Gr ¸ � Z=w2��¹ ;j7� _ ��¸ � � r|Z=uvn � �qr ¸ � Z=w2��¹v¹Ow2�@rGm�7� ��z]� ¸ Ã��qrG¡.r>m7w|� � Zw2��¹ ;�Gl+� e7wLZ=w2r>u¥Â :ù»kr>w4e+}@�G�GrGuvuvz=t2u ¸ Ã��qrG¡.rGmPw4¹ ;

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�k�]� Ã��quvr�|Á7� ��z]� ¸ � Zw2��¹ ; e7wLZw2rGu¥Â :Ö»kr>w4e+}@�G�GrGuvuvz=t2u ¸ w2z]� ¸ � Z=w2��¹v¹ ;� � � _ �9¸°¿ �>�GrG�@w4ePwLZ=w2rGu ¸ ePwLZ=w2rGuL¹v¹� � � �Ot2nqw2rG�[tLZk�Gr ¸ � Z=w2��¹ ;�|h7� � , �� ¸ � Zw2� 6= ∅ ¹ ;� �+�� S� �� U�� Y[r>w§}ou§Zkuvuv}@¡.r�w2��Zw

M = (S, L, C, P, V, V0, P red,Ass, s0, T )nqu�Z=mÃ��c_vú ¿ uv}o�L��w2��Zw

C = {c1, ..., ck}�V = {v1, ..., vm}

�V0 = {v01, ..., v0m}

Zkmo{ρ = t1...tnnqu�Z-uv}@nxw2r§z � wvtLZ=mouvnxw2nqz]mou�z � M � t2zk¡ w2�or!nqmonxw2nXZk��u�wLZw2r]�H�c�or!u�¤+¡ � zk�qnX�!wvtLZk�>r§z � ρnqu

ρuv}o�L�w2�oZ=w

∀ ti = (si−1, a, pred, ass, si)z � ρ

�¦Zkmo{∀v ∈ V

�vnqu�t2rG�@�ÅZ=�Gr|{�nqm

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nqu`Z§psr>�>w2zkt�z � m�Zw2}@tLZk�Am7}o¡ � r>t2uG�V 2[q]

u�w2zP� �7u�w2�@r¥nqm�{+r>~�z � wvtLZ=mouvnxw2nqz]mº��or4t2r¥w2�or¥�G�qzP� � xq ∈ C�OZ=u$�XZ=u�w`t2r>uvr>w2r|{H�

� " � �]� ��1� �� U�� 23-5�k�� "H�� "[� � "[� 5ρ = t1...tn

�+��nqw2�ti = (si−1, a, predi, assi, si)

�ÁP� � � � � ��o�� o�G� �[�cz�p]rG�>w2zkt2uGÂV 1

z � uvn��Gr mZkm�{

V 2z � uvn��Gr k

�� 768�� 9�� _9m@nqw2nXZ=�Xn��|Zw2nqz]m � �� oz=t

i := 1w2z

m& z

V 1[i]← v0i ;hP� �oz=ti := 1

w2zk& z

V 2[i]← 0 ;�� f��A{@Z=w2nqmo» ��7� �oz=t

i := 1w2z

n& z

�P�predi ← updatePredicates(predi, V 1, V 2, i) ;j7�updateContext(assi, V 1, V 2, i) ;�7��c�@r � }om@�>w2nqz]m��<�� o� �� ]�@� � � t2rG�@�XZk�GrGu w2�orOpkZ=t2nXZ � �qrGu ��nqw2��w2�@rGnxt��G}@tvt2rGmPw�pkZk�q}orGu � t2z]¡

V 1�@�oz=t��G�qzP��7uG�+n � cp

nquO�XZku�wOt2rGuvr4w2r|{önqmöw2�@rtj

Z=m�{inqucw2�@r�nqm�{+r>~-z � w2�or��>}@tvt2rGmPwOu�w2rG��w2�orGm

ck

nquOt2rG�o�XZk�>r|{ � ¤hi − hj = hi − hV 2[p] ¸ �qnXm@r � ¹4�

� " � �]� ��1�� @� �� ]�o� � � 23-5�k�� "H� 5 ¿ �@t2rG{@nq�|Z=w2rpred

�@Zkmönqm�{@r4~i��Zkmo{�w9�Uz�psrG�4w2zkt2u

V 1Zkmo{

V 2�ÁP� +/"H� � "[� 5 ¿ �+t2r|{@nq�|Zw2r

predUpdated�� 768�� 9��

predUpdate← pred[hi − hV 2[1], ..., hi − hV 2[k], V 1[1], ..., V [m], P ] ;hP��c�@r � }omo�4w2nXzkm � � � � �o� �"! �� $# � }@�A{oZw2rGu$�|¹�w2�or`�G}@tvt2r>m7w�pkZk�q}orGuUz � p]Zt2nÅZ � �qrGucnqm V 1 � t2z]¡w2�@r�m@r>�ìZkuvuvnq»kmo¡.rGmPw2u ¸ �qnqmorGu � Zkmo{�h]¹4�@Zkmo{öÁk¹�w2�or`�G�qzP��.t2rGuvr4w2u V 2

� ¤-Zkuvuvnq»kmonqmo»«w2�@r�nqm�{+r>~z � w2�or��>}@tvt2rGmPw�u�w2rG� ¸ �Xnqm@rGu �«r>w �]¹4�� " � �]� ��1�� @� �"! �1� � �$# �)243-5�k�� "H� 5 ¿ mºZ=uvuvnq»]mo¡.r>m7w ass

�@Zkmo{ºZkmönXmo{@r>~i�ÁP�� "H�� + "[� � "H� 5 �[�Uz�psrG�4w2zkt2u

V 1Zkm�{

V 2�� 768�� 9�� oz=t

j := 1w2z

m& zhP� _ � vj := f(v1, .., vm, P ) ∈ ass

w2�or>mV 1[j] := f(V [1], .., V [m], P ) ;�7� �oz=t

j := 1w2z

m& z

�P� _ � cj := 0 ∈ assw2�orGm

V 2[j] := i ;j7��

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Testing Communicating Systems: a Model, a Methodology, and a Tool

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