HAL Id: hal-00408505
https://hal.archives-ouvertes.fr/hal-00408505
Submitted on 30 Jul 2009
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Generating interoperability test cases from conformance test case generation tools
Ismail Berrada, Richard Castanet, Patrick Felix
To cite this version:
Ismail Berrada, Richard Castanet, Patrick Felix. Generating interoperability test cases from con-
formance test case generation tools. 24th IFIP International Conference on Formal Techniques for
Networked and Distributed Systems (FORTE’04), Sep 2004, Madrid, Spain. �hal-00408505�
&'(-.+/01!#$%&'$23"!#4$
576984:<;>=@?BACDCD:FEG:GHJI;LKMN:<CEPOB:Q6SRD:<TNARU:<TNEV.:-RDC9;LKWYXZ=>;\[
] ^`_acbd efBaBgdhijalknmno`oh0prqts*uDv7wxqzy7{_|vS}Fu~^FY
nn
o*k^ \uDpruUu~}QuDGFFvS^npFu
uDvxvS^n}r^
|~^wyS^npru9y
|u tqzJnB \^
v7q
v
,Jn` Fqtw J^uDv
|-rwxuw.|npwy7J}FqtpFu9qtup-y wx|n \Qy7qt|`prw
|nv}QuDv7qts<q\pF
qtp-y7uDv7|`u9vS^ qt tqzy¡ ¢y7uDwy7w%b¡p¢y7Fq\wU£ |v7¤£ uFv7|n|`wxu¥rv7wy¦^4|`FuDv7up-y
|nv7§^
vS^n§uD£|nv7¤
|vUq\p-y7uDv7|nuDvS^
qt \qzy¨ Yy7uDwy7q\pF
^nwxu~}Y|`p¢^J^vS^n§uDyxv7qt©u}Y£.v7qzy7qtpr
|
y7Fuªqtp-y7uDv7|`u9vS^ qt tqzy¡ «v7uD ¬^y7qt|`prw cp®^nrQv7|*^9Y^npr}4^nwxwx|-q\^y7u~}^ \n|nv7qzy7r§
qtwBy7Fup4qtp<yxv7|<}Qru}
|nvy7Fqtw
vS^§uD£ |v7¤N0w^|nprwxu~¯-FuprunG^`}F^nFyS^y7qt|`pY|
|nFvUv7uwxr zy7wy7|«|np
|nv7§^npFuy7uwy7qtpr«y7|-|n tw
|nv`upFuDvS^y7qtpF4q\p-y7uDv7|nuDvS^ qt \qzy¨
y7uwy7w°qtw
F \ z ª^nQy7|`§^y7q\n*_ Uy7Fu£.^ -£ u.wxF|£±y7r^y%y7ruFv7|`|nwxu~}^rFv7|`^nS
^rr tqtuw
|vcy7uDwy7q\pFqtp«|np<y7u9Qy~
² ³r´cµ¶G·¸ª¹º»µG¼7·c´
VC9½QR9½K½F=N69¾ A`K;¬¿ K:<R9;>½QTN6:QC9AÀ 6SA`EjR9½,EAnÁQAn=¬½F¾j¾NC9½EÀNKRD6:QTNE469ACDÁr;LKA`6ÂFÃ@½AnTN6SÀNC9AUK½QC9Ä
C9A`K~R9TNAn6D6°½<ÅN69ÀNKM¾NC9½EÀNKRD6nHRDAn6SR9;>TGÆNHnR9MNAc¾GCD½KAn6D6°½QÅNKMGAnKWJ;>TGÆRDMN:-R :69ÇJ6SR9An8Ⱦ ½r6969An6D6SA`6
:P6SAR,½<ÅUEA`6S;>C9A`EɾGC9½F¾ AnCSRD;¬A`6:<T E Ê*½FCË AnMN:*ÁJ;¬½FCD6nH%;>6R9MGAY½QTGA®½QÅR9MGA®À 6SA`E#Á*:Q=¬;LEG:<R9;>½QT
R9AnKMNTG;>ÌrÀGA`6ÂFÍ:<CD;¬½FÀN6.RDAn6SR9;>TGÆ,8«AR9MG½E½F=¬½FÆQ;>An6.MN:*ÁFAUË»AATY¾GC9½F¾ ½r6SA`E«:<TNE®:Q¾G¾G=>;¬A`E%ÂJΪTNA
:<¾G¾GCD½F:FKMY;L6K½FTÅϽQCD84:<TNKAªRDAn6SR9;>TGÆNHN;¬T¢ÐMG;LKM:469;>TGÆQ=>A;¬8«¾G=>A8«ATrR:-R9;>½QT¢;L6K½F8j¾ :<CDAnE
R9½#R9MNAÑ67R:<TNEN:<CEÒRD½ÓË AÑ69ÀGCDA¢R9MN:<R4R9MGAÑ;¬8«¾G=>A8«ATrR:-R9;>½QTÔE½JA`64ÐMN:-R4RDMGAÑ6SRD:QTNEG:<CE
6S¾»AnK;\¿NA`6Õ R9MNA,RDMGA½FC9ÇË AnMG;>TNEK½QTÅϽFC984:QTNKARDAn6SR9;>TGÆ;L6R9MN:<R¦:<=>= K½QTGÅϽQCD8Ö;>8«¾G=>A8«ATÄ
RD:-RD;¬½FTN6R9½®RDMGA«:<ËN6SR9C:QKRª67R:<TNEN:<CEP6SMG½FÀG=LEP;¬TrRDACD½Q¾»AC:-R9A,Ð;\RDMÑAn:FKMP½<RDMGAC`H»:Q=\RDMG½QÀNÆQM
;¬T¢¾GC:QKR9;LKA¦R9MG;L6U;L6TG½QRUTGAnKAn6D69:QC9;>=>Ç«R9MGAKn:Q69AQÂGÃMGA½QR9MGAnC:<¾G¾NC9½r:QKMY;L6;>TrR9ACD½Q¾»AC:<ËN;¬=¬Ä
;\R7Ç#RDAn6SR9;>TGÆNH ;>T×ÐMG;LKMÒR7ÐB½Ñ½FC8«½QCDAY;>8«¾G=>A8«ATrRD:<R9;>½QTN6«:QC9A4RDAn6SR9A`EØE;>CDAnK~RD=¬ÇÓ:QÆF:<;>TN6SR
An:QKM½<RDMGAC`H%Ð;\RDMÑRDMGA467R:<TNEN:<CE±ÀN69AnEÉ:Q6:¾GCD;¬84:<CD;>=¬Ç±:F6¦:CDAÅÏACDAT KAR9½P:QE*Ù7À E;>Kn:-RDA
¾GC9½FËG=>A846:<TNE;>TNK½F8j¾ :-R9;>ËG;>=¬;¬R9;>An6nH°:<T E69AnK½QTNEG:QC9;>=>DZ:Q6:ÆQÀG;LEAjR9½RDMGA«ÅÏÀGTNKR9;>½QTN6¦RD½
Ë ARDAn6SR9AnE¢:QTNE®RDMGAÆQAnTGAC:<=Ë»AMN:*ÁJ;>½QCBR9½4Ë»AA[¾»AnKR9AnE°Â
O0½QTÅϽFC984:<T KABR9A`67RD;¬TGÆ;>TN69¾G;>C9A`6.=¬;¬RSRD=¬A¦K½FT¿ EAnTNKA;>T«R9MGAÀN6SAnCcK½F8«8,ÀGTG;¬R7ÇQÂQ5xT®K½QTGÄ
R9C:Q6SRnHK½QTÅϽFC984:<T KAR9A`67RD;¬TGƾ ½QR9ATrRD;>:Q=¬=>ǾGCD½-ÁJ;>EGAn6Ë»ATGA¿GRD6°R9½U:<T;>8«¾G=¬An8«ATrR9½FCEÀGCD;>TGÆ
R9MGAA`:<CD=¬Ç67R:<ÆFAn6½<ÅEAnÁQAn=¬½F¾G8«ATrR:Q6U:469;>8j¾N=¬A,KMNAnKWÂNÚÛ=>;¬8«;¬RD:<R9;>½QTP½<Å.K½FTÅϽQCD84:<TNKA
R9An6SR9;>TGÆÉË A`K½F8jAYÅÏC9½F8ÜR9MGAÆQAnTGAC:<=>;\R7Çɽ<ÅR9MGA¾GCD½<R9½K½Q=L6Ë»A;>TGÆÑRDAn6SR9A`E%H ¾N:<C9R9;LKÀG=L:<CD=>Ç
:-RR9MNAÎÝJ5ª8«½EAn=c:<¾G¾N=¬;LK:<R9;>½QTN6=L:*ÇQAnCnH%¾GCD½<RD½K½Q=L6:<CDAjR7Çr¾N;>Kn:<=>=¬ÇÁQACDÇÑK½Q8«¾G=>A[:QTNE
ÆQATNAC:<=¡Hr½QÞ»AnC9;>TGÆ«84:<TJÇ®½F¾R9;>½QTN6:QTNEKMG½Q;LKA`6Â
5xTl½FCDEGACjR9½ÒEA`K;LEA¢R9MNAÑK½FC9CDAnKR9TGA`696j½<Å:<Tß;>8«¾G=¬An8«ATrRD:<R9;>½QT°Hc:#K=¬A`:<C®KCD;¬R9ACD;>½QT
;>6¦TGAnAnEA`E%Â5xT±R9MNAjK½QTrR9A[rR¦½<Å0K½QTÅϽFC984:QTNKARDAn6SR9;>TGÆNH84:<TJÇ¢¾GCD½Q¾»½F6D:<=L6ÅϽFC¦69ÀNKMÑK½QC9Ä
C9A`K~R9TNAn6D6Y;>TàRDMGAÑÅϽFC98á½QÅ;¬8«¾G=>A8«AnTFR:-RD;¬½FTâCDA=L:-R9;>½QT 6YMN:*ÁFA±Ë»AATã84:QEAlä¬åFHDæ-ç¡ÂèUTÄ
ÅϽQC9R9ÀGTN:<R9An=¬ÇFH@;>TFRDACD½Q¾»AC:<ËG;>=>;\R7ÇR9A`67RD;¬TGÆÉE;LEÓTG½<RWrTN½-Ðé69ÀNKMÓÅϽFC984:Q=¬;>ên:<R9;>½QT°Â@ÚTG½<RDMGAC
E;>6DKÀ 6969AnEË An=¬=>½-ÐÂ
!#"ÔMN;¬=>A:¾GCDAnK;>69AªEA¿NTG;¬R9;>½QT®½QÅ@;>TFRDACD½Q¾»AC:<ËG;>=>;\R7Çj;>6
6S½F8jAnÐMN:-R.An=¬ÀN69;>ÁQAQH`ÅÏÀGT K~R9;>½QT :<=>=¬Ç,R9MGA8«An:QTG;>TGƪ;L6K=¬A`:<C%$*K½Q8«¾»½QTGAnTFR6.K½F8j8ÀGTG;LK:<R9;>TGÆ
Ð;\RDMj½FTGAU:<TN½<R9MNAC.K½FC9CDAnKR9=>Ç:<TNEj¾GCD½-ÁJ;>E;>TGƪR9MGAA[¾ A`K~R9A`E«6SAnC9ÁJ;LKAn6nÂ<ÝJ½Q8«AUEA¿NTG;¬R9;>½QTN6
½<Å@;>TrR9ACD½Q¾»AC:<ËN;¬=>;\R7Ç«:<CDA&$JÃMGA:<ËG;>=>;\R7Ç«½<Å@R7Ð0½½QCB8j½FC9A¦6SÇ6SR9An8«6cR9½jA[GKMN:QTGÆQA;¬TÅϽFC984:<Ä
R9;>½QTP:<TNE8,ÀGR9ÀN:Q=¬=>Ç®ÀN69A¦R9MGA;>TÅϽQCD84:-RD;¬½FTYRDMN:-RUMN:F6Ë AnAT¢A[GKMN:QTGÆQA`E±ä'<çÂGÃMGA:<ËG;>=>;\R7Ç
½<ÅU:PE;L67RDC9;>ËGÀRDAnEÓ69ÇJ6SR9An8 RD½P;¬TrRDACKMN:<TGÆFA«V)(ªèª6,ÁJ;L:R9MGAK½F8j8ÀGTG;LK:<R9;>TGÆ¢¾G=>:<RSÅϽFC98
ä*-ç¡ÂÃMJÀN6nHFRDMGA:QK~RD;¬ÁJ;¬R7Ç«½<Å@;>TrR9ACD½Q¾»AC:<ËN;¬=>;\R7ÇjRDAn6SR9;>TGÆjK½QTN69;L67R6c;>TKMGA`KWJ;¬TGÆjK½FC9CDAnKR0½Q¾GÄ
AC:-R9;>½QT 6.½<Ű:69ÇJ6SR9An8 ½QŰK½Q8«¾»½QTGAnTrRD6nÂFÚKK½QCE;>TGƦR9½®äzæåç¡H-RDMG;L60:FK~R9;>ÁJ;\R7Çj6SMN½QÀG=LE4KMGAnKW
½QTG=>Ç,A[rRDACDTN:<=8«A`696D:<ÆFAn6R9MN:<Rc=>An:QERD½;¬TrR9AnCSÄxK½F8«¾ ½FTGATrRK½F8j8ÀGTG;LK:<R9;>½QT°Â<ÃMG;L6.;L6.TG½QR
R9MGAYKn:Q69A«½<Åä+<çc;¬T#ÐMG;LKMÉR9MG;L6,:FK~RD;¬ÁJ;¬R7ÇÑ6SMN½QÀG=LE#KMGAnKWÑ:QT#;¬TrR9AnC9½F¾ AnCD:QËG;>=¬;¬R7DZCDA=L:-R9;>½QT@Â
ÃMGAj:QÀR9MN½QC6Ær:*ÁQA,TN;¬TGAj;>TFRDACD½Q¾»AC:<ËG;>=>;\R7Ç¢CDA=L:-R9;>½QT 6ªEAn¾ AnTNE;>TGƽQT±RDMGA«:<CKMG;\RDAnKR9ÀGCDA
ÀN6SA`E%Â
-,./1023/4%563 !YÃMGAYEAnÆQCDAA«½<ŽFËN6SAnC9Á-:QËG;¬=>;¬R7ÇÑ:<TNE#K½QTrR9CD½Q=>=>:<Ä
ËG;¬=>;¬R7ÇQH-:<TNER9MGAK½FT¿NÆFÀGCD:<R9;>½QT½QÅGR9MGAK½Q8«8,ÀGTN;>Kn:-R9;>TGƦ6SÇ6SR9A846MN:*ÁQAB:UÆFC9A`:-R;>T7NÀNATNKA
½QTR9MGA;>TFRDACD½Q¾»AC:<ËG;>=>;\R7Ç:<CKMG;¬R9A`K~R9ÀNC9A0R9½:QE½F¾RnÂ<ÃMNAÚª67RDC9;LEA:<CKMG;¬R9A`K~R9ÀNC9A0½<Åä98`çÀN69An6
ÀG¾G¾»ACRDAn6SR9AC6:<T E:RDAn6SRK½J½QCE;>TN:-RD;¬½FTY¾GCD½KAnEGÀGC9AFÂGÃMGAÚ.Ã;:1XG½FC9ÀG8 ä<<ç°¾GCD½Q¾»½F69AnE
:YRDAn6SRK½QTG¿NÆQÀGC:-RD;¬½FTK½QTGTGA`K~RD;¬TGÆR9A`67RDAC6¦R9½R9MNA«EG;\ÞACDATrR5x8«¾G=¬An8«ATrRD:<R9;>½QTN6èTNEAC
Ã@A`67R.=Ï57èªÃ6>~H°:QTNE±¾N=>:FKAn6¦V ½Q;>TrRD6½QÅc½QËN69ACDÁ-:-RD;¬½FT?=ÏVBÎ@>:QTNE±V ½F;¬TrRD6¦½QÅO0½QTrRDC9½F=:QTNE
ΪËN6SAnC9Á-:<R9;>½QT?=VBOÎ@>¦Ë AR7Ð0AnAT57èÃ6:<TNEË AR7Ð0AnATÑR9An6SR9AnCD6:QTNEÑ57èªÃ6nÂ.äA-ç.¾GCD½Q¾»½F69AnE
:,ÆFATGAnC9;LKª:QCDKMN;\RDAnK~RDÀGCDA¦EA`6S;>ÆQTNAnEY:F60R9½J½Q=>Ë ½*[®ÐMN½F69A¦K½Q8«¾ ½FTGATrR6K:<TË AK½QT¿NÆFÀGCDAnE
:Q6TGAnAnEA`E%Â
CB3 2D2!ÃMGAªC9A`KATrRBC9A`6SA`:<CKMjÐB½QCDW6½FT®;¬TrRDACD½Q¾»AC:<ËG;>=¬;¬R7ÇR9An6SRSÄ
;¬TGÆ:<CDAC9An=>:<R9AnEjRD½,69ÇJ6SR9An84:-R9;LKRDAn6SR06SÀN;\RDAÆQAnTGAC:-RD;¬½FT°ÂGä98`ç»ÐB:F6.½QTGA½<ÅR9MGA¿NC67Rc¾ :<¾»AC6
;¬TYR9MGAª¿NA=LE%ÂÃMGA:<¾G¾NC9½r:QKM4:QE½F¾R9A`E®;L6cË :Q69AnE4½FT®C9A`:QKMN:QËG;>=¬;¬R7Çj:QTN:<=>Ç6S;L6nÂE:QTGÆNHE;¬8
AR0:Q=¨Â<M :*ÁQA¾GCD½Q¾»½F69AnEj:ÐMG½Q=>A½<ÅÐ0½FC9W6 CDA=L:-RD;¬TGƦRD½;¬TrR9AnC9½F¾ AnCD:QËG;>=¬;¬R7ÇR9A`67RD;¬TNÆ4ä¬å%F1GæGåçÂ
ä¬å%FGHå'NHnå18`ç¾GC9½F¾ ½r6SA`EP:®RDAn6SR¦ÆFATGAnCD:<R9;>½QT¢RDAnKMGTG;LÌrÀGAÅϽQC6SÇJ8«8«AR9CD;LK¾GCD½<RD½JK½Q=L6Ë :Q69AnE
½QTY69Ç67RDA8)K½F8j¾»½F69;¬R9;>½QT°Â»äæGåç%EAn:Q= Ð;¬R9MEACD;¬Á-:<R9;>½QT®½QÅ@;¬TrRDACD½Q¾»AC:<ËG;>=¬;¬R7ÇRDAn6SRD60ÅϽQC0R9MNA
K½QTrRDC9½F=:<T EPR9MNAjEG:<RD:Y¾N:<C9Rª½QžGC9½QR9½K½F=>6nÂÚ'69WQA=>ARD½QTPRDAn6SR69ÀG;¬R9AÅϽQCK½FTFRDC9½F=@¾N:QCSR¦;>6
EACD;¬ÁFAnE%Â2Hc:QKMÒR9An6SRjKn:Q69AY;L6RDMGAT×¾N:<C:<8«ARDACD;¬ênAnE%ÂÃMGA®RDAn6SRj69ÀG;¬R9AY;L6jK½Q8«¾G=>ARDAnEÓËJÇ
:Q6D6S;>ÆQTG;>TGÆÁ-:<=>ÀGAn6¦RD½¾ :<C:<8«ARDAC6Â%ÃMGA4:<¾N¾GC9½r:QKMÉ:QE½F¾R9A`EÑËJÇÒäzæQæ-ç;>669½PK:<=>=>AnEJIKML
NPONQ
KSRUTV ;¬TÐMG;LKMÑ:Y69;¬TNÆQ=>A,ATrRD;\R7Ç¢;>TFRDACD½Q¾»AC:-RDAn6UÐ;¬R9MÑR9MGAjCDAn6SRª½<Å.RDMGAj;¬TrR9AnÆQC:-RDAnE
K½Q8«8ÀGTG;LK:-RD;¬TNÆj69Ç67RDA846ÂGÃMNA:Q¾G¾GCD½F:FKM4;>6BRDMGAT¢CDA¾»½QC9R9AnEY½QTR9MGAÍ.½F5xVl69Ç67RDA8¢Â5xT
½QCEACRD½:*ÁF½Q;LEÑRDMGA6SRD:<R9A6S¾N:FKA®A[¾G=¬½r6S;>½QT@HäF<çB¾NC9½F¾ ½r6SA`EÉ:±R9A`67Rj¾GÀGCD¾ ½r6SA®½FC9;>ATrRDAnE
8jAR9MG½E%ÂÃMNA¾NC9;>TNK;>¾G=>AÐ:Q6RDMGAEGA¿NTG;¬R9;>½QTl½<Å6SÇJTNKMNC9½FTG;¬ê`:-RD;¬½FTÓC9ÀG=>An6ÅϽFCj¾ :<C:<=>=¬An=
K½Q8«¾»½F69;\RD;¬½FT°ÂcÃC9AR984:<T 64AR:Q=¨Âªäæ&F-çª69MG½-ÐBAnE×R9MN:<RnH0ÀGTNEAnC69½Q8«A±:Q6D6SÀN8j¾GR9;>½QTN6nH.R9MNA
W/ GÄ¡R9A`67RR9MNA½QCDÇ«ÅϽQCUK½QTÅϽFC984:QTNKA;L66SÀG;¬RD:QËG=>AªÅϽFCUK½F8j¾»½F69;¬R9;>½QTN:Q=°6SÇ6SR9A846nÂ
X 52?,.2 MS/10)!ÃMG;>6«¾ :<¾»AC«¾GCD½Q¾»½F69An6j:±ÅÏC:<8«AÐB½QCDWÅϽQCjR9A`67RD;¬TGÆ#;>TrR9ACD½Q¾»AC:<ËN;¬=¬Ä
;\R7ÇÉ;¬T 6S¾G;>CDAnEÉËJÇÑÐB½QCDWѽ<Åä+-çÂÝJ½F8jA4¾ :<C:<8«ARDACD;¬ênAnEC9An=>:<R9;>½QTN6nH%RD:QWJ;¬TGÆP;>TrR9½±:FKK½FÀGTrR
:<T¢:<¾G¾GCD½F:FKM®:<TNE:Q6D69½JK;>:<R9A`E®:<=>ÆQ½FC9;¬R9MG8éÅϽFCKMGAnKWJ;>TGÆ,RDMGAK½FC9CDAnKR9TGA`6960½<Å K½Q8«8ÀGTG;¬Ä
K:-RD;¬TNÆY6SÇ6SR9An8«6nÂÃMGA:Q¾G¾GCD½F:QKM¢;L6Ë :Q69AnE¢½QT:4=>:QêÇPK½F8«¾ ½r6S;¬R9;>½QTP;>T±½QCEAnCUR9½:*ÁQ½F;>E
R9MGA®6SRD:<R9A®69¾N:QKA4A[¾G=>½F69;¬½FT°Â°ÃMGA4½QCD;>ÆQ;>TN:<=>;\R7ÇP½QÅB½FÀGC:<¾N¾GC9½r:QKM;>6RDMGA®¾»½F6D6S;>ËG;>=¬;¬R7ÇPRD½
;¬TrR9AnCSÅ:FKA69½Q8«AK½QTGÅϽQCD8«:QTNKAªR9A`67RRD½J½Q=L6BÅϽQCÆQAnTGAC:-RD;¬TNÆ;>TrR9ACD½Q¾»AC:<ËN;¬=>;\R7Ç«RDAn6SRD6nÂ
ÃMGA4C9An84:<;>TNEAC,½<ÅBR9MGA®¾ :<¾»AC;L6½FC9Ær:<TG;>êA`E:F6ÅϽQ=>=¬½-ÐU6$@ÝJA`K~R9;>½QT׿¾NC9A`6SAnTFR6R9MNA
ÅϽQCD8«:Q=8«½EA=B:<TNE#TG½QRD:<R9;>½QTN6À 6SA`E%ÂÝJA`K~R9;>½QTF±;¬TrR9CD½EÀNKAn6:QTNEÉA[¾G=L:<;>TN669½Q8«A®¾N:<Ä
CD:Q8jAR9AnC9;>êA`EY;>TrR9ACD½Q¾»AC:<ËN;¬=>;\R7Ç4CDA=L:-RD;¬½FTN6nÂG?B:F6SA`EY½FTR9MGACDAn69ÀG=¬RD6½<Å.69AnK~RD;¬½FT FGHG69AnK~RD;¬½FT
'69MG½-ÐU6.¿NC6SRnHrMG½-ÐßR9½ÆQATNAC:-R9A;¬TrR9AnC9½F¾ AnCD:QËG;>=¬;¬R7Ç,RDAn6SRD6cÅϽQC0R9MG;L6cÅÏCD:Q8jAnÐ0½FC9Wj:<TNE®R9MGAnT
MG½-ÐÔ½QÀGC:<¾N¾GC9½r:QKM®Kn:<T®Ë»AªÀ 6SA`E4R9½jÆQAnTGAC:-RDAU;>TFRDACD½Q¾»AC:<ËG;>=>;\R7ÇR9A`67R6cÅÏCD½Q8 69½Q8«A¦K½QTGÄ
ÅϽQCD8«:QTNKAªR9A`67RRD½J½Q=L6 O0½FTNK=>ÀN69;¬½FTY;L6;¬TP69AnK~RD;¬½FT*GHG:<TNE6S½F8«A¦A`ÌrÀG;¬Á-:Q=¬AnTNKA¾GCD½J½<Å6:<CDA
¾GC9A`6SAnTrR9AnE;>T¢69AnKR9;>½QT +GÂ
·¸S¼9´ ؼxµ ³
ÃMGAcË»AMN:*ÁJ;>½QC°½QÅGK½Q8«8ÀGTG;LK:-RD;¬TNÆK½F8j¾»½QTNATrRD6K:<TË»A0EGAn6DKCD;¬Ë»AnEËJǦ8«An:<T 6°½<ÅÅϽFC984:Q=
8j½EAn=>6ª6SÀ KM±:Q6U5xTN¾GÀRΪÀGR9¾GÀR@:QË An=¬A`EPÃ@C:<TN69;¬R9;>½QT±ÝJÇ67RDA8 =Ï59ÎÃUÝ>~ ڪ6À 6SÀN:Q=@;>T
R9MGABR9A`67RD;¬TNƪRDMGA½FC9ÇFH*Ð0ATGAnAnERD½8j½EAn=;¬8«¾G=>A8«AnTFR:-RD;¬½FTN6H-AnÁQAnT,;¬ÅNR9MNA;>C.Ë AnMN:*ÁJ;¬½FCD6:<CDA
ÀGTGWJTG½-ÐT°ÂÚUT57èÃàÐ;¬=>=°:<=L6S½Ë ACDA¾GCDAn69ATrRDAnE4ËJÇ®:<T59ÎÃUÝÂGÝJAnKR9;>½QT¢æÂ>åª;>TrR9CD½JEGÀNKA`6
R9MGA459ÎÃUÝ8«½EA=c:QTNE#6S½F8«A4TG½<RD;¬½FTN6ÀN69AnEÉ;¬T#RDMGA4CDAn6SR½<ÅBR9MGA4¾N:Q¾ AnCnÂÝJAnKR9;>½QTÒæÂzæ
EA¿NTNAn6RDMGA59ÎÃUÝYK½Q8«¾»½F69;\RD;¬½FT°Â
! X B "!3
°AR S Ë A:,6SÇ6SR9A8éK½F8«¾ ½r6SA`E½QŰ:6SARc½<ŰK½F8«8,ÀGTG;LK:<R9;>TGÆK½F8«¾ ½FTGATrRD6
(Mi)ÂHÁQAnC9Ç
K½Q8«¾»½QTGAnTrR
Mi
EA¿ TGAn6B:,69AR½<Å@:FK~R9;>½QT 6 =AÁQAnTrRD6>
AMi ¾»AC9ÅϽQCD8«AnE4ËJÇ
Mi
HJ:QTNE®:6SAR
½<Å;¬TrR9AnCD:FK~RD;¬½FTN6 ¾ ½F;¬TrR6;=Ͼ»½QC9RD6.½FC.;¬TrR9AnCSÅ:FKA`6 >
PMi RDMGCD½QÀGÆFMÐMG;LKM
Mi
K½F8«8,ÀGTG;LK:<R9A`6
Ð;\RDM®R9MNAª½QR9MGAnCBK½Q8«¾ ½FTGATrR60:QTNE4Ð;¬R9MY;¬RD6BAnTrÁJ;>C9½FTG8«ATrRnÂrÃ@½jEA¿ TGAÅϽFC984:Q=¬=>Ç4:,K½F8jÄ
¾ ½FTGATrR
Mi
HNÐBAÐ;>=¬=ÀN69AR9MGA8«½JEGA=½<Å.5xTG¾GÀRΪÀR9¾NÀR:<Ë»A=>=¬A`EPÃ@C:<TN69;¬R9;>½QT±ÝJÇ67RDA8
=Ï59ÎÃUÝS>ªÐMG;LKM;L6:<T#:QEN:<¾R:-R9;>½QT½<Å0R9MGA«ÀN69ÀN:<=#ÃUÝÑ8«½EA=¡Â°5xTR9MG;L68«½JEGA=¡H%AÁQAnC9Ç
:QK~RD;¬½FT±;L6:Q6D69½JK;>:<R9A`ER9½:QT±;>TFRDAC9Å:QKAR9MGCD½QÀNÆQMPÐMG;LKMPR9MNAj69Ç67RDA83C9A`KAn;¬ÁFAn6½FCª69ATNEG6
R9MGAAnÁQATrR`Â
2 M$!&% K('*),+#-".
QR N T/1032L
M= (QM4ΣM4→M4 qM0 ) 576 L98 L1:
; QM QR N RPLT;I=< RUT N TLUR
N
K3>
qM0 ∈QM QR T6 L QK QTQN 26RT N TL1?
; ΣM ⊆ PM × AM 576 L@8L PM QR NBA K QTLRPLT IC< QKT L98D< NFE LRHGI0I*8UTRKJ T6 8 I*/
O 6
576 QLE
6 M E INMOM/K QLEN TLR 5 QT6 QTR LPKQP Q8 IKRM LPKT N KS> AM QR T6 L N 20 6 NFTLPTIC<
NUE TQ
I4KSR LWV
E 6 N K O LX>
T9Y M T6 8I*/ O 6 PM?Q'UT QRZ0 N 8UT QTQIKLX> QKTI T6 8 LL RPLTR@: ΣM = ΣiM ∪ ΣoM ∪ IM:3<I*8 (p, a) ∈ ΣM4 T6 LPK (p, a) ∈ ΣMi Q< a QR QK*03/T NFE TQIK 4 (p, a) ∈ ΣoM Q< a QR N K IN/T[03/T NFE TQIK 4 N KS> (p, a) ∈ IM Q< a QR N K QKTL@8UK N 2
NUE TQ
I4K IC<
M?
; →M ⊆QM × ΣM × QM QR T6 L T\8 N KR QTQI4K]8 L92N TQIKS?O^ L KMITL q α→M q0 <IN8 (q, α, q0)∈→M
N
K3>
q→αM
<I*8
∃q0:q→αM q0?
V LWV&T
4 IOLT S 5 Q2_2`>&LPKMI4TL T6 L RLPT#IC<
Q
K*03/T#IN/T[03/T,2
NFT L@2LX> T8
N
KSR
QTQ IK R Y
RUT L@M R9?
V ITLU?
p?α67R:<TNEG6ÅϽFC
(p, α)∈ΣiM :<T E p!αÅϽFC (p, α)∈ΣoM µ¯=p!α;¬Å µ=p?α
:<TNE
¯
µ=p?α;¬Å µ=p!αÂ
V N
M0S2LU?ªÝJ¾»AnK;¬¿ Kn:-R9;>½QT
M1
½QÅR9MNAX;¬Æ ÂåjK½Q8«8ÀGTG;LK:-RDAn6ªÐ;\RDM69¾ A`K;¬¿ K:<R9;>½QT
M2
R9MGCD½QÀGÆFM±;>TFRDAC9Å :QKAn6
C1:<TNE C2 :<T E±Ð;¬R9MÑ;¬RD6¦AnTrÁJ;>C9½FTG8«ATrRRDMGCD½QÀGÆFMP;¬TrR9AnCSÅ:FKA`6
C3
:<TNE
C4ÂBÝJ¾ A`K;¬¿ K:<R9;>½QT
M2
K½F8j8ÀGTG;LK:<R9An6®Ð;\RDMÔ;\R6®ATJÁJ;>C9½FTG8«ATrR4R9MGCD½QÀNÆQMß;¬TrRDAC9Ä
Å:QKA
C5ÂGXG½QC M1
$ PM1 ={C1, C2, C3, C4}H AM1 ={!start,?ack,!init,?status}H ΣoM1 ={C1!start, C4!init}H:<TNE ΣiM1 ={C2?ack, C3?status}Â
Canal3
1
3 2
1
2 3
Canal1 Canal2
C1!start
C1?start
C2?ack
C2!ack C3?status
Canal5
Canal4 C4!init
C5!ready M1
M2
C1?start C2?ack
C1?start C2?ack
r e|n§§¦Fprqt~^y7qtpFªwxuDqt¥r~^y7qt|nprw
"AÀN69A¦R9MGAÅϽF=¬=>½-Ð;>TGÆ467R:<TNEG:QCDEYTG½<R:-RD;¬½FT½QÅ59ÎÃUÝÂ
% $ +6LPT
M ∈ IOLT S4 µ(i) ∈ΣM4 α(i) ∈ ΣM \IM4 τ(i) ∈ IM4 σ ∈ (ΣM \IM)∗4 S ⊆ΣM4 P ⊆QM4 N K3> q, q0, qi∈QM?
; qµ1...µn−→ M q0 =∆ ∃q0=q, q1..., qn=q0,∀i∈[1, n], qi−1 µi
→M qi
?
; out(q) =∆ {α∈ΣMo | ∃q0 N K3> q α→M q0}?
; out(P) =∆ {out(q)|q∈P}?
- 6 LOP
QR QLT
2L T L 6 N P Q IN8 IC<
M QR&>LUR E 8
QLT LW>
5 QT6 ⇒
; q ⇒M q0 =∆ q=q0 IN8 qτ...τ−→M q0?
; q α⇒M q0 =∆ ∃q1, q2, q ⇒M q1
→αM q2
⇒M q0?
; q σ⇒M q0 =∆ ∃q0=q, q1. . . , qn =q0,∀i∈[1, n], qi−1 µi
⇒M qi, σ=µ1· · ·µn
?
; q σ⇒M =∆ ∃q0, q σ⇒M q0?
; q af ter σ =∆ {q0∈QM |q σ⇒M q0}? M af ter σ =∆ qM0 af ter σ?
; Out(M, σ) =∆ out(M af ter σ)? OutS(M, σ) =∆ Out(M, σ)∩S?
; T races(q) =∆ {σ∈(ΣM \IM)∗|q af ter σ6=∅}? T races(M) =∆
T races(qM0 )?
V ITL ?UXN½QC
M ∈ IOLT SH X ⊆ PMH S ⊆ ΣMH µ ∈ ΣMHª:QTNE (σ, σ0) ∈ T races(M)$
; σ.σ0 Ð;¬=>=@EAnTG½<RDAR9MGAK½QTNKn:-RDATN:<R9;>½QTY½QÅ@RDMGAR7Ð0½jRDCD:FKAn6nÂ
; σ/S
Ð;>=>=EATN½<R9A¢RDMGA±¾GCD½<Ù7A`K~RD;¬½FTؽQÅ
σ ½QT S EA¿ TGAnElËJÇ$
/S = ,(α.σ)/S = σ/S if α6∈SHG:<TNE (α.σ)/S =α.(σ/S)if α∈SÂ
; ΣM/X = {(p, a) ∈ ΣM|p ∈ X} Ð;>=¬=EAnTG½<RDAYRDMGA¢¾GCD½<Ù7AnKR9;>½QTÒ½QÅ
ΣM ½FTÒR9MNA
;¬TrRDAC9Å:QKA69AR
XÂ
; PM(σ, X) ={σ0 ∈T races(M)|σ/ΣM/X =σ0/ΣM/X
Ð;>=¬=.EAnTG½<RDAR9MNAj69AR¦½<Å
R9C:QKAn6½<Å
M RDMN:-RK½QCDC9A`6S¾»½QTNEYÐ;\RDM
σ ½FT XÂ
; card(S) Ð;¬=>=@EAnTG½<RDAªRDMGATJÀG8,Ë»AC½QÅAn=¬An8«ATrRD6½QÅ
SÂ
ÚUT¢59ÎÃUÝ
M ;L6;¬TG¾NÀRK½F8j¾N=¬AR9A;¬Å;¬RU;>6K½Q8«¾G=>ARDA=>Ç69¾ A`K;¬¿NAnEYÅϽQC;>TG¾GÀR¦:QK~RD;¬½FTN6nÂ
2 M
!&+2LT
M T L N K '*),+#-".3?
; M QR QK*0S/T E I*M0S2LPTL Q< ∀q∈QM4 ∀a∈ΣMi 4 q a⇒M
?
; M QR2QKL N 8 Q< ∀q ∈ QM4 card(out(q)) ≤1?#'K T6 QR EN RL 4 T6 L 038 IPL E TQI4K I=<
M IK S ⊆ ΣM QR T6 L 2QKML N 8 'N),+#-". KMI4T LX>
T9Y M/S
8 LRT\8
QLE T LX>CTI
S GT6 /3R T races(M/S) ={σ/S |σ∈T races(M)}JU?
!
WW2/1021 M 5 ) %% M XB BO
O0½Q8«8,ÀGTN;>Kn:-R9;>½QT8«AnKMN:QTG;L6S8 ½QÅ@R7ÐB½«59ÎÃUÝYKn:<TË A8«½EA=>AnEËJÇY:QT59ÎÃUÝ%Â
2 M W!&+2LT
M1
N
KS>
M2
T L T5 I '*),+#-". RX/
E 6 T6 N T
ΣiM1 ∩ΣiM2 =ΣMo 1∩ ΣoM2 = ∅?- 6 L R Y K E 6 8 IKI*/3R E I*M0SIR QTQI4K IC< M1
N
K3>
M2
QR T6 L 'N)#+,- .
M = (QM, ΣM,→M, qM0 ) KITLW> M1kM24
>L
A
KMLX>
T@Y
:
; I*8UTR I=<
M QR T6 L /K QIK I=< 0I*8UTR I=< M1
N
KS>
M2
:
PM =PM1∪PM2?
; ΣMo =ΣM1o ∩ΣM2o ?
; ΣMi = (ΣM1i \ΣM2o )∪(ΣM2i \ΣM1o )?
; IM =IM1∪IM2?
; qM0 = (qM10 , qM20 )?
; QM ={q1kq2|q1∈QM1, q2∈QM2}?
; →M
QR T6 L RXM
N
2_2LURUT 8 L92
N TQ IK >L
A
KMLX>
T@Y T6
L<I*2_2I 5 QK O 8 /2LRBG
µ∈ΣMJU:
F?
q1
→µM1 q104 µ6∈ΣM2\IM2 ⇒ q1kq2
→µM q01kq2
?
q2
→µM2 q204 µ6∈ΣM1\IM1 ⇒ q1kq2
→µM q1kq02
?
q1
→µM1 q104 q2
→µM2q204 µ6∈IM ⇒ q1kq2
→µM q01kq20
5xT;>TrR9ACD½Q¾»AC:<ËN;¬=>;\R7Ç«RDAn6SR9;>TGÆNHÐBAÀN69ÀN:<=>=¬ÇYTGAA`E®RD½4½QËN69ACDÁQAª½QTG=>ÇY69½Q8«A¦69¾»AnK;¬¿ KAnÁQATrR6
:<8«½QTGƪ:<=>=r¾»½F6D69;¬ËG=>AcAnÁQAnTFR6Â*ÃMN:<R;L6H*ÐBA0EA¿NTGA
MvisibleXÂ*ÃMGA0½FËN69ACDÁ*:QËG=>AAÁFATrRD6
½<Å
MvisibleX :QC9AjRDMG½F69A®A[GKMN:QTGÆQA`Eѽ-ÁFAC
XÂ@ÃMNA®½<RDMGACAnÁQAnTFR6:<CDA4K½FTN6S;LEAnC9A`E
;¬TrR9AnC9T :<=°:QKR9;>½QTN6
τÂ
2 M6!&+2LT
M T L N K&'*),+#-".
N
KS>
X ⊆PM N RPLTWI=<
Q
KT L98D<
NFE LUR@?
MvisibleX
Q
R'N),+#-". >&L
A
KLW>
T9Y
:
; QMvisibleX =QM4 N K3> qMvisibleX0 =qM0
?
; ΣMvisibleX =ΣM/X∪ {τ}?
; →MvisibleX
QR T6 L R M N
2_2LURUT 8 L@2
N TQ IKR >&L
A
KMLX>
T9Y
G
µ∈ΣMJU:
F? q→µM q04 µ6∈ΣM/X ⇒ q→τMvisibleXq0
?
q→µM q04 µ∈ΣM/X ⇒ q→µMvisibleXq0
V ITL
?@AR
MH M1
Hn:QTNE
M2
Ë»A.R9MGCDAA.59ÎÃUÝ%Â"ÔMGAT
X=PM R9MNAT MvisibleX =
MÂ M1kXM2
!23 %
M1kM2visible XÂ
µG¼S·c´
Ú6SÇ6SR9A8 ½<ÅK½Q8«8ÀGTG;LK:-RD;¬TNÆ#K½Q8«¾»½QTGAnTFR64EA¿ TGAnEß:#6SAR®½<Å:*Á-:<;>=>:QËG=¬A;>TFRDAC9Å:QKAn6nÂ
HÁQAnTFR6 A[GKMN:QTGÆQA`E½-ÁQAnCR9MG;L669AR:<CDA½QËN69ACDÁ-:<ËG=>AB:QTNE,R9MGAnTRDAn6SRD:QËG=¬AFÂ<5xTrR9AnC9½F¾ AnCD:QËG;¬=>;¬R7Ç
C9An=>:<R9;>½QTN6®ÅϽQC69ÀNKMà69Ç67RDA846®8ÀN67RRD:QWQAÑ:FKK½FÀGTrR®R9MNAn69A:*Á-:<;>=>:QËG=>AP;¬TrR9AnCSÅ:FKA`6ÂBÃMG;>6
6SA`K~R9;>½QT;>TFRDC9½EÀ KAn6:QTNEK½Q8«¾N:QC9A`66S½F8jA¾N:QCD:Q8«AR9AnC9;>êA`E®;>TrR9ACD½Q¾»AC:<ËN;¬=>;\R7Ç4CDA=L:-RD;¬½FTN6nÂ
W! @3?3
ΪTGA½<Å.RDMGA,À 6SA`EPK½QTGÅϽQCD8«:QTNKA,C9An=>:<R9;>½QTN6;L6R9MGAC9An=>:<R9;>½QT
ioconf 5R¦6SRD:<R9An6UR9MN:<R¦:QT
;¬8«¾G=>A8«ATrR:-R9;>½QT
I ;L64K½FTÅϽQCD84:<TrR«R9½Ó;¬RD6®69¾»AnK;¬¿ Kn:-R9;>½QT
M ;¬Å:-ÅR9AnC®:ÉR9C:QKA½QÅ
MH
½QÀRD¾GÀRD6«½QÅ
I :<CDAÅϽQCDAn69AAT×;¬T
MÂÃMG;L6jC9An=>:<R9;>½QTl:<=>=¬½-ÐU6¾N:<C9R9;L:<=69¾ A`K;¬¿ K:<R9;>½QTN6«:<T E :<=>=¬½-ÐU6B;>8j¾N=¬An8jAnTrRD:-RD;¬½FTN6BR9½®:FEGEYR9MGAÀGT EAC6S¾»AnK;\¿»K:-RD;¬½FT°Â
2 M !&+2LT
M N KS> I T L T5 I 'N),+#-".3?
I 6/& M M=∆∀σ∈T races(M)⇒Out(I, σ)⊆Out(M, σ)?
Ã@½±K½Q8«¾N:<CDAjËG;¬T :<CDDZC9An=>:<R9;>½QTN6nH%ÐBA4ÀN6SA
v :<TNE ∼=Â@AR Rx
:QTNE
Ry
Ë»A4R7ÐB½ËN;¬TN:QC9Ç
C9An=>:<R9;>½QTN6%½-ÁFAC
IOLT SÂ Ry v Rx
;¬ÅÅϽQCAÁFACDÇ
(I, M)∈ IOLT S6SÀNKMRDMN:-R
IRxM
R9MGAnT
I Ry MÂ Rx∼=Ry
; Ry v Rx
:<TNE
Rxv Ry
Â
W!
, ?%1& ! %D6!
ÃMGA467R:<C9R9;>TGƾ»½Q;>TrRÅϽQC;¬TrRDACD½Q¾»AC:<ËG;>=¬;¬R7ÇR9A`67RD;¬TGÆ¢;L66S½F8«AÆF;¬ÁFAT69¾»AnK;¬¿ Kn:-R9;>½QT 6H;>8Ä
¾G=¬An8«ATrRD:<R9;>½QTN6¦ÅϽFCR9MGA`6SA®69¾ A`K;¬¿ K:<R9;>½QTN6EGA¿NTG;>TGÆP69½Q8«A4:*Á*:Q;¬=L:<ËN=¬Aj;¬TrRDAC9Å:QKA`6H°:QTNEÉ:
KCD;\RDACD;¬½FTÓR9MN:<R4;¬8«¾G=>A8«ATrR:-R9;>½QT 6j69MG½FÀG=>EØ69:<R9;L67ÅÏÇFÂ.ÃMrÀ 6H.ÃÐ0½É;¬8«¾G=>A8«AnTFR:-RD;¬½FTN6j;¬TÄ
R9ACD½Q¾»AC:-RDA;¬Å@RDMGAÇ®KMGA`KW«R9MGA¦;>TFRDACD½Q¾»AC:<ËG;>=>;\R7Ç4KCD;¬R9ACD;>½QT°ÂJÃMGAªÅÏCD:Q8jAnÐ0½FC9W«¾GCDAn69ATrRDAnE
MGACDAQHF;>6cËN:Q69AnE«½FT«R9MGA¦K½Q8«¾N:QC9;L69½QTjË AR7Ð0AnAT«R9MNA½QÀGR9¾GÀR6c½QÅR9MGA¦6SÇ6SR9A8 R9½,Ë AR9An6SR9A`E
:<TNEªR9MNA½QÀRD¾GÀR6°½<ŽFTGA6S¾»AnK;\¿»K:-RD;¬½FT°H8«½EÀG=>½69½Q8«A.;¬TrRDAC9Å:QKA.¾NC9½QÙ7AnK~RD;¬½FT°Â9°AR
I(i)
˻A
:<Tj;¬8«¾G=>A8«ATrR:-R9;>½QT«½QÅNR9MNAU6S¾»AnK;\¿ Kn:-RD;¬½FT
M(i)
Ð;\RDM
i∈ {1,2}H*:<TNE X ⊂PM1∪PM2
Ë A:QT;>TrR9AC9Å:QKA6SARnÂS"ÉAC9A`K:Q=¬=»R9M :-R
M1kXM2
;>6
M1kM2visible XÂ
2 MW!
interopX(I1, I2)4=∀σ∈trace(M1kXM2)4 ⇒
OutΣI1(I1kXI2, σ)⊂ ∪σ0∈PM1kM2(σ,X)OutΣM1/X(M1, σ/Σ0 M1)
ÃMGA¿NC67RCDA=L:-R9;>½QT¢EA¿NTGAnE;L6BR9MGACDA=L:-RD;¬½FT
interopX
ÂG5R6SRD:<R9An6BRDMN:-REGÀGC9;>TGÆjR9MNA;¬TÄ
R9AC:QKR9;>½QTË»AR7ÐBAAnT
I1
:QTNE
I2
H*ÐMGATj:URDCD:FKA
σ½<Å M1kXM2
;>6;>T-Ù7AnKR9A`ERD½RDMGAB69Ç67RDA8
R9½YË»ARDAn6SR9A`E%H»R9MGA½QËN69ACDÁ-:<ËG=>AË»AMN:*ÁJ;>½QC6½<Å.RDMGA69Ç67RDA83¾GCD½<Ù7AnKR9A`E¢½QTPRDMGA:*Á-:<;>=L:<ËG=>A
;¬TrR9AnCSÅ:FKA`6½<Å
I1
;L6ÅϽFC9A`6SAnATÓ;>TÓR9MNAYÀGTG;>½QT×½<ÅU½QË 6SAnC9Á-:<ËN=¬A®Ë»AM :*Ár;>½QC6.=¾GC9½QÙ7AnKR9AnE#½FT
R9MGA4:*Á-:<;>=>:QËG=>A,;>TFRDAC9Å:QKAn6>U½QÅ
M1
HÐMG;>=>A«:Q¾G¾G=>ÇJ;¬TGÆR9MNAj¾NC9½QÙ7AnK~RD;¬½FT°H»½QT±RDMGA4:<=>¾GMN:QË AR
½<Å
M1
HG½QÅA`:QKMR9C:QKA
σ0 ∈T races(M1kM2) =σ0 K½Q;>TNK;LEA`6Ð;\RDM
σ ½FTRDMGA;>TrR9AC9Å:QKA 6SAR
X>~Â
°AR Y =PM1∩PM2 Ë ARDMGAK½F8j8ÀGT¢;¬TrRDAC9Å:QKA`6B½<Å
M1
:<TNE
M2
Â
2 M !
intercomX(I1, I2)4=∀σ∈trace(M1kXM2)4 ∀σ0 ∈PM1kM2(σ, X)4 σ0/Y 6=⇒OutΣI1(I1kXI2, σ)⊂ ∪σ0∈PM1kM2(σ,X)OutΣM1/X(M1, σ0/ΣM1)
intercomX interopX
K:-RD;¬½FTN6n¦AnTGAC:<=>=>ÇQH*K½Q8«¾»½QTGAnTrRD6 :<CDARDAn6SR9AnER9½K½FTÅϽQCD84:<TNKAQH*:<TNER9MJÀN6nH
intercomX
:*ÁQ½Q;LEG60R9MNAK½QTGÅϽQCD8«:QTNKAªR9A`67RD;¬TNÆNHËGÀRª½QTG=>Ç4R9A`67R6BR9MGA;>TrR9AnCSÄxK½F8j8ÀGTG;LK:<R9;>½QTY¾ :<C9RnÂ
ÚUTG½QR9MGAnCBKC9;¬R9AnC9;>½QT«;L6RD½EA¿NTGAª:,6SAR
A⊆ΣM1∪ΣM2 RD½,Ë»AªK½-ÁQACDAnE°Â
intercoverX
K½-ÁQAnCD6:<=>=JR9C:<T 6S;¬R9;>½QTN6ÐMG;LKMj¾N:Q6D6 ËJÇ,:¦ÆQ;>ÁQATAÁFATrR.½<Å
AÂ intercover0X
K½-ÁQAnCD669½Q8«A
R9C:<TN69;\RD;¬½FTN6 ÐMG;LKM¾ :Q6D6 ËrÇj:¦ÆQ;>ÁQATjAÁFATrR.½<Å
AÂQÃMGARDCD:FKA`6R9MN:<R.R9MGA`6SACDA=L:-R9;>½QT 6.K½QTGÄ 6S;LEACUKn:<TË A6984:<=>=¬AnCUK½F8j¾ :<CD;¬TGÆR9½
intercomX
:QTNE
interopX
Â
2 MW!
intercoverX(I1, I2) 4= ∀a ∈ A4 ∀σ ∈ trace(M1kXM2)4 ∀σ0 ∈ PM1kM2(σ, X)4 σ0/a6=⇒
OutΣI1(I1kXI2, σ)⊂ ∪σ0∈PM1kM2(σ,X)OutΣM1/X(M1, σ/Σ0 M1)
2 MW!
intercover0X(I1, I2) 4= ∀a ∈ A4 ∃σ ∈ trace(M1kXM2)4 ∀σ0 ∈ PM1kM2(σ, X)4 σ0/a6=⇒
OutΣI1(I1kXI2, σ)⊂ ∪σ0∈PM1kM2(σ,X)OutΣM1/X(M1, σ/Σ0 M1)
ÃMGAUÅϽFÀGC0CDA=L:-RD;¬½FTN6EA¿NTGA`E®MGAnC9A:QC9Aª6SÀG;¬RD:QËG=>AUÅϽQC:<TJÇR9A`67R:<CKMG;\RDAnKR9ÀGCDAQÂrÃMGAªKMG½F;>KA
½<Å.:CDA=L:-RD;¬½FTEGA¾»ATNEG6U½QTR9MGAK½QT¿ EGATNKAªRDMN:-RUÐBAMN:*ÁFAª;>TP:<T¢;¬8«¾G=>A8«AnTFR:-RD;¬½FT:QTNE
:<=L6S½«½QTR9MNA6S;>êA½<Å.K½F8«¾ ½FTGATrRD60RD½4Ë A;>TJÁQ½QWFAnE%Â
Ú6%CDAn69ÀG=¬RnHRDMGA.TGA[rR@R9MGAn½QCDA8ã69MG½-ÐU6»RDMGAAnÌrÀG;>Á-:<=>ATNKA Ë AR7Ð0AnAT
interopX
:QTNE
ioconf$
B 023
!&+6LPT
M14 M24 I1
N
KS>
I2
T
L<I*/8'N)#+,- . ?^ L N
RR /M L T6 N T
M14 M24
I1
N
K3>
I2
N 8 L Q KN0S/T
E
INM032LT L 4
ΣoM1∩ΣoM2 =∅4 ΣoM1∩ΣoI2 =∅4 ΣoI1∩ΣoM2 =∅4
N
KS>
ΣoI1∩ΣoI2 =∅?- 6 LPKS:
interopX(I1, I2)∧interopX(I2, I1) ∼= I1kXI2 ioconf M1kXM2
ÚUT;¬TrR9AnC9A`67RD;¬TNÆK:F6SAª;>6BÐMGAnTYRDMGA¦ÐMG½Q=>Aª;>TrR9AnCSÅ:FKAn6B:<CDAª:*Á-:Q;¬=L:<ËG=>A&$
X =PM1∪PM2Â
5xT±R9MN;>6Kn:Q69AQH ÅϽQC
σ ∈ M1kM2
HÐ0AMN:*ÁQA
PM1kM2(σ, PM1∪PM2) ={σ}Â%ÃMGAnC9AÅϽQCDAQH R9MGAªC9An=>:<R9;>½QTN6
interopX
:<T E
intercomX
K:QT4Ë AªÐC9;¬RSRDAT®:F6.ÅϽQ=>=>½-ÐU6 =RDMGAª69ÀGËN6DKCD;¬¾GR
X
Ð;¬=>=°Ë»A½Q8«;¬RSR9A`E>U$
interop(I1, I2)=4∀σ∈trace(M1kM2)⇒OutΣI1(I1kI2, σ)⊂Out(M1, σ/ΣM1)Â
intercom(I1, I2)4=∀σ∈trace(M1kM2)σ/Y 6=⇒OutΣI1(I1kI2, σ)⊂Out(M1, σ/ΣM1)
ÃMGA0¾ :<¾»ACBä+<çEGA¿NTGA`ETG;>TGAB;¬TrRDACD½Q¾»AC:<ËG;>=¬;¬R7ǦC9An=>:<R9;>½QTN6ËN:Q69AnE½QT:=>:*ÇFAC:<CKMG;\RDAnKR9ÀGCDA
ÅϽQC.:Q69ÇJTNKMGCD½QTG½FÀN6°AnTrÁJ;>C9½FTG8«ATrRnÂ*ÃMGA`6SABC9An=>:<R9;>½QTN6:<CDA0EGAnK½F8«¾ ½r6SA`E;>TFRD½RDMGCDAAK=L:Q6D6SA`6
EA¾»ATNEG;¬TGÆ,½QT4ÐMG;LKM«;¬TrR9AnCSÅ:FKA`6.½<ÅR9MNAU;¬8«¾G=>A8«AnTFR:-RD;¬½FTN6.RDMGAÇ,ÅϽJKÀN6½FT°ÂFÃMNAn69AC9An=>:<Ä
R9;>½QTN6BK:QT®Ë Aª½QËR:<;>TGAnE4ÅÏC9½F8
interopX
ËJÇ«EA¿NTN;¬TGÆ«:69ÀG;¬RD:<ËN=¬Aª;¬TrR9AnCSÅ:FKA¦6SAR
XÂJXG½FC
A[G:<8«¾G=>AQH»R9MNACDA=L:-RD;¬½FT
interop K½QCDC9A`6S¾»½QT EG6RD½èTG;¬=L:-RDAC:<=.ý<RD:Q= 5xTFRDACD½Q¾»AC:<ËG;>=>;\R7Ç IA=L:-RD;¬½FTEA¿NTGA`E;>T#ä+<ç¡Â
Ã@½4K½FTNK=>ÀNEAFHNK½F8«¾N:<CD;>69½QTYË AR7Ð0AnAT¢C9An=>:<R9;>½QTN6B;L6ÆQ;>ÁQAnTYË»A=>=¬½-Ð $
interopX(I1, I2)∧interopX(I2, I1)∼=I1kXI2 ioconf M1kXM2
intercomX(I1, I2)vinteropX(I1, I2)Â
intercover0X(I1, I2)vintercoverX(I1, I2)vinteropX(I1, I2)Â