Symbolic model checking with fewer fixpoint

0 downloads 0 Views 273KB Size Report
Model checking is an algorithm for computing the truth of a formula .... â inary Decision Diagrams 8â DDs for short C form a heuristically e§ffi cient data structure ...
      !"$#%&'(*)+-,. 

&/0,13245 /6 748:9=-7@B? A 8%CED @ F 8%GH=IGJ8%KL8%CE;>8 MN8%CPOP;QGJR&MSTC @ ;QC!8 UWVYX[Z:\E]_^`XbaR_OE; ä R ð  G n@Bä OP;QSTG õ þ  @ éÞC @ R @ GRjO AÞ@ R @ OÒS%ç&ReOE8vO @ [R mReê ä!A O A 8vOuO AÞ@ C @ ;>Rm8éJ8vO A ç§CPSYK 8%G;QGÞ;bOE;Q8 ã R_O!8vO @ OPS O A ;>RReOE8%O @  … _\U‡ m1o _ˆ2p9w'a8&2&,w.&e*ô + o c9+n‰Šp |~ ô a8&„w.& | +.\ m +2+Œ‹ &_%ô + I éÞCPSYé @ CeO Ž ö  ;QR8%G CFE4‘;C„E@ STç Z þÞ;Äç  ;QRWOECPê @ S%ç @ 8 ä!A R_O!8vO @ mjS%'ç … _xð YêH8T=½CEêÞé ãQ@[Z]\^&`_ a2b#a2ca2d?+ 

’"“`”

Z \¤&`_'a¥b#ac4ad¦+ D t &,§ a{{8{§ ¨ +sðHxAJ@ ä!A 8TCE8 8TR :  W

@O

•Y–/—˜—V™0š*›œ˜`žš*„™kŸ¡ ¢/™0š*„£}¢ž

@ 8 J CP;Qé Tå @ ReOPCEê ä OEêÞC @ Sv9 @ C6X ä O @ CE;QReOP; ä §ç êÞG ä OP;QSTG.S%ç8-R_O!8vO @

ñ m ó¡& © ¦+ \

ª«Žª«­¬ ®2¯°±H²³µ´

§ €`¶· ‰

O ©î= @ GÞS%O @ \^‡8§ : a{{8{La¥§0¨"‹Yð W @ # m o _ þÎ= @ GJS%O @ = ñ m ó þÎ;>R4= @ üJG @ =

ª«¸¬ ®¯°¹ ±H²³µ´º

§ €„¶·¶·

xAÞ@ = @ üJGÞ;ÄOP;QSTG÷S%çxO AÞ@ä!A 8TCE8 ä O @ CE;QReOP; ä §ç êÞG ä OE;ÄSYG÷;QR @së O @ GJ= @ =.OPSNR @ O!RmS%çReOE8%O @ R[&;bO A O AÞ@ ç§S ãÄã S&;ÄGJæ= @ üJGÞ;ÄOP;QSTGHR  Dñ ‡œ‹ Bó & © +¦\gH»9¼ m*½ Dñ ‡*¾n‹¦¿ŠÀBó & © +¦\×ñ ¾Þóµ& © +Áñ Àó¡& © +

W @

O XÂq \Ç8§ q a8{{8{§ ¨q ‹ D @ 8†R @ O”STç½ç§C @ R A DgSnS ãQ@ 8TGméÞCESTégSYRP;bOE;ÄSYGJR ð*xAÞ@kä!A 8%C!8 ä O @ CE;QReOP; ä ç§êÞG ä OE;ÄSYGS%ç"8ÒOECE: 8TGJRP;bOE;ÄSYGŠÄ \^& m : a m*z + o b þÞ= @ GÞSTO @ = ñ Ä ó þJ;QR= @ üJG @ =8TR  ñ Ä ¡ó & © a © q +¦\ ñ m : óµ& © +n‰.ñ m*z óµ& © q + xA ;QRL= @ üJGÞ;ÄOP;QSTG ä 8TG D @@së O @ GJ= @ = OPS C @ éÞC @ R @ GR_OE; ä §ç êÞG ä OP;QSTGS%ç3O AÞ@ ;QKL8%æ @ STç À Þþ = @ GÞSTO @ =kÍÂÎ%Ï%Ð ÍÂÎ%Ï%Ð » %Ï Ñ ,& ÀÓ+L& © q +\gp © a¥Àj& © +n‰Šb& © a © q +

Ô STGn9 @ CER @ ãQö þHO AÞ@ ;QGn9 @ CER @ ;QKL8%æ @ STçx8R @ OmSTçWReOE8vO @ R ç§CPSYKÖ A ; ä!AÀ ä 8TGD @ C @ 8 ä!AJ@ =;QGSTG @ OECE8TGJRe;ÄOP;QSTG 

ÀÕf¤_

þg;>R 

» Ï Ñ „& ÀÒ+

þÕ;>R4O AÞ@ R @ OmSTçWReOE8%O @ R

‡ mÂo _Ȉ¥p m q o ÀÆa*& m a m q + o b‹

xAÞ@ä!A 8TCE8 ä O @ CP;>ReOP; ä ç§êÞG ä OE;ÄSYGîS%çxO AÞ@ ;QGR  À

þ3= @ GJS%O @ =

× »9ØÙ Ð » ÏÑ &,ÀÒ+& © + \Úp © q a¥ÀÛ& © q +‰ŽbY& © a © q +

߆âÞ àÊÜVÞ'árT âk;QGJ8TC ö 7 @Bä ;QRP;QSTG 7;>8%æYCE8TKR & âW7474Ruç§STCmR A SYCeO + ç§SYCPK 8 AÞ@ êÞCE;>R_OE; ä 8 ãQãÄöí@ä ; @ GRO AÞ@ RP;Äÿ @ ;ÄçÒO A ;>Râx747 ðmñ vó R A S @ =O A 8%O1âx747†Rj8%C @ 8 ä 8TGÞSTGÞ; ä 8 ã C @ éJC @ R @ GYO!8vOE;ÄSYG  O WS @ YêJ;Ä9v8 ãQ@ GR†éJ8%é @ Cþ4 @ &; ãÄã êJR @ êJRPêJ8 ã DgSReSYG %¾ : åõô : ‰R¾ z å ô z ð4xAJ@ DÞ;ÄGH8%C ö OPC @ @ C @ éÞC @ R @ GR þ";QG Z þ ÍÂÎ%Ï%Ð » Ï%Ñ &`Ò‰ æV+Èf ïA S ã =ÞR8%GH=Œ.CPSYéHSRBþ Z ˆ \ڍ þYO A CESTêJæ A ê   0ø >m“Aå   EHGLET“  @ æ @ O Z ˆ \ e ñ æ`Ž k Hó¯ð õö

¾"“…„ à1˜£n£}Ÿ¡žxŸ¡£˜){?—`á/Ê`›Ò’ }›m\o\̗”}“gâ G@  E2ø æxã G@üû   ‘ ã CF@B‘2‘úý˜ š&› ¢   ‘úêY>Aéb“Åç/þ2éVGE î e ñ 2jŽæ‘2G¬çBè ¢ @‹éVGMCFE%G‘”“G CÕê ÅëÉG   ¢1 CFE Z C…[ “ ½;“ > ã “ G@   R¢ Y‰ æŒì,x‰ æŽf × »9ØÙ Ð » ÏÑ &B"+ íî @‹éVGE Z ˆ \ elf &`"‘ a ñ æmkHó+ ç ï ‘  ¬  ¢ ç IæY8T;ÄG¥þ  @ éÞº CESv9 @ O AJ@mº ä STGR   ç58 J CE;Äé åT@ R_OECPê ä OPêJC @[Z ;>RRPê ä!A O A 8%O Z ˆ \ eƒf &`"‘ a ñ æ`kŠHó+ O AÞ@ G º M‰ æ f p × »9ØÙ Ð » Ï%Ñ &`"+L{ O  AÞ@ G @ 9 @ C Z º ˆ \ elf &B"‘ a ñ æ`Ž $@ R A 8 ãÄã R A S  O A 8v? k HFó + þTO AÞ@ C @@ ë ;QReOERk8mR_O!8vO @ S%ç Z  AÞ@ C [ S J = & R % 8 J G = S J = & R Ä ;  G Þ G Y S G % S 3 ç b ; ! O  R e R ê @ Y‰ æA 㠍A ã @ ä äs@ RPRPSTC!R ð ;3 QC!R_Oþ  º @ C @ &CE;bO @ ç§SYCPK/ê ã 8 elf &`º "‘ a ñ æ`Ž Y 8 k HFó + RWç§S ãQã S R  ef &`"‘ a ñ æmŽk H,ó +Að º adh &B"‘ a ñ æ`Žk H,ó + º ð adh º&BY‰ a ñ æ`Šk HFó + ð adh &BY‰ eº ñ æ`j H,ó + ð adh &BY‰Ó& Mº ÁÓ& º æ1‰ ece ñ æ`j HFó +2+¥+ ð adh &BY‰ º æ1‰ eºc)e ñ æ`j Hº ,ó + º º

º

º

xAÞ@ R @ KL8%GRBþ ‰ æ f × »9ØÙ Ð » ÏÑ &`"+ÒA S ã =ÞR/;ÄG Z ðxAÞ@ C @ ç§STC @ þŸ.CPSYéHS ý Re;ÄOP;QSTG  8%éÞé ã ; @ Ru8%GH= Z ˆ \ eƒº f &`"‘ a ñ æmkŠHóF+sð â ö  @ 8 åY@ GÞ;QGÞæJþH @Lä 8%G;ÄGÞç @ C @ O A 8%O Z ˆ \U"‘ a ñ æmkHóðH ;ÄG äs@YZ ˆ \UÛ& D öAnö éHSTO AÞ@ Re;>R + þÞO A CESTêÞæ A ê   ø>m“Oå   E}GEi“  @ æ @ O Z ˆ \ a ñ æmkHóð  ¥F àÊÝÊÜJâ_ÛRárT 

Q; æTêJC @÷òìä STGR_OE; ä ç§êJG ä OE;ÄSYGS%çO AÞ@ R @ OWSTç¥R_O!8vO @ R AJ@ C @ O AJ@ ç§STCEKÒê ã 8 ;QRx9v8 ã ;>= ð ä ÑÉÑ | òHn¼ |µ½m4;>R8 DHSnS ãQ@ 8TGéJC @ =½; ä 8vO @ 8%GJ=O @ R_O!R&;bç5;ÄOERxüJC!ReO8%CEæTêÞK @ GR&;ÄGn9YS åT@ =SYG 3ð k  Fó + êÞGÞ;Q9 @ CERE8 ã NTNQP ù¥úû ç§STCEKÒê ã 8 e  çkSYGíO AJ@ STO AÞ@ C A 8%GJ=Õþ  ;QRj8elf &B : ‘ e ñ  z Š ;&§ã ÄG @ R )07 OES )œ+ þDgS%O A 8%CEæTêÞK @ GR ä 8TR @ þn;ÄORP8:9 @ RW8mü ë égST;QGÇ =iȽƋ 8x;‰ÈbÈ =TJà i!Ƌ Ë`jË 8€ÞLÇT‰ßQÆAÇUÄ@ȽƒM Á 8  < Ë`Ë eµ GCÚ , ¶ÅÚ%µ + ¶ , µE¶ + Ú ÜùܐRÈ QUSUT Vw>X½< ZÇ Y>T \U]l^l_LXHUÉ ë mn^ Vo_ ÚQÙ>´”Ú ¶ÅÚ%µ + ¶ ,p/xÃ@%È 1J2K365L1sÂ‰ß ÇHÈÊÉ Æ’M Á 8¥ò½Ë ÚQÙ>´”Ú ¶ Ú%µ + ¶ ,q) ·mÙ>´”Ú ÚQÙ>´  )1òFE ² ¨„Æ ò < Ë©R¦ ì ò ë Ì ò < îQË eµ GCÚ , ܋ܐZÈ QUSUT Vvw[XnZÇ Y[T \U]l^Cr  < ` /xÃ@%È 1J2K365L1sÂ‰ß ÇHÈÊÉ Æ’MÁ 8¥ò < Ë Â ë ` /xÃ@%È 1J2K365L1sÂ‰ß ÇHÈÊÉ Æ’MÁ 8¥ò ë Ë ')C;‰ÈbÈ a§Ágb2a1 À:ƒÁPd À78;‰ÈbÈ Ç>=iȽƋ 8x;‰ÈbÈ =TÃJi!Ƌ Ë`Ëj8€ÞLÇT‰ßQÆAÇUÄ@ȽƒÁM8  < Ë`Ë µeGCÚ , ¶ Ú%µ + ¶ , µ!¶ + Ú Ü‹ÜRÈ Q%SUT Vvw[XnZÇ Y[T XgÉ mn^ Vvë _ ÚQÙ>´”Ú ¶ Ú%µ + ¶ ,p/oÃÅ%È 1J2K36571}Â”ß ÇJÈÉ Æ’P Á 8¥ò½Ë Ú ,-y

ð*)+-,

Ž@? ·