A Formal Approach to Fault Tree Synthesis for the Analysis of Distributed Fault Tolerant Systems Mark L. McKelvin, Jr. , Gabriel Eirea , Claudio Pinello , Sri Kanajan , and Alberto L. Sangiovanni-Vincentelli Department of Electrical Engineering and Computer Sciences University of California, Berkeley Berkeley, CA 94720 General Motors Berkeley Lab Berkeley, CA 94703 [email protected], [email protected], [email protected], [email protected], [email protected] ABSTRACT !"#$%!"'&()*&(+,$- . */00 * 1#2"*+&(23*4* $% *&657*8907+ &(!:*;<+26=07+>*4?@&A*2=B<.C;&D&A2 .C#/ 2 E/F83&(28.3!"0 *'8?G"+2'CHI*& ?%0 $% J8K!J57???:&L,M*I84*N !"0 !"+-68K 7 8!"6:K07 5$:?% [email protected]+2 "0*&P*! 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V !"+- Z8@&P2Y"90%2:1#2+-*)&P2J4?2 !" &A*2!" <B 9C*+ E;;8. #+ :*07+;84* ;MV8\+O%0 T N8Y+C ¸* g*&68Y!:B8d&P*!J2 * ©&P"8d$%#8 @ +U=578_&PT?%0 $%!"#"*4? &P*@&A*2@^2+ DU68*J8TMæ_*g07 M>8c?%k+#@&A* 2%d!"-?+a&P*"8^84*C?-M=B`!"07+- ;?% k.#=&P!:*'`<V;&(>8&(2+ 4* b$#E 7. ACKNOWLEDGEMENTS Z)M2?a H<V;CH-M> ?8V+2+ <?% 2 M>8Zl#aª$%#.H-)?N .H\V !"&L! ;Ð_ÐW*57C** T"M+ J +C`*^NB.8©C*3U>07j $ ;!"V572HZ?[F8!:@h28!:*DE9Sb[04B+2*U6;Ð k.?\8K+O%07+ J \8a2J*&V8aS! #H-UWh42 FDNN4$% U%?J; CH@V !"607+&P*!"?@ 8N4*$+ 8:&A*2@+@84*aM^$#8 ¸?iE[Ñ3 J 2Z*4? d*OcV8-?%g&L!ñ8 J +C;`*:¾V+H<+.$cÐD5M+ Z 2!"#C= © -f+ *N&(?5CH©8`?E F8; 02%6&L!æÑ3&( ßK2u ßK2¸++U%; J C2N*4? *à 7 *à 9!:a*I*"**&(2 $9*.H-M> ?%?kE F8 3M*HYM/2007?Y @04B/5-$I8>V#+3&P*VN$%5? ? ² !J57???Î-&L,M=B\?ªÎ-$%!"a2?+@8# +B 4* Î%++h24?B TSFC*-;=V>bý ±± Ám-ý-U8 J < Î-$%!"TN*C8V#+d24?%+^8g`.# + ?% +?@;+*C8dV*07CB`*C# ± ýýBKFVbmmý-U4*4? J % +C*3`*E 8.n.~ag REFERENCES E4¾* U7YEh+CB U4Ð)E4d+2%U YEÎ* BxÒ; # AU7gE4Ñ'+AU4*4?9Î7EÑ'¸¸ AE h42 .C#N0*&(!"=&P**2!" <B&P+b$%+ * 00 * E4S,` Wía» =»U0YÄVý á4BÄÄ-UDÎ%dlU &P%Uk³KÎ%YU ± ýý-EkN=Ñ/E n ± ~agE4¾B57C*HkU7gE7d* H7U7?dYE%K*8-52C-EF8 2N0%5+!æ^&A2 +C#N!"02 %E4^ í Wÿ )¡¯Ù4-A¼P¤#Û:»%[£ ¢.¿*ØCU ± Á Q± R. BÄ-[ á ±± ý%UDl2Jëë%E n B~YYE¾V-< U4Ñ'E40 U7ÎkE ² ?-M=BC?<U +aE 5#M=*.8U Ñ3EÐ)E J 2. U4?TYE?KÎ% !"EF8K$%C82 L*24K,M+$#*>*.E ⣡½+äØ ã6¡,®K(ߢî !U ë% Q R. mW á#ü-Uil<iE ± ýý-E n *~YhVE ÒYE¾)C UiÑ'EaE ² ¸8 C8 iUkÎkiE ß@E4Î%8%C%U +aEYE4Î%07U?dÎkEF'*E4Sb!"0 !"# K&P b # -?+>&(;? 52%?^$%!"E7î !Ý £¤Ø+½+A¼ ¡¤Øa¡¤ )¡¯Ù4-b¢.£CØU7#Á Q BR. ±± Vm á4 ± ü-U +;B<!J57.ëëm%E n Á~a;E !:-U4IE J C*2Uk;EÐW*U ? åJE4Î%*AE e;7b ; !"&A2 +C#N.8?2 ES, =-£¡*¯J¼ ½+£¡ æiçlçÎè*Ukd*#*%USbC*$#U4h+524B$ ± ýý%E n mB~IS.ESb!ÏÎ-&L,M=BEkD% £¢S¢ é[®+¡/ £ ê^¼(¤7°<¡¦/ØU%< 2!" ü%E ý%ES,*C089ÐD !"?iUkëëü-E n Ä~IaEÐW*!J57+E%³K*&3&A*2>I$%>&P*;2!" < L*5 ,$9*4?T*&P.,$`4*$ !E )¡¯Ù4-b¢.£CUk Q ë<R. 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E ⣡½+äØ ã)¡,®I(ߢî !U7Ä*ë Q ë<R. ý<Á á4 ± ý-UWÎ%0%!J57+ëë-E n*~a;E7Ñ/ U4Ð)E4* AU7?dYEÎ% * Ò +# AE h4*2 +C#;?+0 $!"+-&3!a57??%?:&(bM=BI&( b+ <K !"&P?54*.H#-W*00 B E S,# â=£¡½C¢C¢°¼(¤-ÛØa¡®;¥a¢.ؼۤdíN-¡¯"*A¼ ¡¤f¤7°\ k¢.ØV¼P¤ %£¡.Ù¢.U7Ñ3B UkhCUh5%24*$ ± ýý*E n+ ~ ß@<E ß@<E Ò)!J2AU%lE4¾;E2DU ? ß@ElE4Î%2 *DE ;2%!:B$#8 N*&'&A*2>=&P*+!"02%+54*? $%!"E4î !Ò £¤Ø.<½+A¼ ¡*¤ØY¡# ¤ ¡>¢+ ¼ <Ú+¼A ¼PA¿*U <ü Q #R. ë*W á<<ý ± Ui!a57+Këëë-E nÁB~K·E ² <E Ò)$#UhVE4hVE J ?57.U +YEYE%;57+U4*4? JEhVE* E4h42=K84*4?57#H7E4FW+.8 iN07 +³; ² J býë ± U³aE4Îk<E +2 *>N2**$9V!"!" 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