O. Kupferman and M.Y. Vardi. Verification of fair transition systems. In Computer Aided Verification (CAV'96), LNCS 1102, pages 372--382, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....theoretical properties. In particular, we proved that it is the weakest equivalence that preserves the logic CTL interpreted on the fair paths [8] We demonstrated that E fair bis could be decided in PSPACE, and conjectured that it was also hard for PSPACE; this was recently proved [69]. Thus it is not of much help in finding equivalent states. Dill et al. 39] gave techniques for language containment by simulation relations for Buchi automaton. We extend his definitions to obtain conservative approximations to E fair bis which are polytime computable. Definition 14 ....

O. Kupferman and M. Vardi. Verification of Fair Transition Systems. In Proc. of the Computer Aided Verification Conf., July 1996.

....If there exists a simulation from to , we say that Cz simulates C and we write Cx C2. The time complexity of checking trace containment and simulation between two graphs is well known. The trace containment problem is PSPACE complete and the simulation problem is PTIME complete [16] 24] [12]. Getting back to our subject matter, an object system can be seen to induce a labeled state transition graph, by taking the states of the graph to be the reachable configurations of the system and its labeled transitions to be the relation succ. Formally, we set this up as follows: Consider a ....

O. Kupferman and M.Y. Vardi, "Verification of Fair Transition Systems," Chicago J. Theoretical Computer Science, Mar. 1998.

....constitute the implementation (cf. LT87,Kur94] The theory behind trace equivalence and bisimulation is well known. We know that two states are trace equivalent iff they agree on all LTL specifications, and the problem of deciding whether two states are trace equivalent is PSPACE complete [MS72,KV98b] In the branching approach, two states are bisimilar iff they agree on all CTL formulas, which turned out to be equivalent to agreement on all CTL and calculus formulas [BCG88,JW96] The problem of deciding whether two states are bisimilar is PTIMEcomplete [Mil80,BGS92] and a witnessing ....

..... Finally, the different definitions induce different computational costs. The exact complexity depends on the fairness condition being used. For the case of the Buchi fairness condition, for example, the problem of checking whether two systems are bisimilar is PSPACE complete for 9 bisimulation [KV98b] NP complete for 8 bisimulation [Hoj96] and PTIME complete for game bisimulation [HKR97,HR00] There are various types of fairness conditions with which we can augment labeled state transition systems [MP92] Our work here relates fair transition systems and automata on infinite objects, and we ....

[Article contains additional citation context not shown here]

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. Chicago Journal of TCS, 1998(2).

....in terms of the implementation, assuming the specification is fixed. Since the implementation is typically much larger than the specification, this measure is of particular interest. The implementation complexity of simulation is PTIME complete, whereas that of containment is NLOGSPACE complete [KV98] So, according to this measure, containment is easier than simulation. 3. The joint complexity of fair containment and fair simulation. When we consider fair transition systems [MP92] which enable the description of behaviors that satisfy both liveness and safety properties, containment and ....

....that satisfy both liveness and safety properties, containment and simulation are revised to consider only the fair computations of the implementation and the specification. The resulting problems, of fair containment and fair simulation [BBLS92, ASB 94, GL94] are both PSPACE complete [KV98] 4. The implementation complexity of fair containment and fair simulation. Here, the advantage of the trace based approach reappears. Indeed, the implementation complexity of fair simulation stays PSPACE complete, whereas that of fair containment is NLOGSPACEcomplete [KV98] We address the ....

[Article contains additional citation context not shown here]

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. Chicago Journal of Theoretical Computer Science, 1998(2), March 1998.

....simulation. This measure considers the complexity in terms of the implementation, assuming the specification is fixed. Since the implementation is typically much larger than the specification, this measure is of particular interest. According to this measure, containment is easier than simulation [KV96] 3. The joint complexity of fair containment and fair simulation. When we consider fair transition systems [MP92] which enable the description of behaviors that satisfy both liveness and safety properties, containment and simulation are revised to consider only the fair computations of the ....

....that satisfy both liveness and safety properties, containment and simulation are revised to consider only the fair computations of the implementation and the specification. The resulting problems, of fair containment and fair simulation [BBLS92, ASB 94, GL94] are both PSPACE complete [KV96] 4. The implementation complexity of fair containment and fair simulation. Here, the advantage of the trace based approach reappears [KV96] We address the question about the power of concurrency in program verification by examining the four measures when applied to concurrent transition ....

[Article contains additional citation context not shown here]

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. In Computer Aided Verification, Proc. 8th Int. Conference, volume 1102 of Lecture Notes in Computer Science, pages 372--382. Springer-Verlag, 1996.

....0 such that H(w;w 0 ) If there exists a simulation from M to M 0 , we say that M 0 simulates M and we write M M 0 . Intuitively, it means that the system M 0 has more behaviors than the system M . In fact, every possible behavior of M is also a possible behavior of M 0 . Theorem 1. [18,32] For every M and M 0 such that M M 0 , and for every 8CTL formula , we have that M 0 j= implies M j= A system M is a maximal model for an 8CTL formula if it allows all behaviors consistent with . Formally, M is a maximal model of if M j= and for every system M we ....

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. Chicago Journal of Theoretical Computer Science, 1998(2), March 1998.

.... problem for CTL is 2EXPTIMEcomplete [VS85, EJ88] In the rest of this paper we examine four additional verification scenarios: modular verification [KV95] verification of open systems [KV96, KVW98] verification of concurrent systems [BVW94, Kup95] and automata theoretic verification [KV98] In each case we show that CTL does not dominate LTL computationally. In the concluding section of the paper we discuss the implication of these results on the linearvs. branching time discussion. We assume familiarity with the syntax and semantics of temporal logic [Eme90, KT90, Sti92] 2 ....

....is easy to see that simulation implies containment and fair simulation implies fair containment. The opposite, however, is not true in general. Without fairness, the tree based approach is easier than the trace based approach (assuming that PSPACE is different than PTIME) Theorem 5. 1 (1) MS72, KV98] The containment problem is PSPACE complete. 2) Mil80, BGS92, KV98] The simulation problem is PTIME complete. One we introduce fairness, however, the advantage of the tree based approach disappears. Theorem 5.2 (1) Wol82] The fair containment problem is PSPACE complete. 2) KV98] The fair ....

[Article contains additional citation context not shown here]

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. Chicago Journal of Theoretical Computer Science, 1998(2), March 1998.

....PSPACE completeness extend to the fair case. It is not so obvious how to generalize the branching framework of simulation to account for fairness. Indeed, several proposals can be found in the literature. The definition suggested by Grumberg and Long [GL94] and used among others by [ASB 94, KV96] rests on the motivation that S fairly simulates I iff every Fair 8CTL formula that holds for S holds also for I (the universal path quantifier of Fair 8CTL ranges over fair computations only) This definition, however, is neither robust (Fair 8CTL induces a weaker preorder [ASB 94] ....

.... (the universal path quantifier of Fair 8CTL ranges over fair computations only) This definition, however, is neither robust (Fair 8CTL induces a weaker preorder [ASB 94] and Fair 8AFMC, as we show here, induces a stronger one) nor can it be checked efficiently (it is complete for PSPACE [KV96] Following [Hoj96] we call the Grumberg Long version of fair simulation 9 simulation, because it can be defined as simulation where each fair computation of I is related to some fair computation of S. In manual verification, by Lynch and others [LT87, Lyn96] usually a stronger notion of fair ....

O. Kupferman, M.Y. Vardi. Verification of fair transition systems. In Computer-aided Verification, LNCS 1102, pp. 372--381. Springer, 1996.

....PSPACE completeness extend to the fair case. It is not so obvious how to generalize the branching framework of simulation to account for fairness. Indeed, several proposals can be found in the literature. The definition suggested by Grumberg and Long [GL94] and used among others by [ASB 94, KV96] rests on the motivation that S fairly simulates I iff every Fair 8CTL formula that holds for S holds also for I (the universal path quantifier of Fair 8CTL ranges over fair computations only) This definition, however, is neither robust (Fair 8CTL induces a weaker preorder [ASB 94] ....

.... (the universal path quantifier of Fair 8CTL ranges over fair computations only) This definition, however, is neither robust (Fair 8CTL induces a weaker preorder [ASB 94] and Fair 8AFMC, as we show here, induces a stronger one) nor can it be checked efficiently (it is complete for PSPACE [KV96] Following [Hoj96] we call the Grumberg Long version of fair simulation 9 simulation, because it can be defined as simulation where each fair computation of I is related to some fair computation of S. In manual verification, by Lynch and others [LT87, Lyn96] usually a stronger notion of fair ....

[Article contains additional citation context not shown here]

O. Kupferman, M.Y. Vardi. Verification of fair transition systems. In Computer-aided Verification, LNCS 1102, pp. 372--381. Springer, 1996.

....PSPACE completeness extend to the fair case. It is not so obvious how to generalize the branching framework of simulation to account for fairness. Indeed, several proposals can be found in the literature. The definition suggested by Grumberg and Long [GL94] and used among others by [ASB 94, KV96] rests on the motivation that S fairly simulates I iff every Fair 8CTL formula that holds for S holds also for I (the universal path quantifier of Fair 8CTL ranges over fair computations only) This definition, however, is neither robust (Fair 8CTL induces a weaker preorder [ASB 94] ....

.... (the universal path quantifier of Fair 8CTL ranges over fair computations only) This definition, however, is neither robust (Fair 8CTL induces a weaker preorder [ASB 94] and Fair 8AFMC, as we show here, induces a stronger one) nor can it be checked efficiently (it is complete for PSPACE [KV96] Following [Hoj96] we call the Grumberg Long version of fair simulation 9 simulation, because it can be defined as simulation where each fair computation of I is related to some fair computation of S. In manual verification, by Lynch and others [LT87, Lyn96] usually a stronger notion of ....

[Article contains additional citation context not shown here]

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. In Proc. 8th CAV, Springer LNCS 1102, pp. 372--382, 1996.

....simulation. This measure considers the complexity in terms of the implementation, assuming the specification is fixed. Since the implementation is typically much larger than the specification, this measure is of particular interest. According to this measure, containment is easier than simulation [KV96] 3. The joint complexity of fair containmentand fair simulation. Whenwe consider fair transition systems [MP92] which enable the description of behaviors that satisfy both liveness and safety properties, containment and simulation are revised to consider only the fair computations of the ....

....that satisfy both liveness and safety properties, containment and simulation are revised to consider only the fair computations of the implementation and the specification. The resulting problems, of fair containment and fair simulation [BBLS92, ASB 94, GL94] are both PSPACE complete [KV96] 4. The implementation complexity of fair containment and fair simulation. Here, the advantage of the trace based approach reappears [KV96] We address the question about the power of concurrency in program verification by examining the four measures when applied to concurrent transition ....

[Article contains additional citation context not shown here]

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. In Proc. 8th CAV, LNCS 1102, pages 372--382. Rutgers, 1996.

....be performed in time polynomial in ffi (q; A) and ffi 0 (q 0 ; A) Since the number of checks for each H i is bounded by jQ Theta Q 0 j, the overall effort is polynomial in S and S 0 . Hardness in PTIME follows from the PTIME hardness of ordinary simulation on labeled transition systems [BGS92, KV98]. ut Recall that alternating simulation can be used on labeled transition systems to specify both directions of simulation. Since the complexity of the simulation problem S sys S 0 for labeled transition systems S and S 0 is hard for PTIME already for a fixed S 0 [KV98] it follows that ....

....systems [BGS92, KV98] ut Recall that alternating simulation can be used on labeled transition systems to specify both directions of simulation. Since the complexity of the simulation problem S sys S 0 for labeled transition systems S and S 0 is hard for PTIME already for a fixed S 0 [KV98], it follows that the alternating simulation problem is PTIME complete even when either S or S 0 is fixed. 4 Alternating Trace Containment We now study the refinement relation on ATS that corresponds to trace containment on labeled transition systems. Consider an ATS S = h Pi; Omega ; Q; q ....

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. Chicago J. Theoretical Computer Science, 1998(2).

No context found.

O. Kupferman and M.Y. Vardi. Verification of fair transition systems. In Computer Aided Verification (CAV'96), LNCS 1102, pages 372--382, 1996.

No context found.

Orna Kupferman, Moshe Y. Vardi. "Verification of Fair Transition Systems", CAV 1996.

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O. Kupferman and M.Y. Vardi. Verification of fair transition systems. In R. Alur and T.A. Henzinger, editors, CAV 96: Computer Aided Verification, Lecture Notes in Computer Science 1102, pages 372--381. Springer-Verlag, 1996.

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O. Kupferman and M. Vardi. Verification of fair transition systems. Chicago J. Theoretical Computer Science, 2, 1998.

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