A. P. Sistla and E.M. Clarke. Complexity of propositional temporal logics. Journal of the ACM, 32(3):733--749, July 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....whether # is valid on all possible computation paths in G. This question is natural when a closed system is verified, by which we mean one whose future behavior only depends on its current state but not on any kind of environment. Model checking for LTL conditions is known to be PSPACE complete [SC85] (combined complexity) Although, if # and # are the only modalities allowed in the formula then model checking is NP complete [SC85] Other fragments of LTL with easy model checking problem (in NP or even in P) are identified in [DS98] Partially supported by Polish KBN grant 2 PO3A 01818. ....

....one whose future behavior only depends on its current state but not on any kind of environment. Model checking for LTL conditions is known to be PSPACE complete [SC85] combined complexity) Although, if # and # are the only modalities allowed in the formula then model checking is NP complete [SC85]. Other fragments of LTL with easy model checking problem (in NP or even in P) are identified in [DS98] Partially supported by Polish KBN grant 2 PO3A 01818. Partially supported by Polish KBN grant 8T11C 04319. In this paper we are interested in the second kind of decision problems in this ....

A. P. Sistla and E.M. Clarke, The complexity of propositional temporal logics, The Journal of ACM 32 (1985), no. 733, 733--749.

.... that the recent interest in counter machine models [4, 5, 7, 13, 6] is not motivated by investigations of their formal language properties but by their applications to model checking of infinite state systems, motivated by the recent successes of modelchecking techniques for finite state systems [2, 3, 21, 15, 22]. The main result in this paper would be useful in establishing a number of new decidability results concerning various verification problems for infinite state systems containing integer counters and parameterized constants. The rest of this paper is organized as follows. In Section 2, we ....

A. P. Sistla and E. M. Clarke. Complexity of propositional temporal logics. Journal of ACM, 32(3):733--749, 1983.

....augmenting the model with reversal bounded counters, discrete clocks, etc. In particular, we settle an open problem in [10] 1 Introduction Recently, there has been significant progress in automated verification techniques for finite state systems. One such technique, called model checking [5, 6, 22, 20, 23], explores the state space of a finite state system and checks that a desired temporal property is satisfied. In recent years, model checkers like SMV [20] and SPIN [16] have been successful in some industrial level applications. Successes in finite state modelchecking have inspired researchers to ....

A. P. Sistla and E. M. Clarke. Complexity of propositional temporal logics. Journal of ACM, 32(3):733--749, 1983.

....# LTLw is linear in the size of #. Thus, by Corollary 4.2.11 on page 53, we conclude: Corollary 6.2.8 Let # be a formula of LTLw (#) Deciding whether # is satisfiable can be done in exponential time and polynomial space with respect to the size of #. It was shown by Sistla and Clarke [SC82, SC85] that these bounds are optimal: Satisfiability of LTLw formulas is Pspace complete. The previous result was shown by a reduction of Turing machine. The authors also showed that satisfiability of LTL w formulas is Pspace complete where LTL w is the logic in which no until operator is ....

A. P. Sistla and E. M. Clarke. Complexity of propositional temporal logics. Journal of the ACM, 32:733--749, 1985.

....and the proof of soundness (and sometimes completeness) of this algorithm. The choice of the specification model is closely related to the properties one should express about programs; for parallel programs a good candidate could be some class of temporal logics formulae (LTL, CTL, CTL , [Sis85] since they enable to state safety, liveness and fairness properties. The program model should offer the parallel mechanisms that the real program will include (e.g. message passing and or shared variables and or semaphores . The common semantics of these models must at least include ....

A.P. Sistla, E.M. Clarke "Complexity of propositional temporal logic" JACM 32(3), 1985 pp 733-749 -l -

....in LTL: Namely, by checking whether T y is deterministic. Theorem 3 Deciding whether an ACTL formula y can be expressed in LTL is PSPACE complete. Proof: The lower bound follows by a reduction from ACTL satisfiability, which can be shown to be PSPACE complete analogously to LTL satisfiability ([21]) by using the tableau construction. Let p be a boolean variable that does not occur in y. It is easy to see that y is not satisfiability iff y#AFAG p is expressible in LTL. We describe a nondeterministic polynomial space algorithm for deciding whether T y is not deterministic. Assume that y is ....

A. P. Sistla and E. M. Clarke. The complexity of propositional temporal logic. In Proc. 14th ACM Symposium on Theory of Computing, pages 159--167, 1982.

....checking problem for CTL is solvable in deterministic linear time. The situation is different for CTL . Unfortunately, the method of assigning the subformulas of a tested formula to the states of the model cannot be applied. One has to use more powerful automata theoretic methods. Theorem 2. 15 [36] Model checking for CTL is PSPACE complete. 2 The main reason that CTL is not broadly applied is the high complexity of checking satisfiability and performing model checking. There are, however, many logics between CTL and CTL (which were not mentioned here) like CTL [11] ECTL and ECTL ....

A. P. Sistla, E. M. Clarke (1982): The Complexity of Propositional Temporal Logic. ACM Symp. on Theory of Computing.

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A. P. Sistla and E.M. Clarke. Complexity of propositional temporal logics. Journal of the ACM, 32(3):733--749, July 1986.

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A. P. Sistla and E.M. Clarke. Complexity of propositional temporal logics. Journal of the ACM, 32(3):733--749, July 1986.

....logic, but they did not analyze its complexity or show how to handle an interesting notion of fairness. Later Clarke, Emerson, and Sistla [27] devised an improved algorithm that was linear in the product of the length of the formula and in the size of the global state graph. Clarke and Sistla [74] also analyzed the model checking problem for a variety of other temporal logics and showed, in particular, that for linear temporal logic the problem was PSPACE complete. A number of papers demonstrated how the temporal logic model checking procedure could be used for verifying network protocols ....

....f . By definition M; s j= A f iff M; s j= E:f . Consequently, it is sufficient to be able to check the truth of formulas of the form E f where f is a restricted path formula. If the Kripke structure is represented explicitly as a state transition graph, this problem is known to be PSPACE complete [74] in general. Lichtenstein and Pnueli [56] developed an algorithm for the problem that was linear in the size of the model M and exponential in the length of the formula f . Although their algorithm was linear in the size of the model, it was still impractical for large examples because of the ....

A. P. Sistla and E.M. Clarke. Complexity of propositional temporal logics. Journal of the ACM, 32(3):733--749, July 1986.

....has been relatively little research, however, on efficient model checking algorithms for linear temporal logic (LTL) and practical verification tools are virtually non existant. In fact, the question of whether it is possible to develop such tools has been argued for many years. Sistla and Clarke [17] showed in 1982 that the model checking problem for LTL was, in general, PSPACE complete. Later, Pnueli and Lichtenstein [14] gave an LTL model checking algorithm that was exponential in the size of the formula, but linear in the size of the model. Based on this result, they argued that the high ....

....f . By definition M; s j= A f iff M; s j= E:f . Consequently, it is sufficient to be able to check the truth of formulas of the form E f where f is a restricted path formula. If the Kripke structure is represented explicitly as a state transition graph, this problem is known to be PSPACE complete [17] in general. Lichtenstein and Pnueli [14] developed an algorithm for the problem that was linear in the size of the model M and exponential in the length of the formula f . Although their algorithm was linear in the size of the model, it was still impractical for large examples because of the ....

A. P. Sistla and E.M. Clarke. Complexity of propositional temporal logics. Journal of the ACM, 32(3):733--749, July 1986.

....liveness properties (see [OL82] Temporal Logic has been proposed in [Pn77] also see [MP92] as an appropriate formalism in the specification and verification of concurrent programs. Since then, many different versions of temporal logics have been used in the verification of concurrent programs [MP89, LPZ85, SC85, CES86]. Due to this wide interest, it becomes important to present a syntactic classification of formulas in temporal logic that specify safety and liveness properties. Knowing whether a formula specifies a safety or a liveness property, helps us in choosing the right proof method for verifying that a ....

....(c) of lemma 5.4. Such an algorithm will take time exponential in the length of f . This algorithm also uses exponential space. Instead of building cross tab(f ) the algorithm can guess a path through cross tab(f ) and using an approach similar to the satisfiability algorithm for PTL given in [SC85] it can check if f is a safety property or not. The resulting algorithm uses space which is only polynomial in the length of f. The set of safety formulae is PSPACE hard due to the following reduction from the set of valid formulae in PTL. Any formula f is valid iff f 3Q is a safety formula where ....

A.P.Sistla,E.M.Clarke, Complexity of Propositional Temporal Logics, Journal of the Association for Computing Machinery, Vol.32,No.3, July 1985.

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A. P. Sistla, E. M. Clarke (1982): The Complexity of Propositional Temporal Logic. ACM Symp. on Theory of Computing.

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A. P. Sistla and E. M. Clarke, Complexity of propositional temporal logics. J. ACM 32 733-749 (1986).

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A.P. Sistla and E. Clarke. The complexity of propositional temporal logic. In 14th ACM Symposium on Theory of Computing, pages 159--167, 1982.

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A.P. Sistla and E. Clarke. The complexity of propositional temporal logic. In 14th ACM Symposium on Theory of Computing, pages 159--167, 1982.

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