The Complexity of Model Checking for Boolean Formulas

Abstract. The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations-restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup.We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL + , and ECTL + .

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“…Proof. The first and third claim follow from Theorem 4.2 and the monotone formula value problem being NC 1 -complete [Sch10].…”

Section: Model Checking Extensions Of Ctlmentioning

confidence: 87%

“…Proof. If T ⊆ {A, E} then deciding CTL + -MC(T ) is equivalent to the problem of evaluating a propositional formula, which is known to be NC 1 -complete [Bus87,Sch10].…”

Section: Model Checking Extensions Of Ctlmentioning

confidence: 99%

Model Checking CTL is Almost Always Inherently Sequential

Beyersdorff

Meier

Thomas

et al. 2009

2009 16th International Symposium on Temporal Representation and Reasoning

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“…The main reason for this phenomenon is, that circuits can be regarded as a succinct representation of formulas. Partial results in this direction have been obtained in [Rei01,Sch10].…”

Section: Discussionmentioning

confidence: 99%

Applying CEGAR to the Petri Net State Equation

Wolf¹,

Wimmel²

2012

Logical Methods in Computer Science

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Abstract. We propose a reachability verification technique that combines the Petri net state equation (a linear algebraic overapproximation of the set of reachable states) with the concept of counterexample guided abstraction refinement. In essence, we replace the search through the set of reachable states by a search through the space of solutions of the state equation. We demonstrate the excellent performance of the technique on several real-world examples. The technique is particularly useful in those cases where the reachability query yields a negative result: While state space based techniques need to fully expand the state space in this case, our technique often terminates promptly. In addition, we can derive some diagnostic information in case of unreachability while state space methods can only provide witness paths in the case of reachability.

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“…Analogous to the fragments CTL pos (T ), CTL a.n. (T ), and CTL mon (T ), we define CTL + -MC(T ) is equivalent to the problem of evaluating a propositional formula, which is known to be NC 1 -complete [Bus87,Sch10]. If {X} T ⊆ {A, E, X}, then CTL + -MC(T ) can be solved using a labelling algorithm: Let K = (W, R, η) be a Kripke structure, and ϕ be a CTL + ({A, E, X})-formula.…”

Section: Model Checking Extensions Of Ctlmentioning

confidence: 99%