Enriched μ–Calculus Pushdown Module Checking

CONCUR 2007 – Concurrency Theory

Vardi

Self Cite

The model checking problem for finite-state open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinite-state systems (pushdown module checking). In this paper, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system's control states and pushdown store content. We study the complexity of this problem with respect to the branching-time temporal logics CTL, CTL * and the propositional µ-calculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information. 2 Work supported in part by NSF grants CCR-9988322, CCR-0124077, CCR-0311326, CCF-0613889, and ANI-0216467, by BSF grant 9800096, and by gift from Intel. Preprint submitted to Information and ComputationNovember 16, 2012 We also show that undecidability relies on hiding information about the pushdown store. Indeed, we prove that with imperfect information about the control states, but a visible pushdown store, the problem is decidable and its complexity is 2Exptime-complete for CTL and the propositional µ-calculus, and 3Exptime-complete for CTL * .

Section: Theoremmentioning

confidence: 99%

“…Accordingly, there are many different possible environments to consider. It is shown in [19,31,34] that for formulas in branching time temporal logics, module checking open finitestate systems is exponentially harder than model checking closed finite-state systems.…”

Section: Introductionmentioning

confidence: 99%

Pushdown Module Checking with Imperfect Information

CONCUR 2007 – Concurrency Theory

Vardi

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“…The lower bound follows from the known bound for pushdown module checking with perfect information (see [FMP07] for propositional and graded µ-calculus, and [BMP05] for CTL * ). For the upper bound, by Theorem 2, it is enough to check that A S,¬ϕ is empty.…”

Section: Theorem 2 Consider An Opd S and A Propositional Or A Gradementioning

confidence: 99%

“…The finite-state system module checking problem, for CTL and CTL * formulas, has been investigated in [KV96,KVW01]; while for propositional µ-calculus formulas it has been investigated in [FM07]. In all these cases, it has been shown that module checking is exponentially harder than model checking.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the module checking idea has been extended to pushdown systems [BMP05], and it has been shown that CTL and µ-calculus pushdown module checking is 2Exptime-complete, while CTL * pushdown module checking is 3Exptime-complete [BMP05,FMP07]. Another extension of the module checking idea has been the investigation of environments with imperfect information.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

μ-calculus Pushdown Module Checking with Imperfect State Information

Legay

Fifth Ifip International Conference on Theoretical Computer Science – TCS 2008

et al.

Self Cite

Abstract. The model checking problem for open systems (module checking) has recently been the subject of extensive study. The problem was first studied by Kupferman, Vardi, and Wolper for finite-state systems and properties expressed in the branching time logics CTL and CTL * . Further study continued mainly in two directions: considering systems equipped with a pushdown store, and considering environments with imperfect information about the system. A recent paper combined the two directions and considered the CTL pushdown module checking problem in the imperfect information setting, i.e., in the case where the environment has only a partial view of the system control states and pushdown store content. It has been shown that this problem is undecidable when the environment has imperfect information about the pushdown store content, while it is decidable and 2Exptime-complete when the imperfect information only concerns control states. It was left open whether the latter remains decidable also for more expressive logics. In this paper, we answer this question in the affirmative, showing that the pushdown module checking problem with imperfect information about the control states is decidable and 2Exptime-complete for the propositional and the graded µ-calculus, and 3Exptime-complete for CTL * .

Pushdown module checking with imperfect information

Legay

Information and Computation

et al. 2013

Self Cite

The model checking problem for finite-state open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinite-state systems (pushdown module checking). In this paper, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the systems control states and pushdown store content. We study the complexity of this problem with respect to the branchingtime temporal logics CTL, CTL. and the propositional μ-calculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information. We also show that undecidability relies on hiding information about the pushdown store. Indeed, we prove that with imperfect information about the control states, but a visible pushdown store, the problem is decidable and its complexity is 2Exptime-complete for CTL and the propositional μ-calculus, and 3Exptime-complete for CTL. © 2012 Elsevier Inc. All rights reserved