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Complexity results on branching-time pushdown model checking

Complexity results on branching-time pushdown model checking,10.1016/j.tcs.2007.03.049,Theoretical Computer Science,Laura Bozzelli

Complexity results on branching-time pushdown model checking   (Citations: 3)
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The model checking problem of pushdown systems (PMC problem, for short) against standard branching temporal logics has been intensively studied in the literature. In particular, for the modal μ-calculus, the most powerful branching temporal logic used for verification, the problem is known to be Exptime-complete (even for a fixed formula). The problem remains Exptime-complete also for the logic CTL, which corresponds to a fragment of the alternation-free modal μ-calculus. For the logic CTL∗, the problem is known to be in 2Exptime. In this paper, we show that the complexity of the PMC problem for CTL∗ is in fact 2Exptime-complete. Moreover, we give a new optimal algorithm to solve this problem based on automata theoretic techniques. Finally, we prove that the program complexity of the PMC problem against CTL (i.e., the complexity of the problem in terms of the size of the system) is Exptime-complete.
Journal: Theoretical Computer Science - TCS , vol. 379, no. 1-2, pp. 286-297, 2007
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    • ...Several model-checking algorithms have been proposed for both lineartime logics [1,13,9,14,17], and branching-time logics [1,2,6,24,18,19,14,17]...
    • ...However, these algorithms either allow only to decide whether a given configuration satisfies the formula i.e., they cannot compute all the set of PDS configurations where the formula holds [5,6,24,18], or have a high complexity [19,2,1,12,11,14,17]...
    • ...Our procedure is more e cient than the existing model-checking algorithms for -calculus and CTL* that are able to compute the set of configurations where a given property holds [19,2,1,12,11,14,17]...
    • ...[2] considers the emptiness problem in Alternating Parity Pushdown Automata...
    • ...Model checking CTL* for PDS is 2EXPTIME-complete (in the size of the formula) [2]...
    • ...Algorithms for model-checking CTL* specifications for PDSs have been proposed in [14,12,11,2]...

    Fu Songet al. Efficient CTL Model-Checking for Pushdown Systems

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