Abstract
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. However, the exact complexity in the size of the pushdown system (for a fixed CTL formula) is an open question: it lies somewhere between Pspace and Exptime. To the best of our knowledge, the PMC problem for CTL * has not been investigated so far. In this paper, we show that this problem is 2Expspace-complete. Moreover, 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.
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References
Alur, R., Etessami, K., Madhusudan, P.: A temporal Logic of Nested Calls and Returns. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 467–481. Springer, Heidelberg (2004)
Bouajjani, A., Esparza, J., Maler, O.: Reachability Analysis of Pushdown Automata: Application to Model-Checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)
Caucal, D.: On infinite transition graphs having a decidable monadic theory. In: Meyer auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 194–205. Springer, Heidelberg (1996)
Clarke, E.M., Emerson, E.A.: Design and verification of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)
Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. Journal of the ACM 28(1), 114–133 (1981)
Emerson, E.A., Halpern, J.Y.: Sometimes and not never revisited: On branching versus linear time. Journal of the ACM 33(1), 151–178 (1986)
Esparza, J., Hansel, D., Rossmanith, P., Schwoon, S.: Efficient algorithms for model checking pushdown systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 232–247. Springer, Heidelberg (2000)
Emerson, E.A., Jutla, C.S.: Tree automata, μ-calculus and determinacy. In: FOCS 1991, pp. 368–377 (1991)
Esparza, J., Kucera, A., Schwoon, S.: Model checking LTL with regular valuations for pushdown systems. Inf. Comput. 186(2), 355–376 (2003)
Kupferman, O., Piterman, N., Vardi, M.Y.: Pushdown specifications. In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 262–277. Springer, Heidelberg (2002)
Kupferman, O., Thiagarajan, P.S., Madhusudan, P., Vardi, M.Y.: Open systems in reactive environments: Control and Synthesis. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 92–107. Springer, Heidelberg (2000)
Kupferman, O., Vardi, M.Y., Wolper, P.: An Automata-Theoretic Approach to Branching-Time Model Checking. Journal of the ACM 47(2), 312–360 (2000)
Muller, D.E., Shupp, P.E.: The theory of ends, pushdown automata, and second-order logic. Theoretical Computer Science 37, 51–75 (1985)
Muller, D.E., Shupp, P.E.: Alternating automata on infinite trees. Theoretical Computer Science 54, 267–276 (1987)
Piterman, N., Vardi, M.Y.: Global model-checking of infinite-state systems. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 387–400. Springer, Heidelberg (2004)
Sistla, A.P., Clarke, E.M.: The complexity of propositional linear temporal logics. Journal of the ACM 32(3), 733–749 (1985)
Vardi, M.Y.: A temporal fixpoint calculus. In: POPL 1988, pp. 250–259. ACM Press, New York (1988)
Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998)
Walukiewicz, I.: Pushdown processes: Games and Model Checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 62–74. Springer, Heidelberg (1996)
Walukiewicz, I.: Model checking CTL properties of pushdown systems. In: Kapoor, S., Prasad, S. (eds.) FST TCS 2000. LNCS, vol. 1974, pp. 127–138. Springer, Heidelberg (2000)
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Bozzelli, L. (2005). Complexity Results on Branching-Time Pushdown Model Checking. In: Emerson, E.A., Namjoshi, K.S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2006. Lecture Notes in Computer Science, vol 3855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11609773_5
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DOI: https://doi.org/10.1007/11609773_5
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