Abstract
We consider qualitative and quantitative model-checking problems for probabilistic pushdown automata (pPDA) and various temporal logics. We prove that the qualitative and quantitative model-checking problem for ω-regular properties and pPDA is in 2-EXPSPACE and 3-EXPTIME, respectively. We also prove that model-checking the qualitative fragment of the logic PECTL* for pPDA is in 2-EXPSPACE, and model-checking the qualitative fragment of PCTL for pPDA is in 2-EXPSPACE. Furthermore, model-checking the qualitative fragment of PCTL is shown to be EXPTIME-hard even for stateless pPDA. Finally, we show that PCTL model-checking is undecidable for pPDA, and PCTL + model-checking is undecidable even for stateless pPDA.
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References
Abdulla, P.A., Baier, C., Iyer, S.P., Jonsson, B.: Reasoning about probabilistic channel systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 320–330. Springer, Heidelberg (2000)
Abdulla, P.A., Rabinovich, A.: Verification of probabilistic systems with faulty communication. In: Gordon, A.D. (ed.) FOSSACS 2003. LNCS, vol. 2620, pp. 39–53. Springer, Heidelberg (2003)
Alur, R., Etessami, K., Yannakakis, M.: Analysis of recursive state machines. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 207–220. Springer, Heidelberg (2001)
Aziz, A., Singhal, V., Balarin, F., Brayton, R., Sangiovanni-Vincentelli, A.: It usually works: The temporal logic of stochastic systems. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 155–165. Springer, Heidelberg (1995)
Baier, C., Engelen, B.: Establishing qualitative properties for probabilistic lossy channel systems: an algorithmic approach. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 34–52. Springer, Heidelberg (1999)
Bertrand, N., Schnoebelen, P.: Model checking lossy channel systems is probably decidable. In: Gordon, A.D. (ed.) FOSSACS 2003. LNCS, vol. 2620, pp. 120–135. Springer, Heidelberg (2003)
Brázdil, T., Kučera, A., Stražovský, O.: Deciding probabilistic bisimilarity over infinite-state probabilistic systems. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 193–208. Springer, Heidelberg (2004)
Brázdil, T., Kučera, A., Stražovský, O.: On the decidability of temporal properties of probabilistic pushdown automata. Technical report FIMU-RS-2005-01, Faculty of Informatics, Masaryk University (2005)
Canny, J.: Some algebraic and geometric computations in PSPACE. In: Proceedings of STOC 1988, pp. 460–467. ACM Press, New York (1988)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. JACM 42(4), 857–907 (1995)
Couvreur, J.M., Saheb, N., Sutre, G.: An optimal automata approach to LTL model checking of probabilistic systems. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 361–375. Springer, Heidelberg (2003)
Esparza, J., Knoop, J.: An automata-theoretic approach to interprocedural data-flow analysis. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 14–30. Springer, Heidelberg (1999)
Esparza, J., Kučera, A., Mayr, R.: Model-checking probabilistic pushdown automata. In: Proceedings of LICS 2004, pp. 12–21. IEEE, Los Alamitos (2004)
Esparza, J., Kučera, A., Schwoon, S.: Model-checking LTL with regular valuations for pushdown systems. I&C 186(2), 355–376 (2003)
Etessami, K., Yannakakis, M.: Algorithmic verification of recursive probabilistic systems. Technical Report, School of Informatics, U. of Edinburgh (2005)
Etessami, K., Yannakakis, M.: Recursive Markov chains, stochastic grammars, and monotone systems of non-linear equations. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 340–352. Springer, Heidelberg (2005)
Grigoriev, D.: Complexity of deciding Tarski algebra. Journal of Symbolic Computation 5(1-2), 65–108 (1988)
Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 512–535 (1994)
Hart, S., Sharir, M.: Probabilistic temporal logic for finite and bounded models. In: Proceedings of POPL 1984, pp. 1–13. ACM Press, New York (1984)
Huth, M., Kwiatkowska, M.Z.: Quantitative analysis and model checking. In: Proceedings of LICS 1997, pp. 111–122. IEEE, Los Alamitos (1997)
Iyer, S.P., Narasimha, M.: Probabilistic lossy channel systems. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214, pp. 667–681. Springer, Heidelberg (1997)
Kwiatkowska, M.Z.: Model checking for probability and time: from theory to practice. In: Proceedings of LICS 2003, pp. 351–360. IEEE, Los Alamitos (2003)
Lehman, D., Shelah, S.: Reasoning with time and chance. I&C 53, 165–198 (1982)
Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)
Rabinovich, A.: Quantitative analysis of probabilistic lossy channel systems. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1008–1021. Springer, Heidelberg (2003)
Vardi, M.: Automatic verification of probabilistic concurrent finite-state programs. In: Proceedings of FOCS 1985, pp. 327–338. IEEE, Los Alamitos (1985)
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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Brázdil, T., Kučera, A., Stražovský, O. (2005). On the Decidability of Temporal Properties of Probabilistic Pushdown Automata. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_12
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DOI: https://doi.org/10.1007/978-3-540-31856-9_12
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