Abstract
Probabilistic automata are finite-state automata where the transitions are chosen according to fixed probability distributions. We consider a semantics where on an input word the automaton produces a sequence of probability distributions over states. An infinite word is accepted if the produced sequence is synchronizing, i.e. the sequence of the highest probability in the distributions tends to 1. We show that this semantics generalizes the classical notion of synchronizing words for deterministic automata. We consider the emptiness problem, which asks whether some word is accepted by a given probabilistic automaton, and the universality problem, which asks whether all words are accepted. We provide reductions to establish the PSPACE-completeness of the two problems.
This work has been partly supported by the MoVES project (P6/39) which is part of the IAP-Phase VI Interuniversity Attraction Poles Programme funded by the Belgian State, Belgian Science Policy.
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References
Baier, C., Bertrand, N., Größer, M.: On decision problems for probabilistic büchi automata. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 287–301. Springer, Heidelberg (2008)
Baier, C., Größer, M.: Recognizing omega-regular languages with probabilistic automata. In: Proc. of LICS: Logic in Comp. Science, pp. 137–146. IEEE, Los Alamitos (2005)
Benenson, Y., Adar, R., Paz-Elizur, T., Livneh, Z., Shapiro, E.: DNA molecule provides a computing machine with both data and fuel. Proc. National Acad. Sci. 100, 2191–2196 (2003)
Chadha, R., Sistla, A.P., Viswanathan, M.: On the expressiveness and complexity of randomization in finite state monitors. In: Proc. of LICS: Logic in Computer Science, pp. 18–29. IEEE Comp. Soc., Los Alamitos (2008)
Doyen, L., Massart, T., Shirmohammadi, M.: Synchronizing objectives for Markov decision processes. In: Proc. of iWIGP, pp. 61–75 (2011)
Doyen, L., Massart, T., Shirmohammadi, M.: Infinite synchronizing words for probabilistic automata. Tech. Rep, 138, Université Libre de Bruxelles (ULB), Belgium (June 2011)
Kfoury, D.J.: Synchronizing sequences for probabilistic automata. Studies in Applied Mathematics 29, 101–103 (1970)
Korthikanti, V.A., Viswanathan, M., Kwon, Y., Agha, G.: Reasoning about mdps as transformers of probability distributions. In: Proc. of QEST: Quantitative Evaluation of Systems, pp. 199–208. IEEE Computer Society, Los Alamitos (2009)
Kwon, Y., Agha, G.: Linear inequality ltl (iltl): A model checker for discrete time Markov chains. In: ICFEM, pp. 194–208 (2004)
Paz, A.: Introduction to Probabilistic Automata. Academic Press, New York (1971)
Rabin, M.O.: Probabilistic automata. Information and Control 6(3), 230–245 (1963)
Sistla, A.P., Vardi, M.Y., Wolper, P.: The complementation problem for Büchi automata with applications to temporal logic. Theor. Comput. Sci. 49, 217–237 (1987)
Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: Proceedings of the 5th Annual Symposium on Theory of Computing, pp. 1–9. ACM Press, New York (1973)
Tracol, M., Baier, C., Größer, M.: Recurrence and transience for probabilistic automata. In: Proc. of FSTTCS: Foundations of Software Technology and Theoretical Computer Science. LIPIcs, vol. 4, pp. 395–406. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2009)
Volkov, M.V.: Synchronizing automata and the Černý conjecture. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 11–27. Springer, Heidelberg (2008)
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Doyen, L., Massart, T., Shirmohammadi, M. (2011). Infinite Synchronizing Words for Probabilistic Automata. In: Murlak, F., Sankowski, P. (eds) Mathematical Foundations of Computer Science 2011. MFCS 2011. Lecture Notes in Computer Science, vol 6907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22993-0_27
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