Abstract
Probabilistic ω-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word requires that the probability for the accepting runs is positive. In this paper, we provide a summary of the fundamental properties of probabilistic ω-automata concerning expressiveness, efficiency, compositionality and decision problems.
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References
Ambainis, A., Freivalds, R.: 1-way quantum finite automata: strengths, weaknesses and generalizations. In: Proc. of the 39th Symposium on Foundations of Computer Science (FOCS 1998). IEEE Computer Society Press, Los Alamitos (1998)
Baier, C., Bertrand, N., Grösser, M.: On decision problems for probabilistic Büchi automata. In: Amadio, R. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 287–301. Springer, Heidelberg (2008)
Blondel, V., Canterini, V.: Undecidable problems for probabilistic finite automata. Theory of Computer Systems 36, 231–245 (2003)
Baier, C., Grösser, M.: Recognizing ω-regular languages with probabilistic automata. In: Proc. of the 20th IEEE Symposium on Logic in Computer Science (LICS 2005), pp. 137–146. IEEE Computer Society Press, Los Alamitos (2005)
Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Algorithms for ω-regular games with imperfect information. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 287–302. Springer, Heidelberg (2006)
Chadha, R., Sistla, A.P., Viswanathan, M.: On the expressiveness and complexity of randomization in finite state monitors. In: Proc. of the 23rd IEEE Symposium on Logic in Computer Science (LICS 2008), pp. 18–29. IEEE Computer Society Press, Los Alamitos (2008)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)
de Alfaro, L.: The verification of probabilistic systems under memoryless partial-information policies is hard. In: Proc. of the 2nd International Workshop on Probabilistic Methods in Verification (ProbMiV 1999), vol. 9, pp. 19–32. Birmingham University, Research Report CSR-99-9 (1999)
Dwork, C., Stockmeyer, L.: A time-complexity gap for two-way probabilistic finite state automata. SIAM Journal of Computing 19, 1011–1023 (1990)
Freivalds, R.: Probabilistic two-way machines. In: Gruska, J., Chytil, M.P. (eds.) MFCS 1981. LNCS, vol. 118, pp. 33–45. Springer, Heidelberg (1981)
Größer, M.: Reduction Methods for Probabilistic Model Checking. PhD thesis, Technical University Dresden, Faculty for Computer Science (2008)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)
Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Proc. of the 38th Symposium on Foundations of Computer Science (FOCS 1997), pp. 66–75. IEEE Computer Society Press, Los Alamitos (1997)
Lovejoy, W.: A survey of algorithmic methods for partially observable Markov decision processes. Annals of Operations Research 28(1), 47–65 (1991)
Madani, O., Hanks, S., Condon, A.: On the undecidability of probabilistic planning and related stochastic optimization problems. Artificial Intelligence 147(1-2), 5–34 (2003)
Monahan, G.: A survey of partially observable Markov decision processes: Theory, models, and algorithms. Management Science 28(1), 1–16 (1982)
Paz, A.: Some aspects of probabilistic automata. Information and Control 9 (1966)
Papadimitriou, C., Tsitsiklis, J.: The comlexity of Markov decision processes. Mathematics of Operations Research 12(3) (1987)
Rabin, M.O.: Probabilistic automata. Information and Control 6(3), 230–245 (1963)
Safra, S.: On the complexity of ω-automata. In: Proc. of the 29th Symposium on Foundations of Computer Science (FOCS 1988), pp. 319–327. IEEE Computer Society Press, Los Alamitos (1988)
Sondik, E.J.: The Optimal Control of Partially Observable Markov Processes. PhD thesis, Stanford University (1971)
Safra, S., Vardi, M.Y.: On ω-automata and temporal logic. In: Proc. of the 21st ACM Symposium on Theory of Computing (STOC 1989), pp. 127–137. ACM Press, New York (1989)
Thomas, W.: Languages, automata, and logic. Handbook of formal languages 3, 389–455 (1997)
Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proc. of the 1st IEEE Symposium on Logic in Computer Science (LICS 1986), pp. 332–345. IEEE Computer Society Press, Los Alamitos (1986)
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Baier, C., Bertrand, N., Größer, M. (2009). Probabilistic Acceptors for Languages over Infinite Words. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science. SOFSEM 2009. Lecture Notes in Computer Science, vol 5404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95891-8_3
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DOI: https://doi.org/10.1007/978-3-540-95891-8_3
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