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Probabilistic Acceptors for Languages over Infinite Words

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5404))

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

  1. 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)

    Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  3. Blondel, V., Canterini, V.: Undecidable problems for probabilistic finite automata. Theory of Computer Systems 36, 231–245 (2003)

    Article  MATH  Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. 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)

    Google Scholar 

  9. Dwork, C., Stockmeyer, L.: A time-complexity gap for two-way probabilistic finite state automata. SIAM Journal of Computing 19, 1011–1023 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  10. Freivalds, R.: Probabilistic two-way machines. In: Gruska, J., Chytil, M.P. (eds.) MFCS 1981. LNCS, vol. 118, pp. 33–45. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  11. Größer, M.: Reduction Methods for Probabilistic Model Checking. PhD thesis, Technical University Dresden, Faculty for Computer Science (2008)

    Google Scholar 

  12. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  13. 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)

    Google Scholar 

  14. Lovejoy, W.: A survey of algorithmic methods for partially observable Markov decision processes. Annals of Operations Research 28(1), 47–65 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  15. 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)

    Article  MathSciNet  MATH  Google Scholar 

  16. Monahan, G.: A survey of partially observable Markov decision processes: Theory, models, and algorithms. Management Science 28(1), 1–16 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  17. Paz, A.: Some aspects of probabilistic automata. Information and Control 9 (1966)

    Google Scholar 

  18. Papadimitriou, C., Tsitsiklis, J.: The comlexity of Markov decision processes. Mathematics of Operations Research 12(3) (1987)

    Google Scholar 

  19. Rabin, M.O.: Probabilistic automata. Information and Control 6(3), 230–245 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  20. 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)

    Google Scholar 

  21. Sondik, E.J.: The Optimal Control of Partially Observable Markov Processes. PhD thesis, Stanford University (1971)

    Google Scholar 

  22. 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)

    Google Scholar 

  23. Thomas, W.: Languages, automata, and logic. Handbook of formal languages 3, 389–455 (1997)

    Article  MathSciNet  Google Scholar 

  24. 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)

    Google Scholar 

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-95890-1

  • Online ISBN: 978-3-540-95891-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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