Probabilistic Acceptors for Languages over Infinite Words

  • Christel Baier
  • Nathalie Bertrand
  • Marcus Größer
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AF98]
    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. [BBG08]
    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)CrossRefGoogle Scholar
  3. [BC03]
    Blondel, V., Canterini, V.: Undecidable problems for probabilistic finite automata. Theory of Computer Systems 36, 231–245 (2003)CrossRefMATHGoogle Scholar
  4. [BG05]
    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. [CDHR06]
    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)CrossRefGoogle Scholar
  6. [CSV08]
    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)CrossRefGoogle Scholar
  7. [CY95]
    Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)MathSciNetCrossRefMATHGoogle Scholar
  8. [dA99]
    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. [DS90]
    Dwork, C., Stockmeyer, L.: A time-complexity gap for two-way probabilistic finite state automata. SIAM Journal of Computing 19, 1011–1023 (1990)MathSciNetCrossRefMATHGoogle Scholar
  10. [Fre81]
    Freivalds, R.: Probabilistic two-way machines. In: Gruska, J., Chytil, M.P. (eds.) MFCS 1981. LNCS, vol. 118, pp. 33–45. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  11. [Grö08]
    Größer, M.: Reduction Methods for Probabilistic Model Checking. PhD thesis, Technical University Dresden, Faculty for Computer Science (2008)Google Scholar
  12. [GTW02]
    Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)MATHGoogle Scholar
  13. [KW97]
    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. [Lov91]
    Lovejoy, W.: A survey of algorithmic methods for partially observable Markov decision processes. Annals of Operations Research 28(1), 47–65 (1991)MathSciNetCrossRefMATHGoogle Scholar
  15. [MHC03]
    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)MathSciNetCrossRefMATHGoogle Scholar
  16. [Mon82]
    Monahan, G.: A survey of partially observable Markov decision processes: Theory, models, and algorithms. Management Science 28(1), 1–16 (1982)MathSciNetCrossRefMATHGoogle Scholar
  17. [Paz66]
    Paz, A.: Some aspects of probabilistic automata. Information and Control 9 (1966)Google Scholar
  18. [PT87]
    Papadimitriou, C., Tsitsiklis, J.: The comlexity of Markov decision processes. Mathematics of Operations Research 12(3) (1987)Google Scholar
  19. [Rab63]
    Rabin, M.O.: Probabilistic automata. Information and Control 6(3), 230–245 (1963)MathSciNetCrossRefMATHGoogle Scholar
  20. [Saf88]
    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. [Son71]
    Sondik, E.J.: The Optimal Control of Partially Observable Markov Processes. PhD thesis, Stanford University (1971)Google Scholar
  22. [SV89]
    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. [Tho97]
    Thomas, W.: Languages, automata, and logic. Handbook of formal languages 3, 389–455 (1997)MathSciNetCrossRefGoogle Scholar
  24. [VW86]
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christel Baier
    • 1
  • Nathalie Bertrand
    • 2
  • Marcus Größer
    • 1
  1. 1.Faculty Computer ScienceTechnical University DresdenGermany
  2. 2.INRIA Rennes Bretagne AtlantiqueFrance

Personalised recommendations