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Equivalence of Games with Probabilistic Uncertainty and Partial-Observation Games

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Automated Technology for Verification and Analysis (ATVA 2012)

Abstract

We introduce games with probabilistic uncertainty, a model for controller synthesis in which the controller observes the state through imprecise sensors that provide correct information about the current state with a fixed probability. That is, in each step, the sensors return an observed state, and given the observed state, there is a probability distribution (due to the estimation error) over the actual current state. The controller must base its decision on the observed state (rather than the actual current state, which it does not know). On the other hand, we assume that the environment can perfectly observe the current state. We show that controller synthesis for qualitative ω-regular objectives in our model can be reduced in polynomial time to standard partial-observation stochastic games, and vice-versa. As a consequence we establish the precise decidability frontier for the new class of games, and establish optimal complexity results for all the decidable problems.

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References

  1. 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)

    Chapter  Google Scholar 

  2. Bertrand, N., Genest, B., Gimbert, H.: Qualitative determinacy and decidability of stochastic games with signals. In: LICS, pp. 319–328. IEEE Computer Society (2009)

    Google Scholar 

  3. Berwanger, D., Doyen, L.: On the power of imperfect information. In: FSTTCS, Dagstuhl Seminar Proceedings 08004. IBFI (2008)

    Google Scholar 

  4. Billingsley, P.: Probability and Measure. Wiley-Interscience (1995)

    Google Scholar 

  5. Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Transactions of the AMS 138, 295–311 (1969)

    Article  MATH  Google Scholar 

  6. Chatterjee, K., Chmelik, M., Majumdar, R.: Equivalence of games with probabilistic uncertainty and partial-observation games. CoRR, abs/1202.4140 (2012)

    Google Scholar 

  7. Chatterjee, K., Doyen, L., Henzinger, T.A.: Qualitative Analysis of Partially-Observable Markov Decision Processes. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 258–269. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Algorithms for omega-regular games of incomplete information. LMCS 3 (2007)

    Google Scholar 

  9. Condon, A.: The complexity of stochastic games. I. & C. 96(2), 203–224 (1992)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. de Alfaro, L., Henzinger, T.A., Kupferman, O.: Concurrent reachability games. TCS 386(3), 188–217 (2007)

    Article  MATH  Google Scholar 

  12. de Alfaro, L., Majumdar, R.: Quantitative solution of omega-regular games. In: STOC 2001, pp. 675–683. ACM Press (2001)

    Google Scholar 

  13. Filar, J., Vrieze, K.: Competitive Markov Decision Processes. Springer (1997)

    Google Scholar 

  14. Kupferman, O., Vardi, M.Y.: μ-Calculus Synthesis. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 497–507. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  15. Rabin, M.O.: Automata on Infinite Objects and Church’s Problem. Conference Series in Mathematics, vol. 13. American Mathematical Society (1969)

    Google Scholar 

  16. Reif, J.H.: Universal games of incomplete information. In: STOC, pp. 288–308. ACM Press (1979)

    Google Scholar 

  17. Thomas, W.: Languages, automata, and logic. In: Handbook of Formal Languages. Beyond Words, vol. 3, ch. 7, pp. 389–455. Springer (1997)

    Google Scholar 

  18. Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state systems. In: FOCS 1985, pp. 327–338. IEEE Computer Society Press (1985)

    Google Scholar 

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Chatterjee, K., Chmelík, M., Majumdar, R. (2012). Equivalence of Games with Probabilistic Uncertainty and Partial-Observation Games. In: Chakraborty, S., Mukund, M. (eds) Automated Technology for Verification and Analysis. ATVA 2012. Lecture Notes in Computer Science, vol 7561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33386-6_30

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  • DOI: https://doi.org/10.1007/978-3-642-33386-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33385-9

  • Online ISBN: 978-3-642-33386-6

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