Abstract
We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor state is chosen accordingly to some fixed probability distribution depending on the previous state and on the pair of actions chosen by the players. Imperfect information is modeled as follows: both players have an equivalence relation over states and, instead of observing the exact state, they only know to which equivalence class it belongs. Therefore, if two partial plays are indistinguishable by some player, he should behave the same in both of them. We consider reachability (does the play eventually visit a final state?) and Büchi objective (does the play visit infinitely often a final state?).
Our main contribution is to prove that the following problem is complete for 2-ExpTime: decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her oponent. We also characterise those strategies needed by the first player to almost-surely win.
Supported by the anr project jade and by the esf project gasics.
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References
de Alfaro, L., Henzinger, T.A.: Concurrent omega-regular games. In: Proceedings of LICS 2000, pp. 141–154 (2000)
de Alfaro, L., Henzinger, T.A., Kupferman, O.: Concurrent reachability games. Theoretical Computer Science 386(3), 188–217 (2007)
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)
Bertrand, N., Genest, B., Gimbert, H.: Qualitative Determinacy and Decidability of Stochastic Games with Signals. In: Proceedings of LICS 2009 (to appear, 2009)
Berwanger, D., Chatterjee, K., De Wulf, M., Doyen, L., Henzinger, T.A.: Alpaga: A tool for solving parity games with imperfect information. In: TACAS 2009. LNCS, vol. 5505, pp. 58–61. Springer, Heidelberg (2009)
Berwanger, D., Chatterjee, K., Doyen, L., Henzinger, T.A., Raje, S.: Strategy construction for parity games with imperfect information. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 325–339. Springer, Heidelberg (2008)
Chatterjee, K.: Stochastic ω-Regular Games. PhD thesis, University of California (2007)
Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Algorithms for omega-regular games with imperfect information. Logical Methods in Computer Science 3(3) (2007)
Chatterjee, K., Henzinger, T.A.: Semiperfect-information games. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 1–18. Springer, Heidelberg (2005)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)
Gurevich, Y., Harrington, L.: Trees, automata, and games. In: Proceedings of STOC 1982, pp. 60–65 (1982)
Horn, F.: Private communication (February 2009)
Paz, A.: Introduction to probabilistic automata. Academic Press, New York (1971)
Ramadge, P.J., Wonham, W.M.: Supervisory Control of a Class of Discrete Event Processes. SIAM Journal on Control and Optimization 25, 206 (1987)
Reif, J.H.: The complexity of two-player games of incomplete information. Journal of Computer and System Sciences 29(2), 274–301 (1984)
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Gripon, V., Serre, O. (2009). Qualitative Concurrent Stochastic Games with Imperfect Information. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_17
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DOI: https://doi.org/10.1007/978-3-642-02930-1_17
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