Abstract
A stochastic graph game is played by two players on a game graph with probabilistic transitions. We consider stochastic graph games with ω-regular winning conditions specified as Rabin or Streett objectives. These games are NP-complete and coNP-complete, respectively. The value of the game for a player at a state s given an objective Φ is the maximal probability with which the player can guarantee the satisfaction of Φ from s. We present a strategy-improvement algorithm to compute values in stochastic Rabin games, where an improvement step involves solving Markov decision processes (MDPs) and nonstochastic Rabin games. The algorithm also computes values for stochastic Streett games but does not directly yield an optimal strategy for Streett objectives. We then show how to obtain an optimal strategy for Streett objectives by solving certain nonstochastic Streett games.
This research was supported in part by the NSF grants CCR-0225610 and CCR-0234690, and by the SNSF under the Indo-Swiss Joint Research Programme.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bjorklund, H., Sandberg, S., Vorobyov, S.: A discrete subexponential algorithms for parity games. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 663–674. Springer, Heidelberg (2003)
Chatterjee, K., de Alfaro, L., Henzinger, T.A.: Trading memory for randomness. In: QEST, pp. 206–217. IEEE Computer Society, Los Alamitos (2004)
Chatterjee, K., de Alfaro, L., Henzinger, T.A.: The Complexity of Stochastic Rabin and Streett Games. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 878–890. Springer, Heidelberg (2005)
Chatterjee, K., Henzinger, T.A.: Strategy Improvement and Randomized Subexponential Algorithms for Stochastic Parity Games. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 512–523. Springer, Heidelberg (2006)
Chatterjee, K., Jurdziński, M., Henzinger, T.A.: Simple Stochastic Parity Games. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 100–113. Springer, Heidelberg (2003)
Condon, A.: The complexity of stochastic games. Information and Computation 96, 203–224 (1992)
Condon, A.: On algorithms for simple stochastic games. In: Advances in Computational Complexity Theory. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 13, pp. 51–73. AMS (1993)
de Alfaro, L.: Formal Verification of Probabilistic Systems. PhD thesis, Stanford University (1997)
de Alfaro, L., Henzinger, T.A.: Concurrent ω-regular games. In: LICS, pp. 141–154. IEEE Computer Society, Los Alamitos (2000)
Emerson, E.A., Jutla, C.: The complexity of tree automata and logics of programs. In: FOCS, pp. 328–337. IEEE Computer Society, Los Alamitos (1988)
Hoffman, A., Karp, R.: On nonterminating stochastic games. Management Science 12, 359–370 (1966)
Kupferman, O., Vardi, M.Y.: Weak alternating automata and tree-automata emptiness. In: STOC, pp. 224–233. ACM Press, New York (1998)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, Heidelberg (1992)
Piterman, N., Pnueli, A.: Faster solutions of Rabin and Streett games. In: LICS, IEEE Computer Society, Los Alamitos (to appear, 2006)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL, pp. 179–190. ACM, New York (1989)
Ramadge, P.J., Wonham, W.M.: Supervisory control of a class of discrete-event processes. SIAM J. Control and Optimization 25, 206–230 (1987)
Thomas, W.: Languages, automata, and logic. In: Beyond Words. Handbook of Formal Languages, vol. 3, pp. 389–455. Springer, Heidelberg (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chatterjee, K., Henzinger, T.A. (2006). Strategy Improvement for Stochastic Rabin and Streett Games. In: Baier, C., Hermanns, H. (eds) CONCUR 2006 – Concurrency Theory. CONCUR 2006. Lecture Notes in Computer Science, vol 4137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11817949_25
Download citation
DOI: https://doi.org/10.1007/11817949_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37376-6
Online ISBN: 978-3-540-37377-3
eBook Packages: Computer ScienceComputer Science (R0)