Abstract
We consider imperfect-information parity games in which strategies rely on observations that provide imperfect information about the history of a play. To solve such games, i.e. to determine the winning regions of players and corresponding winning strategies, one can use the subset construction to build an equivalent perfect-information game. Recently, an algorithm that avoids the inefficient subset construction has been proposed. The algorithm performs a fixed-point computation in a lattice of antichains, thus maintaining a succinct representation of state sets. However, this representation does not allow to recover winning strategies.
In this paper, we build on the antichain approach to develop an algorithm for constructing the winning strategies in parity games of imperfect information. We have implemented this algorithm as a prototype. To our knowledge, this is the first implementation of a procedure for solving imperfect-information parity games on graphs.
This research was supported in part by the NSF grants CCR-0132780, CNS-0720884, and CCR-0225610, by the Swiss National Science Foundation, by the European COMBEST project, and by the Deutsche Forschungsgemeinschaft (DFG).
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References
Berwanger, D., Chatterjee, K., Doyen, L., Henzinger, T.A., Raje, S.: Strategy construction for parity games with imperfect information. Technical Report MTC-REPORT-2008-005, EPFL (2008), http://infoscience.epfl.ch/record/125011
Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Algorithms for omega-regular games of incomplete information. Logical Methods in Computer Science 3(3:4) (2007)
De Wulf, M., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Antichains: A new algorithm for checking universality of finite automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 17–30. Springer, Heidelberg (2006)
De Wulf, M., Doyen, L., Maquet, N., Raskin, J.-F.: Antichains: Alternative algorithms for LTL satisfiability and model-checking. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 63–77. Springer, Heidelberg (2008)
Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy. In: Proc. of FoCS 1991, pp. 368–377. IEEE, Los Alamitos (1991)
Fudenberg, D., Tirole, J.: Game Theory. MIT Press, Cambridge (1991)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)
Henzinger, T.A., Jhala, R., Majumdar, R.: Counterexample-guided control. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 886–902. Springer, Heidelberg (2003)
McNaughton, R.: Infinite games played on finite graphs. Annals of Pure and Applied Logic 65(2), 149–184 (1993)
Reif, J.: The complexity of two-player games of incomplete information. Journal of Computer and System Sciences 29, 274–301 (1984)
Thomas, W.: On the synthesis of strategies in infinite games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995)
Thomas, W.: Languages, automata, and logic. Handbook of Formal Languages 3, 389–455 (1997)
Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoretical Computer Science 200, 135–183 (1998)
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Berwanger, D., Chatterjee, K., Doyen, L., Henzinger, T.A., Raje, S. (2008). Strategy Construction for Parity Games with Imperfect Information. In: van Breugel, F., Chechik, M. (eds) CONCUR 2008 - Concurrency Theory. CONCUR 2008. Lecture Notes in Computer Science, vol 5201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85361-9_27
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DOI: https://doi.org/10.1007/978-3-540-85361-9_27
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