Strategy Construction for Parity Games with Imperfect Information

Dietmar Berwanger, Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger, and Sangram Raje

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 with 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.

Proceedings of the 19th International Conference on Concurrency Theory (CONCUR), Lecture Notes in Computer Science 5201, Springer, 2008, pp. 325-339.

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