Strategy Construction for Parity Games with Imperfect Information

  • Authors:

  • Dietmar Berwanger;Krishnendu Chatterjee;Laurent Doyen;Thomas A. Henzinger;Sangram Raje

  • Affiliations:

  • RWTH Aachen, Germany;CE, University of California, Santa Cruz, U.S.A.;I&C, ÉÉÉcole Polytechnique Fédérale de Lausanne (EPFL), Switzerland;I&C, ÉÉÉcole Polytechnique Fédérale de Lausanne (EPFL), Switzerland and EECS, University of California, Berkeley, U.S.A.;IIT Bombay, India

  • Venue:
  • CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
  • Year:
  • 2008

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Abstract

We consider imperfect-informationparity 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-informationgame. 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.