Algorithms for omega-regular games with imperfect information Journal Article

Author(s): Chatterjee, Krishnendu; Doyen, Laurent; Henzinger, Thomas A; Raskin, Jean-François
Article Title: Algorithms for omega-regular games with imperfect information
Abstract: We study observation-based strategies for two-player turn-based games on graphs with omega-regular objectives. An observation-based strategy relies on imperfect information about the history of a play, namely, on the past sequence of observations. Such games occur in the synthesis of a controller that does not see the private state of the plant. Our main results are twofold. First, we give a fixed-point algorithm for computing the set of states from which a player can win with a deterministic observation-based strategy for any omega-regular objective. The fixed point is computed in the lattice of antichains of state sets. This algorithm has the advantages of being directed by the objective and of avoiding an explicit subset construction on the game graph. Second, we give an algorithm for computing the set of states from which a player can win with probability 1 with a randomized observation-based strategy for a Buechi objective. This set is of interest because in the absence of perfect information, randomized strategies are more powerful than deterministic ones. We show that our algorithms are optimal by proving matching lower bounds.
Keywords: 2-player games; partial information; algorithms; randomized strategies; antichains
Journal Title: Logical Methods in Computer Science
Volume: 3
Issue 3:4
ISSN: 1860-5974
Publisher: International Federation of Computational Logic  
Date Published: 2007-07-27
Start Page: 1
End Page: 23
Copyright Statement: CC-BY
Sponsor: This research was supported in part by the NSF grants CCR-0225610 and CCR-0234690 by the SNSF under the Indo-Swiss Joint Research Programme and by the FRFC project “Centre Fédéré en Vérification” funded by the FNRS under grant 2.4530.02.
DOI: 10.2168/LMCS-3(3:4)2007
Open access: no
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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