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Small Progress Measures for Solving Parity Games

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STACS 2000 (STACS 2000)

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Abstract

In this paper we develop a new algorithm for deciding the winner in parity games, and hence also for the modal μ-calculus model checking. The design and analysis of the algorithm is based on a notion of game progress measures: they are witnesses for winning strategies in parity games. We characterize game progress measures as pre-fixed points of certain monotone operators on a complete lattice. As a result we get the existence of the least game progress measures and a straightforward way to compute them. The worst-case running time of our algorithm matches the best worst-case running time bounds known so far for the problem, achieved by the algorithms due to Browne et al., and Seidl. Our algorithm has better space complexity: it works in small polynomial space; the other two algorithms have exponential worst-case space complexity.

Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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Author information

Authors and Affiliations

  1. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Building 540, 8000, Aarhus C, Denmark

    Marcin Jurdziński

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  1. Marcin Jurdziński
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Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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Jurdziński, M. (2000). Small Progress Measures for Solving Parity Games. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_24

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  • DOI: https://doi.org/10.1007/3-540-46541-3_24

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  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

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