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Clique-Width and Parity Games

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Computer Science Logic (CSL 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4646))

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Abstract

The question of the exact complexity of solving parity games is one of the major open problems in system verification, as it is equivalent to the problem of model-checking the modal μ-calculus. The known upper bound is NP∩co-NP, but no polynomial algorithm is known. It was shown that on tree-like graphs (of bounded tree-width and DAG-width) a polynomial-time algorithm does exist. Here we present a polynomial-time algorithm for parity games on graphs of bounded clique-width (class of graphs containing e.g. complete bipartite graphs and cliques), thus completing the picture. This also extends the tree-width result, as graphs of bounded tree-width are a subclass of graphs of bounded clique-width. The algorithm works in a different way to the tree-width case and relies heavily on an interesting structural property of parity games.

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Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    Jan Obdržálek

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  1. Jan Obdržálek
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Jacques Duparc Thomas A. Henzinger

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Obdržálek, J. (2007). Clique-Width and Parity Games. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_8

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  • DOI: https://doi.org/10.1007/978-3-540-74915-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74914-1

  • Online ISBN: 978-3-540-74915-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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