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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Clique-Width and Parity Games
verfasst von : Jan Obdržálek
Erschienen in: Computer Science Logic
Verlag: Springer Berlin Heidelberg
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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.