About: Clique-Width and Parity Games     Goto   Sponge   NotDistinct   Permalink

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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 $\mu$-calculus. The known upper bound is NP$\cap$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.
  • 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 $\mu$-calculus. The known upper bound is NP$\cap$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. (en)
Title
  • Clique-Width and Parity Games
  • Clique-Width and Parity Games (en)
skos:prefLabel
  • Clique-Width and Parity Games
  • Clique-Width and Parity Games (en)
skos:notation
  • RIV/00216224:14330/07:00022579!RIV10-MSM-14330___
http://linked.open...avai/riv/aktivita
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  • P(1M0545)
http://linked.open...vai/riv/dodaniDat
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  • 413921
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  • RIV/00216224:14330/07:00022579
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  • parity games; mu-calculus; clique-width (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [75C88693E037]
http://linked.open...v/mistoKonaniAkce
  • Lausanne, Switzerland
http://linked.open...i/riv/mistoVydani
  • Berlin
http://linked.open...i/riv/nazevZdroje
  • Computer Science Logic 2007, proceedings
http://linked.open...in/vavai/riv/obor
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http://linked.open...vavai/riv/projekt
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  • Obdržálek, Jan
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http://linked.open...ain/vavai/riv/wos
  • 000250338100007
http://linked.open.../riv/zahajeniAkce
number of pages
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  • Springer-Verlag
https://schema.org/isbn
  • 978-3-540-74914-1
http://localhost/t...ganizacniJednotka
  • 14330
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