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)
  • Otázka přesné složitosti řešení paritních her je jedním hlavních otevřených problémů ve verifikaci systémů, neboť je ekvivaletním problému ověřování modelu pro modální mu-kalkul. Známá horní hranice je NP a co-NP, ale není znám žádný polynomiální algoritmus. Bylo ukázáno, že na grafech podobných stromům (grafy s omezenou stromovou šířkou a DAG-šířkou) takový algoritmus existuje. Zde předkládáme polynomiální algoritmus pro paritní hry na grafech s omezenou klikovou šířkou (třída grafů obsahující například úplné bipartitiní grafy a kliky), čímž doplňujeme obrázek dané oblasti. Tento výsledek také rozšiřuje výsledek pro stromovou šířku, neboť grafy s omezenou stromovou šířkou mají i omezenou klikovou šířku. Algoritmus pracuje odlišně od svého protějšku pro omezenou stromovou šířku a značně využívá zajímavé vlastnosti paritních her. (cs)
Title
  • Clique-Width and Parity Games
  • Clique-Width and Parity Games (en)
  • Kliková šířka a paritní hry (cs)
skos:prefLabel
  • Clique-Width and Parity Games
  • Clique-Width and Parity Games (en)
  • Kliková šířka a paritní hry (cs)
skos:notation
  • RIV/00216224:14330/07:00022579!RIV08-MSM-14330___
http://linked.open.../vavai/riv/strany
  • 54-68
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 413922
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14330/07:00022579
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • parity games; mu-calculus; clique-width (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [60799F9ED06C]
http://linked.open...i/riv/nazevZdroje
  • Lecture Notes in Computer Science
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 4646
http://linked.open...iv/tvurceVysledku
  • Obdržálek, Jan
issn
  • 0302-9743
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http://localhost/t...ganizacniJednotka
  • 14330
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