Regular games provide a very useful model for the synthesis of controllers in reactive systems. The complexity of these games depends on the representation of the winning condition: if it is represented through a win-set, a coloured condition, a Zielonka-DAG or Emerson-Lei formulae, the winner problem is PSPACS-complete; if the winning condition is represented as a Zielonka tree, the winner problem belongs to NP and co-NP. In this paper, we show that explicit Muller games can be solved in polynomial time, and provide an effective algorithm to compute the winning regions.

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Schloss Dagstuhl - Leibniz Center of Informatics
R. Hariharan , M. Mukund , V. Vinay
Leibniz International Proceedings in Informatics
IARCS Annual Conference on the Foundations of Software Technology and Theoretical Computer Science
Networks and Optimization

Horn, F. (2008). Explicit Muller Games are PTIME. In R Hariharan, M Mukund, & V Vinay (Eds.), Proceedings of the 28th IARCS Annual Conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS\'08) (pp. 235–243). Schloss Dagstuhl - Leibniz Center of Informatics.