Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
A Discrete Subexponential Algorithm for Parity Games
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
A deterministic subexponential algorithm for solving parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Facets of Synthesis: Revisiting Church's Problem
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Solving parity games in big steps
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different classes and representations of Muller games lead to problems of varying computational complexity. One such class are parity games; these are of particular significance in computational complexity, as they remain one of the few combinatorial problems known to be in NP @? co-NP but not known to be in P. We show that winning regions for a Muller game can be determined from the alternating structure of its traps. To every Muller game we then associate a natural number that we call its trap depth; this parameter measures how complicated the trap structure is. We present algorithms for parity games that run in polynomial time for graphs of bounded trap depth, and in general run in time exponential in the trap depth.