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The complexity of mean payoff games on graphs
Theoretical Computer Science
Theory of hybrid systems and discrete event systems
Theory of hybrid systems and discrete event systems
An improved algorithm for the evaluation of fixpoint expressions
Theoretical Computer Science
Infinite games on finitely coloured graphs with applications to automata on infinite trees
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Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
Alternating-time temporal logic
Journal of the ACM (JACM)
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On Model-Checking for Fragments of µ-Calculus
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Timed Parity Games: Complexity and Robustness
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Electronic Notes in Theoretical Computer Science (ENTCS)
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Stuttering mostly speeds up solving parity games
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Alternating traps in Muller and parity games
Theoretical Computer Science
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This paper proposes a new algorithm that improves the complexity bound for solving parity games. Our approach combines McNaughton's iterated fixed point algorithm with a preprocessing step, which is called prior to every recursive call. The preprocessing uses ranking functions similar to Jurdzinski's, but with a restricted codomain, to determine all winning regions smaller than a predefined parameter. The combination of the preprocessing step with the recursive call guarantees that McNaughton's algorithm proceeds in big steps, whose size is bounded from below by the chosen parameter. Higher parameters result in smaller call trees, but to the cost of an expensive preprocessing step. An optimal parameter balances the cost of the recursive call and the preprocessing step, resulting in an improvement of the known upper bound for solving parity games from approximately O(m n1/2c) to O(m n1/3c).