Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A Discrete Strategy Improvement Algorithm for Solving Parity Games
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure. Different colorings of the same graph are identified if they determine the same winning regions and strategies, for all ownership structures of nodes. The Rabin index of a parity game is the minimum of the maximal color taken over all equivalent coloring functions. We show that deciding whether the Rabin index is at least k is in P for k=1 but NP-hard for all fixedk≥2. We present an EXPTIME algorithm that computes the Rabin index by simplifying its input coloring function. When replacing simple cycle with cycle detection in that algorithm, its output over-approximates the Rabin index in polynomial time. Experimental results show that this approximation yields good values in practice.