The Rabin index of parity games: Its complexity and approximation

We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure. Colorings of game graphs are identified if they determine the same winning regions and strategies, for all ownership structures of nodes. The Rabin...

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Vydáno v:	Information and computation Ročník 245; s. 36 - 53
Hlavní autoři:	Huth, Michael, Kuo, Jim Huan-Pu, Piterman, Nir
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.12.2015
Témata:	Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) Descriptive complexity and finite models Graph theory: paths and cycles Logic in computer science Specification and verification (program logics, model checking, etc.) Specification and verification (program logics, model checking, etc.) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) Logic in computer science Descriptive complexity and finite models Graph theory: paths and cycles
ISSN:	0890-5401, 1090-2651
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Shrnutí:	We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure. Colorings of game graphs 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. We evaluate this efficient algorithm as a preprocessor of solvers in detailed experiments: for Zielonka's solver on random and structured parity games and for our partial solver psolB on random games.
ISSN:	0890-5401 1090-2651
DOI:	10.1016/j.ic.2015.06.005