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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Veröffentlicht in:Information and computation Jg. 245; S. 36 - 53
Hauptverfasser: Huth, Michael, Kuo, Jim Huan-Pu, Piterman, Nir
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.12.2015
Schlagworte:
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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Abstract 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.
AbstractList 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.
Author Huth, Michael
Kuo, Jim Huan-Pu
Piterman, Nir
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  givenname: Michael
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  givenname: Jim Huan-Pu
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  givenname: Nir
  surname: Piterman
  fullname: Piterman, Nir
  email: nir.piterman@leicester.ac.uk
  organization: Department of Computer Science, University of Leicester, Leicester, LE1 7RH, United Kingdom
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Cites_doi 10.1137/0205048
10.1051/ita:1999129
10.1016/S0019-9958(79)90653-3
10.1016/0304-3975(80)90009-2
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Keywords 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
Language English
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Snippet We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure....
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SubjectTerms 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.)
Title The Rabin index of parity games: Its complexity and approximation
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