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The Rabin Index of Parity Games

(Extended Abstract)
  • Michael Huth
  • Jim Huan-Pu Kuo
  • Nir Piterman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7261)

Abstract

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 fixed k ≥ 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael Huth
    • 1
  • Jim Huan-Pu Kuo
    • 1
  • Nir Piterman
    • 2
  1. 1.Department of ComputingImperial College LondonLondonUnited Kingdom
  2. 2.Department of Computer ScienceUniversity of LeicesterLeicesterUnited Kingdom

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