Small Progress Measures for Solving Parity Games

  • Authors:
  • Marcin Jurdzinski

  • Affiliations:
  • -

  • Venue:
  • STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
  • Year:
  • 2000

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Abstract

In this paper we develop a new algorithm for deciding the winner in parity games, and hence also for the modal µ-calculus model checking. The design and analysis of the algorithm is based on a notion of game progress measures: they are witnesses for winning strategies in parity games. We characterize game progress measures as pre-fixed points of certain monotone operators on a complete lattice. As a result we get the existence of the least game progress measures and a straightforward way to compute them. The worst-case running time of our algorithm matches the best worst-case running time bounds known so far for the problem, achieved by the algorithms due to Browne et al., and Seidl. Our algorithm has better space complexity: it works in small polynomial space; the other two algorithms have exponential worst-case space complexity.