Solving μ-Calculus Parity Games by Symbolic Planning

  • Authors:

  • Marco Bakera;Stefan Edelkamp;Peter Kissmann;Clemens D. Renner

  • Affiliations:

  • Department of Computer Science, Dortmund University of Technology,;Department of Computer Science, Dortmund University of Technology,;Department of Computer Science, Dortmund University of Technology,;Department of Computer Science, Dortmund University of Technology,

  • Venue:
  • Model Checking and Artificial Intelligence
  • Year:
  • 2009

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Abstract

This paper applies symbolic planning to solve parity games equivalent to μ -calculus model checking problems. Compared to explicit algorithms, state sets are compacted during the analysis. Given that $\mbox{\it diam}(G)$ is the diameter of the parity game graph G with node set V , for the alternation-free model checking problem with at most one fixpoint operator, the algorithm computes at most $O(\mbox{\it diam}(G))$ partitioned images. For d alternating fixpoint operators, $O(d \cdot \mbox{\it diam}(G) \cdot (\frac{|V|+(d-1)}{d-1})^{d-1})$ partitioned images are required in the worst case. Practical models and properties stem from data-flow analysis, with problems transformed to parity game graphs, which are then compiled to a general game playing planner input.