Solving μ-Calculus Parity Games by Symbolic Planning

  • Marco Bakera
  • Stefan Edelkamp
  • Peter Kissmann
  • Clemens D. Renner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5348)


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.


Model Check Game Graph Model Check Problem Parity Game Symbolic Exploration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Marco Bakera
    • 1
  • Stefan Edelkamp
    • 1
  • Peter Kissmann
    • 1
  • Clemens D. Renner
    • 1
  1. 1.Department of Computer ScienceDortmund University of TechnologyGermany

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