A Discrete Strategy Improvement Algorithm for Solving Parity Games

  title={A Discrete Strategy Improvement Algorithm for Solving Parity Games},
  author={Jens V{\"o}ge and Marcin Jurdzinski},
A discrete strategy improvement algorithm is given for constructing winning strategies in parity games, thereby providing also a new solution of the model-checking problem for the modal μ-calculus. Known strategy improvement algorithms, as proposed for stochastic games by Hoffman and Karp in 1966, and for discounted payoff games and parity games by Puri in 1995, work with real numbers and require solving linear programming instances involving high precision arithmetic. In the present algorithm… 
Two local strategy improvement algorithms which explore the game graph on-the-fly whilst performing the improvement steps and can outperform existing global strategy improvement algorithm for solving parity games by several orders of magnitude.
An experimental study of algorithms and optimisations for parity games, with an application to
The practical use of various optimisation techniques for solving parity games is investigated, showing that decomposition into strongly connected components and applying efficient algorithms for special cases are highly beneficial and the theoretic dependency on the number of priorities manifests itself in practice.
Solving parity games
This project is to implement and evaluate a recently proposed parameterised algorithm that solves parity games for a class of games which depends on k, and suggests that a small parameter k could suffice for most games, making this algorithm a good candidate for solving parity games in practice.
New Algorithms for Solving Simple Stochastic Games
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Local Strategy Improvement for Parity Game Solving
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Solving parity games through fictitious play
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Two player games played on finite graphs have attracted much interest in the formal methods community and much effort has been expended in an attempt to find an algorithm which solves parity games in polynomial time.
The Fixpoint-Iteration Algorithm for Parity Games
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Two Local Strategy Iteration Schemes for Parity Game Solving
It turns out that local strategy iteration can outperform these others significantly and be compared empirically with existing global strategy iteration algorithms and the currently only other local algorithm for solving parity games.
An ordered approach to solving parity games in quasi polynomial time and quasi linear space
A first implementation for a quasi-polynomial algorithm is provided, and a number of side results are provided, including minor algorithmic improvements, a quasi bi-linear complexity in the number of states and edges for a fixed number of colours, and matching lower bounds for the algorithm of Calude et al.


A Discrete Stratety Improvement Algorithm for Solving Parity Games
A discrete strategy improvement algorithm is given for constructing winning strategies in parity games, thereby providing a new solution of the model-checking problem for the modal -calculus and providing a better conceptual understanding and easier analysis of strategy improvement algorithms for parity games.
Small Progress Measures for Solving Parity Games
A new algorithm for deciding the winner in parity games, and hence also for the modal µ-calculus model checking, based on a notion of game progress measures, characterized as pre-fixed points of certain monotone operators on a complete lattice.
Implementation of a Strategy Improvement Algorithm for Finite-State Parity Games
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On Algorithms for Simple Stochastic Games
  • A. Condon
  • Computer Science, Mathematics
    Advances In Computational Complexity Theory
  • 1990
It is shown that four natural approaches to solving the simple stochastic game problem are incorrect, and two new algorithms for the problem are presented, one of which extends a technique of Shapley called the successive approximation technique by using linear programming to maximize the improvement at each approximation step.
Strategy Construction in Infinite Ganes with Streett and Rabin Chain Winning Conditions
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  • 1998