# A Discrete Strategy Improvement Algorithm for Solving Parity Games

@inproceedings{Vge2000ADS, title={A Discrete Strategy Improvement Algorithm for Solving Parity Games}, author={Jens V{\"o}ge and Marcin Jurdzinski}, booktitle={CAV}, year={2000} }

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…

## 294 Citations

TWO LOCAL STRATEGY IMPROVEMENT SCHEMES FOR PARITY GAME SOLVING

- Computer Science
- 2010

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

- Computer Science
- 2009

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

- Computer Science
- 2008

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

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2005

Local Strategy Improvement for Parity Game Solving

- Computer ScienceGANDALF
- 2010

A local strategy improvement algorithm which explores the game graph on-the-fly whilst performing the improvement steps and can outperform existing global strategy improvement algorithms by several orders of magnitude.

Solving parity games through fictitious play

- Computer Science
- 2013

It is proved that the basic algorithm performs demonstrably well against existing solvers in experiments over a large number and variety of games and is conjectured to have a run time complexity bounded by O(n4 log(n)) and I provide a discussion of strategy graphs and their emperically observed properties.

Solving Mean Payo Parity Games With Strategy Improvement

- Computer Science
- 2008

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

- Computer ScienceGandALF
- 2014

This paper studies the effect of employing the most straight-forward mu-calculus model checking algorithm: fixpoint iteration, and shows that particular exponential-space strategies which are eventually-positional can be extracted from them, and are shown to be positional winning strategies.

Two Local Strategy Iteration Schemes for Parity Game Solving

- Computer ScienceInt. J. Found. Comput. Sci.
- 2012

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

- Computer ScienceSPIN
- 2017

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.

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