# Solving Parity Games in Practice

@inproceedings{Friedmann2009SolvingPG, title={Solving Parity Games in Practice}, author={Oliver Friedmann and Martin Lange}, booktitle={ATVA}, year={2009} }

Parity games are 2-player games of perfect information and infinite duration that have important applications in automata theory and decision procedures (validity as well as model checking) for temporal logics. In this paper we investigate practical aspects of solving parity games. The main contribution is a suggestion on how to solve parity games efficiently in practice: we present a generic solver that intertwines optimisations with any of the existing parity game algorithms which is only…

## 118 Citations

A Comparison of BDD-Based Parity Game Solvers

- Computer ScienceGandALF
- 2018

This paper describes experiments with BDD-based implementations of four parity game solving algorithms, viz.

Improving Parity Game Solvers with Justifications

- Computer ScienceVMCAI
- 2020

This paper improves several parity game solvers by using a justification graph, and experimental evaluation shows the algorithms improve upon the state-of-the-art.

Solving Parity Games Using an Automata-Based Algorithm

- Computer ScienceCIAA
- 2016

Parity games are abstract infinite-round games that take an important role in formal verification and are implemented in a platform named PGSolver, which enabled an empirical evaluation of these algorithms and a better understanding of their relative merits.

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.

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.

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.

Static Analysis of Parity Games: Alternating Reachability Under Parity

- Computer ScienceSemantics, Logics, and Calculi
- 2016

The determinacy of these games is proved and this determinacy is used to define, for each player, a monotone fixed point over an ordered domain of height linear in the size of the parity game such that all nodes in its greatest fixed point are won by said player in the paritygame.

Oink: an Implementation and Evaluation of Modern Parity Game Solvers

- Computer ScienceTACAS
- 2018

A new and easy to extend tool Oink is implemented, which is a high-performance implementation of modern parity game algorithms and solvers, both on real world benchmarks and randomly generated games.

Improving parity games in practice

- Computer ScienceAnn. Math. Artif. Intell.
- 2021

This work deeply revisit the implementation of Zielonka’s recursive algorithm by dealing with the use of specific data structures and programming languages such as Scala, Java, C++, and Go, and shows that these choices are successful.

Improving Priority Promotion for Parity Games

- Computer ScienceHaifa Verification Conference
- 2016

A new instantiation, called region recovery, is proposed that tries to reduce the possible exponential behaviours exhibited by the original method in the worst case, and not only often outperforms the original priority promotion approach, but so far no exponential worst case is known.

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