# Algorithms for Parity Games

@inproceedings{Klauck2001AlgorithmsFP, title={Algorithms for Parity Games}, author={Hartmut Klauck}, booktitle={Automata, Logics, and Infinite Games}, year={2001} }

It is the aim of this chapter to review some of the algorithmic approaches to the problem of computing winning strategies (resp. of deciding if a player has a winning strategy from a given vertex) in parity games with finite arenas and other two-player games. Parity games are equivalent via linear time reductions to the problem of modal μ-calculus model checking (see Chapters 10 and 9), and this model checking problem plays a major role in computer-aided verification. Furthermore we will see…

## 22 Citations

Potential theory for mean payoff games

- Mathematics
- 2007

The paper presents an O(mn2nlog Z) deterministic algorithm for solving the mean payoff game problem, m and n being the numbers of arcs and vertices, respectively, in the game graph, and Z being the…

A Multi-Core Solver for Parity Games Jaco van de Pol

- Computer Science
- 2008

A parallel algorithm for solving parity games, with applications in, e.g., modal μ-calculus model checking with arbitrary alternations, and (branching) bisimulation checking, based on Jurdzinski’s Small Progress Measures, which allows maximum parallelism.

Polynomial-Time Under-Approximation of Winning Regions in Parity Games

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2009

Improvement in Small Progress Measures

- Computer ScienceGandALF
- 2015

The algorithm is modified so that it derives the winning strategy for both players in one pass, which reduces the upper bound on strategy derivation for SPM to O(dm.(n/floor(d/2))^floor( d/2)).

Speeding up the small progress measures algorithm for parity games using the GPU

- Computer Science
- 2013

Here, SPM is adapted to work on the many-core architecture used by modern graphics processing units (GPUs) and a new technique is introduced that can help to reduces parity game solving times by assigning priorities to edges instead of vertices, after which shortcut edges can be added to the graph.

Computing safe winning regions of parity games in polynomial time

- Computer Science
- 2006

A pattern is proposed for designing algorithms that are in P by construction and under-approximate the winning regions of both players in parity games by the interaction of finitely many aspects.

Strategy Derivation for Small Progress Measures

- Computer ScienceArXiv
- 2014

This work provides a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning strategies for both players in one pass, and reduces the upper bound on strategy derivation for SPM.

A Model Checker for Strategy Logic

- Computer Science
- 2014

This report documents the design of the first practical model checking algorithms for two fragments of Sl and their symbolic implementation using binary decision diagrams and explains how they were incorporated in the existing model checker MCMAS and added support for strategy synthesis.

An Effective Solution of Language Inequality XA ⊆ BX In the Case of Codes with Finite Decoding Delay

- Mathematics
- 2010

In this paper, we consider effective constructions of the maximal solution of the language inequality XA ⊆ BX. It has been proved by Kunc in [14] that the maximal solution of XA ⊆ BX is regular…