Algorithms for Parity Games

@inproceedings{Klauck2001AlgorithmsFP,
  title={Algorithms for Parity Games},
  author={Hartmut Klauck},
  booktitle={Automata, Logics, and Infinite Games},
  year={2001}
}
  • H. Klauck
  • Published in
    Automata, Logics, and…
     2001
  • Computer Science
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… 
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22 Citations
Background Citations
9
Methods Citations
8
Results Citations
1

22 Citations

A Multi-Core Solver for Parity Games
Potential theory for mean payoff games
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
TLDR
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
Improvement in Small Progress Measures
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
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…
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