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

@article{Antonik2009PolynomialTimeUO,
  title={Polynomial-Time Under-Approximation of Winning Regions in Parity Games},
  author={Adam Antonik and Nathaniel Charlton and Michael Huth},
  journal={Electron. Notes Theor. Comput. Sci.},
  year={2009},
  volume={225},
  pages={115-139}
}
Parity games : descriptive complexity and algorithms for new solvers
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This thesis studies algorithms that solve parity games in that they determine which nodes are won by which player, and where such decisions are supported with winning strategies, and designs algorithms to reduce the computational complexity of parity games.
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The empirical results will support the conclusion that considerable improvements over the state of the art are possible using a combination of careful tool design and implementation, application of powerful preprocessing operations, and the use of advanced heuristics in the implementation of the Small Progress Measures algorithm.
Practical improvements to parity game solving
TLDR
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Solving Parity Games in Scala
TLDR
PGSolver, written in OCaml, which has been elected by the community as the de facto platform to solve efficiently parity games as well as evaluate their performance in several specific cases.
Toward a multilevel scalable parallel Zielonka's algorithm for solving parity games
TLDR
The feasibility analysis of a multi‐grained parallel version of the Zielonka Recursive (ZR) algorithm exploiting the coarse‐ and fine‐ grained concurrency is performed and it is confirmed that while a fine‐Grained parallelism have a clear performance limitation, the performance gain one can get by employing a multilevel parallelism is significant.
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References

SHOWING 1-10 OF 17 REFERENCES
Small Progress Measures for Solving Parity Games
TLDR
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.
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.
Algorithms for Parity Games
  • H. Klauck
  • Computer Science
    Automata, Logics, and Infinite Games
  • 2001
TLDR
The aim of this chapter is to review some of the algorithmic approaches to the problem of computing winning strategies in parity games with finite arenas and other two-player games, and to underline the importance of looking for an efficient algorithm solving this particular problem.
Three-valued abstractions of games: uncertainty, but with precision
TLDR
A framework for abstracting two-player turn-based games that preserves any formula of the alternating /spl mu/-calculus (AMC) based on 3-valued games, which can be used to prove and disprove formulas of AMC including arbitrarily nested strategy quantifiers.
DAG-Width and Parity Games
TLDR
The natural adaptation of the cops-and-robber game to directed graphs is considered and it is shown that monotone strategies in the game yield a measure with an associated notion of graph decomposition that can be seen to describe how close a directed graph is to a directed acyclic graph (DAG).
Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees
  • W. Zielonka
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1998
Automata logics, and infinite games: a guide to current research
TLDR
The 19 chapters presented in this multi-author monograph give a consolidated overview of the research results achieved in the theory of automata, logics, and infinite games during the past 10 years.
Local Model Checking in the Modal mu-Calculus
Tree Automata
TLDR
This work presents a machine-checked tree automata library for Standard-ML, OCaml and Haskell, and contains a formalization of the class of treeregular languages and its closure properties under set operations.
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