# 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} }

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## 14 Citations

Improving parity games in practice

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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.

Solving Parity Games Using an Automata-Based Algorithm

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- 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.

Solving Parity Games in Practice

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A generic solver is presented that intertwines optimisations with any of the existing parity game algorithms which is only called on parts of a game that cannot be solved faster by simpler methods, showing that using this approach vastly speeds up the solving process.

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.

Practical Improvements to Parity Game Solving

- Computer Science
- 2013

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

- Computer Science
- 2013

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.

Solving Parity Games in Scala

- Computer ScienceFACS
- 2014

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

- Computer ScienceConcurr. Comput. Pract. Exp.
- 2021

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.

A workbench for preprocessor design and evaluation: toward benchmarks for parity games

- Computer ScienceElectron. Commun. Eur. Assoc. Softw. Sci. Technol.
- 2009

A prototype workbench is described that allows for easy composition of preprocessors, can populate databases with games and their meta-data, offers a query language for generating games of interest, and has already found potentially hard games.

Algorithms for Modal μ-Calculus Interpretation

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- 2008

In this essay modal μ-calculus will be defined and several interpretation algorithms will be presented, some more or less intuitive, while others involve automata theory and are more sophisticated.

## References

SHOWING 1-10 OF 17 REFERENCES

Small Progress Measures for Solving Parity Games

- Computer ScienceSTACS
- 2000

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

- 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.

Algorithms for Parity Games

- Computer ScienceAutomata, Logics, and Infinite Games
- 2001

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.

DAG-Width and Parity Games

- Mathematics, Computer ScienceSTACS
- 2006

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

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1998

Automata logics, and infinite games: a guide to current research

- Computer Science
- 2002

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

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1991

Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints

- Computer SciencePOPL
- 1977

A program denotes computations in some universe of objects. Abstract interpretation of programs consists in using that denotation to describe computations in another universe of abstract objects, so…

Entanglement - A Measure for the Complexity of Directed Graphs with Applications to Logic and Games

- Computer ScienceLPAR
- 2004

We propose a new parameter for the complexity of finite directed graphs which measures to what extent the cycles of the graph are intertwined. This measure, called entanglement, is defined by way of…