Solving Parity Games in Practice

  title={Solving Parity Games in Practice},
  author={Oliver Friedmann and Martin Lange},
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… 
A Comparison of BDD-Based Parity Game Solvers
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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
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.
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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 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.
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Oink: an Implementation and Evaluation of Modern Parity Game Solvers
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.
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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.
Improving Priority Promotion for Parity Games
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.


A Multi-Core Solver for Parity Games
Small Progress Measures for Solving Parity Games
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.
A Discrete Strategy Improvement Algorithm for Solving Parity Games
A discrete strategy improvement algorithm is given for constructing winning strategies in parity games, thereby providing also a new solution of the model-checking problem for the modal μ-calculus.
Polynomial-Time Under-Approximation of Winning Regions in Parity Games
Practical Model-Checking Using Games
It is described how model-checking games can be the foundation for efficient local model- checking of the modal mu-calculus on transition systems and a proof technique for verifying such algorithms is given.
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Deciding the Winner in Parity Games is in UP \cap co-Up
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