## Tables from this paper

## 34 Citations

Solving Parity Games in Practice

- Computer ScienceATVA
- 2009

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.

Parity games : descriptive complexity and algorithms for new solvers

- Computer Science
- 2013

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.

Oink: an Implementation and Evaluation of Modern Parity Game Solvers

- Computer ScienceTACAS
- 2018

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.

An experimental study of algorithms and optimisations for parity games, with an application to

- Computer Science
- 2009

The practical use of various optimisation techniques for solving parity games is investigated, showing that decomposition into strongly connected components and applying efficient algorithms for special cases are highly beneficial and the theoretic dependency on the number of priorities manifests itself in practice.

Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

- Computer ScienceGRAPHITE
- 2012

Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal mu-calculus formulae for process algebraic…

Solving µ-Calculus Parity Games by Symbolic Planning

- Computer Science, MathematicsMoChArt
- 2008

This paper applies symbolic planning to solve parity games equivalent to μ-calculus model checking problems with at most one fixpoint operator and partitioned images in the worst case.

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.

An Experiment on Parallel Model Checking of a CTL Fragment

- Computer ScienceATVA
- 2012

One of the most novel contributions of this work is to study a space-efficient variant for CTL model-checking that does not require to store the whole transition graph but that operates, instead, on a reverse spanning tree.

Efficient Parallel Strategy Improvement for Parity Games

- Computer ScienceCAV
- 2017

This paper studies the best way to implement one-player strategy improvement, and develops an efficient parallel algorithm for carrying out this task, by reducing the problem to computing prefix sums on a linked list.

Concurrent Small Progress Measures

- Computer ScienceHaifa Verification Conference
- 2011

A known implementation of multi-core machines (PW solver) is revisited, and an alternative implementation (CSPM), that reduces logical dependency on configuration state and makes performance less dependent on configuration details is suggested.

## References

SHOWING 1-10 OF 44 REFERENCES

An Accelerated Algorithm for 3-Color Parity Games with an Application to Timed Games

- Computer ScienceCAV
- 2007

An acceleration technique is presented that, while leaving the worst-case complexity unchanged, often leads to considerable speed-ups in games arising in practice, and of the symbolic implementation of the classical µ-calculus algorithm of Emerson and Jutla.

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.

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.

A Discrete Strategy Improvement Algorithm for Solving Parity Games

- Computer ScienceCAV
- 2000

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.…

Parallel Model Checking for LTL, CTL*, and Lµ2

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2003

Local Parallel Model Checking for the Alternation-Free µ-Calculus

- Computer ScienceSPIN
- 2002

We describe the design of (several variants of) a local parallel model-checking algorithm for the alternation-free fragment of the µ-calculus. It exploits a characterisation of the problem for this…

UppDMC: A Distributed Model Checker for Fragments of the mu-Calculus

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2005

A linear-time model-checking algorithm for the alternation-free modal mu-calculus

- Computer ScienceFormal Methods Syst. Des.
- 1993

A model-checking algorithm for a logic that permits propositions to be defined using greatest and least fixed points of mutually recursive systems of equations is developed, which improves on the best known algorithm for similar fixed-point logics.

CAESAR_SOLVE: A generic library for on-the-fly resolution of alternation-free Boolean equation systems

- Computer ScienceInternational Journal on Software Tools for Technology Transfer
- 2005

The library has been developed within the Cadp verification toolbox using the generic Open/Caesar environment and is currently used for three purposes: on-the-fly equivalence checking modulo five widely used equivalence relations, on- the-fly model checking of regular alternation-free modal μ-calculus, and on-The-fly reduction of state spaces based on τ-confluence.