# Benchmarks for Parity Games

@inproceedings{Keiren2015BenchmarksFP, title={Benchmarks for Parity Games}, author={Jeroen Keiren}, booktitle={FSEN}, year={2015} }

We propose a benchmark suite for parity games that includes the benchmarks that have been used in the literature, and make it available online. We give an overview of the parity games, including a description of how they have been generated. We also describe structural properties of parity games, and using these properties we show that our benchmarks are representative. With this work we provide a starting point for further experimentation with parity games.

## 22 Citations

Solving Parity Games: Explicit vs Symbolic

- Computer ScienceCIAA
- 2018

It is shown that forrandom games, even for constrained random games, explicit algorithms actually perform better than symbolic algorithms, and for structured games, where symbolic algorithms seem to have the advantage.

A Comparison of BDD-Based Parity Game Solvers

- Computer ScienceGandALF
- 2018

This paper describes experiments with BDD-based implementations of four parity game solving algorithms, viz.

Improving parity games in practice

- Computer ScienceAnn. Math. Artif. Intell.
- 2021

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.

Attracting Tangles to Solve Parity Games

- Computer ScienceCAV
- 2018

It is argued that tangles play a fundamental role in the prominent parity game solving algorithms and it is shown that tangle learning is competitive in practice and the fastest solver for large random games.

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.

BDD-based parity game solving

- Computer Science
- 2018

Zielonka’s BDD-based algorithm beats the B DD-based Priority Promotion algorithm by a small margin for games that are characteristic of practical veriﬁcation problems, and the Fixpoint-Iteration algorithm performs similar to Ziel onka‘s algorithm for games with at most 5 diﬀerent priorities.

Improving Parity Game Solvers with Justifications

- Computer ScienceVMCAI
- 2020

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.

Eﬀective partial solvers for parity games 1

- Computer Science
- 2016

It is shown that an implementation of this semantic framework manually discovers new partial solvers – including those that merge node sets that have the same but unknown winner – by studying games that composed partialsolvers can neither solve nor simplify.

Parity game reductions

- EconomicsActa Informatica
- 2017

This work reconsiders (governed) bisimulation and ( governed) stuttering bisimulations, and gives detailed proofs that these relations are equivalences, have unique quotients and they approximate the winning regions of parity games.

G T ] 5 F eb 2 01 6 Winning Cores in Parity Games

- Computer Science, Economics
- 2015

It is shown that the winning core and the winning region for a player in a parity game are equivalently empty, and a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation is developed.

## References

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Benchmarks for Parity Games (extended version)

- Computer Science, Economics
- 2015

With this work, a benchmark suite for parity games is proposed that includes all benchmarks that have been used in the literature, and it is shown that these benchmarks are representative.

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.

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.

An Exponential Lower Bound for the Parity Game Strategy Improvement Algorithm as We Know it

- Computer Science2009 24th Annual IEEE Symposium on Logic In Computer Science
- 2009

A family of games on which the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdzinski requires exponentially many strategy iterations is outlined, answering in the negative the long-standing question whether this algorithm runs in polynomial time.

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.

A Super-Polynomial Lower Bound for the Parity Game Strategy Improvement Algorithm as We Know it

- Computer ScienceArXiv
- 2009

A new lower bound for the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdziski is presented, answering in the negative the long-standing question whether this algorithm runs in polynomial time.

Algorithmic Analysis of Parity Games

- Computer Science
- 2006

A new algorithm for parity games is presented, in part inspired by the strategy improvement algorithm, based on spines, which has some interesting properties and can give a further insight into parity games.

Stuttering Mostly Speeds Up Solving Parity Games

- LinguisticsNASA Formal Methods
- 2011

It is demonstrated that stuttering equivalent vertices have the same winner in the parity game, which means that solving a parity game can be accelerated by minimising the game graph with respect to stuttering equivalence.

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.…