Benchmarks for Parity Games

Keiren, Jeroen J. A.

doi:10.1007/978-3-319-24644-4_9

Cited by 17 publications

(13 citation statements)

References 64 publications

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“…Second, there is no obvious reason why random games with few priorities would be a good representative for games derived from actual applications. Hence, we implement DFI in the parity game solver OINK and we use as benchmarks those from model-checking and equivalence checking proposed by Keiren [16]. These are 313 model-checking and 216 equivalence checking games.…”

Section: Empirical Evaluationmentioning

confidence: 99%

Simple Fixpoint Iteration To Solve Parity Games

Dijk

Rubbens

2019

Electron. Proc. Theor. Comput. Sci.

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A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the many algorithms for parity games.We now consider a method of solving parity games by means of a naive fixpoint iteration. Several fixpoint algorithms for parity games have been proposed in the literature. In this work, we introduce an algorithm that relies on the notion of a distraction. The idea is that this offers a novel perspective for understanding parity games. We then show that this algorithm is in fact identical to two earlier published fixpoint algorithms for parity games and thus that these earlier algorithms are the same.Furthermore, we modify our algorithm to only partially recompute deeper fixpoints after updating a higher set and show that this modification enables a simple method to obtain winning strategies.We show that the resulting algorithm is simple to implement and offers good performance on practical parity games. We empirically demonstrate this using games derived from model-checking, equivalence checking and reactive synthesis and show that our fixpoint algorithm is the fastest solution for model-checking games.

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Section: Empirical Evaluationmentioning

confidence: 99%

Simple Fixpoint Iteration To Solve Parity Games

Dijk

Rubbens

2019

Electron. Proc. Theor. Comput. Sci.

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“…Priority promotion has a good practical performance for games where computing and attracting individual tangles is not necessary, e.g., when tangles are only attracted once and all tangles in a closed region are attracted to the same higher region, as is the case with the benchmark games of [19].…”

Section: Priority Promotionmentioning

confidence: 99%

Attracting Tangles to Solve Parity Games

Dijk

2018

Lecture Notes in Computer Science

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Abstract. Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely believed to admit a polynomial solution, but so far no such algorithm is known.We propose a new algorithm to solve parity games based on learning tangles, which are strongly connected subgraphs for which one player has a strategy to win all cycles in the subgraph. We argue that tangles play a fundamental role in the prominent parity game solving algorithms. We show that tangle learning is competitive in practice and the fastest solver for large random games.

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“…Such games, however, may be poor predictors for the performance of the algorithms on practical problems. Second, since one of our aims is to assess the scalability and the speed at which BDD-based solvers can solve parity games that encode practical verification problems, we also compare their performance on some of the larger cases of the Keiren benchmark set [24].…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…In [24], Keiren describes and provides a set of parity games that originate from over 300 model checking problems, originating from 21 specifications. The main obstacle in reusing the data set is that the games are encoded as explicit graphs in the PGSolver format.…”

Section: The Keiren Parity Game Solving Benchmark Setmentioning

confidence: 99%

“…While this does not reflect scenarios in which BDDs excel, this does yield important insights into which symbolic algorithms are more sensitive to BDDs with poor compression ratios. Finally, we compare the performance of all four algorithms on several of the larger cases taken from the Keiren benchmark set [24] of parity games and demonstrate that our symbolic algorithms can solve games that cannot be solved using explicit techniques.…”

Section: Introductionmentioning

confidence: 99%

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A Comparison of BDD-Based Parity Game Solvers

Sanchez¹,

Wesselink

Willemse

2018

Electron. Proc. Theor. Comput. Sci.

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Parity games are two player games with omega-winning conditions, played on finite graphs. Such games play an important role in verification, satisfiability and synthesis. It is therefore important to identify algorithms that can efficiently deal with large games that arise from such applications. In this paper, we describe our experiments with BDD-based implementations of four parity game solving algorithms, viz. Zielonka's recursive algorithm, the more recent Priority Promotion algorithm, the Fixpoint-Iteration algorithm and the automata based APT algorithm. We compare their performance on several types of random games and on a number of cases taken from the Keiren benchmark set.

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Benchmarks for Parity Games

Cited by 17 publications

References 64 publications

Simple Fixpoint Iteration To Solve Parity Games

Simple Fixpoint Iteration To Solve Parity Games

Attracting Tangles to Solve Parity Games

A Comparison of BDD-Based Parity Game Solvers

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