Oink: An Implementation and Evaluation of Modern Parity Game Solvers

Dijk, Tom van

doi:10.1007/978-3-319-89960-2_16

Cited by 49 publications

(58 citation statements)

References 45 publications

(94 reference statements)

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“…If we compare with Zielonka's recursive algorithm as presented in [5,Algorithm 3], we see that the frozen vertices in DFI are exactly the vertices in W α that are not recomputed in the second recursion of line 10 of [5, Algorithm 3]. The recursive algorithm and DFI thus use the same mechanism to decide that a vertex is a distraction and to preserve the correct winning strategy.…”

Section: Freezing Below the Fixpointmentioning

confidence: 99%

“…The method exposes the relationship between fixpoint iteration and the famous recursive algorithm by Zielonka. For various treatments of Zielonka's recursive algorithm, we refer to [5,23,25] Solutions to parity games via fixpoint computation essentially translate the game into a formula of the µ-calculus which is then solved naively. Two such algorithms have been proposed in the literature.…”

Section: Introductionmentioning

confidence: 99%

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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: Freezing Below the Fixpointmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simple Fixpoint Iteration To Solve Parity Games

Dijk

Rubbens

2019

Electron. Proc. Theor. Comput. Sci.

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“…QDPM requires time O(n · m · W · log(n · W )) to solve an MPG with n positions, m moves, and maximal positive weight W . In order to assess the effectiveness of the proposed approach, we implemented both QDPM and SEPM [13], the most efficient known solution to the problem and the more closely related one to QDPM, in C++ within OINK [32]. OINK has been developed as a framework to compare parity game solvers.…”

Section: Definition 3 (Quasi Dominion) An Arbitrary Set Of Positionsmentioning

confidence: 99%

Solving Mean-Payoff Games via Quasi Dominions

Benerecetti

Dell’Erba

Mogavero

2020

Lecture Notes in Computer Science

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We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of the two notions can be highly beneficial and significantly speeds up convergence to the problem solution. Experiments show that the resulting algorithm performs orders of magnitude better than the asymptotically-best solution algorithm currently known, without sacrificing on the worst-case complexity.A two-player turn-based arena is a tuple A = Ps ⊕ , Ps ⊟ , Mv , with Ps ⊕ ∩ Ps ⊟ = ∅ and Ps Ps ⊕ ∪ Ps ⊟ , such that Ps, Mv is a finite directed graph without sinks. Ps ⊕ (resp., Ps ⊟ ) is the set of 1. The experiments were carried out on a 64-bit 3.9GHz quad-core machine, with INTEL i5-6600K processor and 8GB of RAM, running UBUNTU 18.04.

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“…A classical exponent of the latter category is Zielonka's recursive algorithm [30] but also the recently introduced Priority Promotion (PP) algorithm [6]. While DI algorithms typically have a worst-case running time complexity that is theoretically less attractive than that of SI algorithms, in practice, the SI are significantly outperformed by DI algorithms [14].…”

Section: Introductionmentioning

confidence: 99%

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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Oink: An Implementation and Evaluation of Modern Parity Game Solvers

Cited by 49 publications

References 45 publications

Simple Fixpoint Iteration To Solve Parity Games

Simple Fixpoint Iteration To Solve Parity Games

Solving Mean-Payoff Games via Quasi Dominions

A Comparison of BDD-Based Parity Game Solvers

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