Improving Parity Game Solvers with Justifications

Lapauw, Ruben; Bruynooghe, Maurice; Denecker, Marc

doi:10.1007/978-3-030-39322-9_21

Cited by 11 publications

(20 citation statements)

References 20 publications

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“…Bogaerts and Weinzierl (2018) used justifications to learn new clauses to improve search in lazy grounding algorithms. Additionally, justifications were used to improve parity game solvers (Lapauw et al 2020).…”

Section: Introductionmentioning

confidence: 99%

Exploiting Game Theory for Analysing Justifications

Marynissen

Bogaerts

Denecker

2020

Theory and Practice of Logic Programming

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Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification: an explanation why a property holds (or does not hold) in a model.In this paper, we continue the study of justification theory by means of three major contributions. The first is studying the relation between justification theory and game theory. We show that justification frameworks can be seen as a special type of games. The established connection provides the theoretical foundations for our next two contributions. The second contribution is studying under which condition two different dialects of justification theory (graphs as explanations vs trees as explanations) coincide. The third contribution is establishing a precise criterion of when a semantics induced by justification theory yields consistent results. In the past proving that such semantics were consistent took cumbersome and elaborate proofs.We show that these criteria are indeed satisfied for all common semantics of logic programming.

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Section: Introductionmentioning

confidence: 99%

Exploiting Game Theory for Analysing Justifications

Marynissen

Bogaerts

Denecker

2020

Theory and Practice of Logic Programming

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“…The effect is that freezing preserves the winning strategy. The FPJ algorithm proposed by Lapauw et al [25] modifies the standard fixpoint iteration by maintaining a justification graph, which essentially records which vertices are currently "justified" and the strategy that witnesses the justification. Justified vertices are not reevaluated, but each time a vertex is updated by the algorithm, the justification graph is pruned by removing vertices that are no longer justified.…”

Section: Fixpoint Iteration Algorithms For Parity Gamesmentioning

confidence: 99%

“…We call these simply the fixpoint iteration algorithms. These are the APT algorithm [32], a fixpoint iteration algorithm we refer to as BFL [4], as well as the recent DFI [13] and FPJ [25] algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…In recent work, Van Dijk and Rubbens [13] and Lapauw et al [25] propose fixpoint algorithms that yield strategies in a straightforward way. Previous fixpoint algorithms either do not produce a winning strategy [24] or require a secondary, complicated algorithm [4].…”

Section: Introductionmentioning

confidence: 99%

“…The contributions of this paper are as follows. We propose and implement two novel symbolic parity game algorithms based on [13] and [25]. We evaluate these algorithms empirically using benchmarks from the 2020 edition of SYNTCOMP [19].…”

Section: Introductionmentioning

confidence: 99%

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Symbolic Parity Game Solvers that Yield Winning Strategies

Lijzenga

Dijk

2020

Electron. Proc. Theor. Comput. Sci.

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Parity games play an important role for LTL synthesis as evidenced by recent breakthroughs on LTL synthesis, which rely in part on parity game solving. Yet state space explosion remains a major issue if we want to scale to larger systems or specifications. In order to combat this problem, we need to investigate symbolic methods such as BDDs, which have been successful in the past to tackle exponentially large systems. It is therefore essential to have symbolic parity game solving algorithms, operating using BDDs, that are fast and that can produce the winning strategies used to synthesize the controller in LTL synthesis. Current symbolic parity game solving algorithms do not yield winning strategies. We now propose two symbolic algorithms that yield winning strategies, based on two recently proposed fixpoint algorithms. We implement the algorithms and empirically evaluate them using benchmarks obtained from SYNTCOMP 2020. Our conclusion is that the algorithms are competitive with or faster than an earlier symbolic implementation of Zielonka's recursive algorithm, while also providing the winning strategies.

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Justifications and a Reconstruction of Parity Game Solving Algorithms

Lapauw

Bruynooghe

Denecker

2023

Lecture Notes in Computer Science

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Parity games are infinite two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification. This paper defines parametrized parity games and introduces an operation, Justify, that determines a winning strategy for a single node. By carefully ordering Justify steps, we reconstruct three algorithms well known from the literature. Verification and parity game solvingTime logics such as LTL are used to express properties of interacting systems. Synthesis consists of extracting an implementation with the desired properties.

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Improving Parity Game Solvers with Justifications

Cited by 11 publications

References 20 publications

Exploiting Game Theory for Analysing Justifications

Exploiting Game Theory for Analysing Justifications

Symbolic Parity Game Solvers that Yield Winning Strategies

Justifications and a Reconstruction of Parity Game Solving Algorithms

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