Solving Infinite-State Games via Acceleration

Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to significant attention towards developing techniques for solving infini...

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Veröffentlicht in:Proceedings of ACM on programming languages 2024-01, Vol.8 (POPL), p.1696-1726, Article 57
Hauptverfasser: Heim, Philippe, Dimitrova, Rayna
Format: Artikel
Sprache:eng
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Zusammenfassung:Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to significant attention towards developing techniques for solving infinite-state games. We propose novel symbolic semi-algorithms for solving infinite-state games with temporal winning conditions. The novelty of our approach lies in the introduction of an acceleration technique that enhances fixpoint-based game-solving methods and helps to avoid divergence. Classical fixpoint-based algorithms, when applied to infinite-state games, are bound to diverge in many cases, since they iteratively compute the set of states from which one player has a winning strategy. Our proposed approach can lead to convergence in cases where existing algorithms require an infinite number of iterations. This is achieved by acceleration: computing an infinite set of states from which a simpler sub-strategy can be iterated an unbounded number of times in order to win the game. Ours is the first method for solving infinite-state games to employ acceleration. Thanks to this, it is able to outperform state-of-the-art techniques on a range of benchmarks, as evidenced by our evaluation of a prototype implementation.
ISSN:2475-1421
2475-1421
DOI:10.1145/3632899