Optimal Transformations of Games and Automata Using Muller Conditions

Casares, Antonio; Colcombet, Thomas; Fijalkow, Nathanaël

doi:10.4230/lipics.icalp.2021.123

Cited by 13 publications

(21 citation statements)

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“…One may wonder why we seek to define a parity condition on top of M to prove that W is ω-regular, rather than a more general Muller condition which would achieve the same goal. Indeed, using M-cycle-consistency and a recent result by Casares et al [11,Section 5], it is straightforward to show that we could relabel such a Muller automaton with a parity condition defining the same language.…”

Section: From Properties Of a Winning Condition To ω-Regularitymentioning

confidence: 96%

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Characterizing Omega-Regularity through Finite-Memory Determinacy of Games on Infinite Graphs

Bouyer¹,

Randour²,

Vandenhove³

2021

Preprint

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We consider zero-sum games on infinite graphs, with objectives specified as sets of infinite words over some alphabet of colors. A well-studied class of objectives is the one of ω-regular objectives, due to its relation to many natural problems in theoretical computer science. We focus on the strategy complexity question: given an objective, how much memory does each player require to play as well as possible? A classical result is that finite-memory strategies suffice for both players when the objective is ω-regular. We show a reciprocal of that statement: when both players can play optimally with a chromatic finite-memory structure (i.e., whose updates can only observe colors) in all infinite game graphs, then the objective must be ω-regular. This provides a game-theoretic characterization of ω-regular objectives, and this characterization can help in obtaining memory bounds. Moreover, a by-product of our characterization is a new one-to-two-player lift: to show that chromatic finite-memory structures suffice to play optimally in two-player games on infinite graphs, it suffices to show it in the simpler case of one-player games on infinite graphs. We illustrate our results with the family of discounted-sum objectives, for which ω-regularity depends on the value of some parameters. ACM Subject Classification Theory of computation → Formal languages and automata theoryKeywords and phrases two-player games on graphs, infinite arenas, finite-memory determinacy, optimal strategies, ω-regular languages

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Section: From Properties Of a Winning Condition To ω-Regularitymentioning

confidence: 96%

“…, n}; function p assigns priorities to every transition of M. This definition implies that we consider deterministic and complete parity automata (i.e., in every state, reading a color leads to exactly one state). Following [11], if M is a skeleton, we say that a parity automaton (M ′ , p) is defined on top of…”

Section: W Is Chromatic-finite-memory Determinedmentioning

confidence: 99%

Characterizing Omega-Regularity through Finite-Memory Determinacy of Games on Infinite Graphs

Bouyer¹,

Randour²,

Vandenhove³

2021

Preprint

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“…It is sufficient to know which of the prohibited and required sets are visited infinitely often. 5 Hence, index appearance record uses the indices of the Rabin pairs instead of particular states in the permutation construction. This provides enough information to decide acceptance.…”

Section: Index Appearance Recordmentioning

confidence: 99%

“…and at least 2k priorities indeed is necessary [26, Theorem 2]. There, a much more generic result is proven, yielding lower bounds for translations from any particular acceptance condition α to parity automata via the notion of Zielonka trees (see [5] for a similar result on Muller conditions). Instantiating the theorem for Rabin condition, observe that the Zielonka tree associated with Rabin has k!…”

Section: Proofmentioning

confidence: 99%

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Index appearance record with preorders

et al. 2021

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Transforming $$\omega $$ ω -automata into parity automata is traditionally done using appearance records. We present an efficient variant of this idea, tailored to Rabin automata, and several optimizations applicable to all appearance records. We compare the methods experimentally and show that our method produces significantly smaller automata than previous approaches.

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Practical Applications of the Alternating Cycle Decomposition

Casares

Duret-Lutz

Meyer³

et al. 2022

Tools and Algorithms for the Construction and Analysis of Systems

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In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties and transformations of Muller automata. We present the first practical implementation of the ACD in two different tools, Owl and Spot, and adapt it to the framework of Emerson-Lei automata, i.e., $$\omega $$ ω -automata whose acceptance conditions are defined by Boolean formulas. The ACD provides a transformation of Emerson-Lei automata into parity automata with strong optimality guarantees: the resulting parity automaton is minimal among those automata that can be obtained by duplication of states. Our empirical results show that this transformation is usable in practice. Further, we show how the ACD can generalize many other specialized constructions such as deciding typeness of automata and degeneralization of generalized Büchi automata, providing a framework of practical algorithms for $$\omega $$ ω -automata.

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Optimal Transformations of Games and Automata Using Muller Conditions

Cited by 13 publications

References 0 publications

Characterizing Omega-Regularity through Finite-Memory Determinacy of Games on Infinite Graphs

Characterizing Omega-Regularity through Finite-Memory Determinacy of Games on Infinite Graphs

Index appearance record with preorders

Practical Applications of the Alternating Cycle Decomposition

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