New Algorithms for Combinations of Objectives using Separating Automata

Ashwani Anand
(Chennai Mathematical Institute, Chennai, India)
Nathanaël Fijalkow
(CNRS, LaBRI, Bordeaux, France, and The Alan Turing Institute, London, United Kingdom)
Aliénor Goubault-Larrecq
(ENS Lyon, Lyon, France)
Jérôme Leroux
(CNRS, LaBRI, Bordeaux, France)
Pierre Ohlmann
(Université de Paris, Paris, France)

The notion of separating automata was introduced by Bojanczyk and Czerwinski for understanding the first quasipolynomial time algorithm for parity games. In this paper we show that separating automata is a powerful tool for constructing algorithms solving games with combinations of objectives. We construct two new algorithms: the first for disjunctions of parity and mean payoff objectives, matching the best known complexity, and the second for disjunctions of mean payoff objectives, improving on the state of the art. In both cases the algorithms are obtained through the construction of small separating automata, using as black boxes the existing constructions for parity objectives and for mean payoff objectives.

In Pierre Ganty and Davide Bresolin: Proceedings 12th International Symposium on Games, Automata, Logics, and Formal Verification (GandALF 2021), Padua, Italy, 20-22 September 2021, Electronic Proceedings in Theoretical Computer Science 346, pp. 227–240.
Published: 17th September 2021.

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