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- Title
HALF-POSITIONAL OBJECTIVES RECOGNIZED BY DETERMINISTIC BÜCHI AUTOMATA.
- Authors
BOUYER, PATRICIA; CASARES, ANTONIO; RANDOUR, MICKAEL; VANDENHOVE, PIERRE
- Abstract
In two-player games on graphs, the simplest possible strategies are those that can be implemented without any memory. These are called positional strategies. In this paper, we characterize objectives recognizable by deterministic Büchi automata (a subclass of ω-regular objectives) that are half-positional, that is, for which the protagonist can always play optimally using positional strategies (both over finite and infinite graphs). Our characterization consists of three natural conditions linked to the language-theoretic notion of right congruence. Furthermore, this characterization yields a polynomial-time algorithm to decide half-positionality of an objective recognized by a given deterministic Büchi automaton.
- Subjects
POLYNOMIAL time algorithms; STRATEGY games; ROBOTS; MEMORY; GAMES
- Publication
Logical Methods in Computer Science (LMCS), 2024, Vol 20, Issue 3, p19:1
- ISSN
1860-5974
- Publication type
Article
- DOI
10.46298/LMCS-20(3:19)2024