Half-Positional Objectives Recognized by Deterministic B\"uchi Automata

• Published in: Logical methods in computer science Vol. 20, Issue 3
• Main Authors: Bouyer, Patricia, Casares, Antonio, Randour, Mickael, Vandenhove, Pierre
• Format: Journal Article
• Language: English
• Published: Logical Methods in Computer Science e.V 29-08-2024
• Subjects: computer science - computer science and game theory; computer science - formal languages and automata theory; computer science - logic in computer science
• ISSN: 1860-5974; 1860-5974
• DOI: 10.46298/lmcs-20(3:19)2024

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 B\"uchi automata (a subclass of omega-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 B\"uchi automaton.