2026/02/10 by Olivier Idir · 1 voice
Computer Science · #cs.FL
paper · pdf · doi:10.48550/arxiv.2602.09896
arxiv published 2026/02/10 · arxiv updated 2026/04/24
An ω-regular language is Eve-positional if, in all games with this language as objective, the existential player can play optimally without keeping any information from the previous moves. This notion plays a crucial role in verification, automata theory and synthesis. Casares and Ohlmann recently gave several characterisations of Eve-positionality of ω-regular languages. For this, they introduce the notion of ε-complete parity automaton and show (among other results) that an ω-regular language is Eve-positional if and only if it can be recognised by some ε-completion of a deterministic parity automaton. Colcombet and Idir built on their work, and obtained a more direct algebraic characterisation of Eve-positionality. We introduce a new formalism that characterises the Eve-positional languages, consisting of a restriction of non-deterministic Büchi automata. This allows us to complete a missing implication in Casares and Ohlmann's work. We then use this formalism to describe a determinization procedure for non-deterministic Büchi automata recognising such languages, with size blow-up at most factorial. We also show that this construction is state-wise optimal for languages over sufficiently complete alphabets.