The Automatic Baire Property and An Effective Property of ω-Rational Functions

We prove that $\omega$-regular languages accepted by B\"uchi or Muller automata satisfy an effective automata-theoretic version of the Baire property. Then we use this result to obtain a new effective property of rational functions over infinite words which are realized by finite state B\"uchi transducers: for each such function $F: \Sigma^\omega \rightarrow \Gamma^\omega$, one can construct a deterministic B\"uchi automaton $\mathcal{A}$ accepting a dense ${\bf \Pi}^0_2$-subset of $\Sigma^\omega$ such that the restriction of $F$ to $L(\mathcal{A})$ is continuous

The Automatic Baire Property and an Effective Property of ω-Rational Functions

International audienceWe prove that ω-regular languages accepted by Büchi or Muller automata satisfy an effective automata-theoretic version of the Baire property. Then we use this result to obtain a new effective property of rational functions over infinite words which are realized by finite state Büchi transducers: for each such function F : Σ^ω → Γ^ω , one can construct a deterministic Büchi automaton A accepting a dense Π^0_2-subset of Σ^ω such that the restriction of F to L(A) is continuous