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

Olivier Finkel (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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.

Mots clés: Decision problems; regular languages of infinite words; infinitary rational relations; omega rational functions; topology; automatic Baire property; points of continuity

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]

Olivier Finkel. The Automatic Baire Property and An Effective Property of ω-Rational Functions. 2019. ⟨hal-01870467v2⟩