An Effective Property of ω-Rational Functions

09/10/2018

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by   Olivier Finkel, et al.

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We 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.