Descriptive Set Theory and $\omega$-Powers of Finitary Languages

Olivier Finkel (1) , Dominique Lecomte (2)

1 ELM - Equipe de Logique Mathématique
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

The ω-power of a finitary language L over a finite alphabet Σ is the language of infinite words over Σ defined by L ∞ := {w 0 w 1. .. ∈ Σ ω | ∀i ∈ ω w i ∈ L}. The ω-powers appear very naturally in Theoretical Computer Science in the characterization of several classes of languages of infinite words accepted by various kinds of automata, like Büchi automata or Büchi pushdown automata. We survey some recent results about the links relating Descriptive Set Theory and ω-powers.

Mots clés: Languages of finite or infinite words; context-free; one-counter automaton; ω-power; topological complexity; Borel class; complete set

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

Olivier Finkel, Dominique Lecomte. Descriptive Set Theory and $\omega$-Powers of Finitary Languages. Adrian Rezus. Contemporary Logic and Computing, 1, College Publications, pp.518-541, 2020, Landscapes in Logic. ⟨hal-02898919⟩