Polishness of some topologies related to word or tree automata

Olivier Finkel (1) , Olivier Carton (2) , Dominique Lecomte (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

We prove that the B\"uchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the B\"uchi and the Muller topologies are not Polish in this case.

Mots clés: automatic topology; B\"uchi topology; finer topologies; Cantor space; B\"uchi automaton; logic in computer science; infinite words; regular $\omega$-language; Automata and formal languages; B\"uchi tree automaton; logic in computer science; Automata and formal languages; space of infinite labelled binary trees; Muller tree automaton; Polish topology; ACM Subject Classification F11 Models of Computation; F13 Complexity Measures and Classes; F41 Mathematical Logic; F43 Formal Languages Keywords and phrases Automata and formal languages

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

Olivier Finkel, Olivier Carton, Dominique Lecomte. Polishness of some topologies related to word or tree automata . 2018. ⟨hal-01593160v2⟩