Deciding the topological complexity of Büchi languages *

Michał Skrzypczak (1) , Igor Walukiewicz (2)

1 Institute of Mathematics [Warsaw]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We study the topological complexity of languages of Büchi automata on infinite binary trees. We show that such a language is either Borel and WMSO-definable, or Σ 1 1-complete and not WMSO-definable; moreover it can be algorithmically decided which of the two cases holds. The proof relies on a direct reduction to deciding the winner in a finite game with a regular winning condition.

Mots clés: decidability; 1998 ACM Subject Classification F11 Models of Computation Keywords and phrases tree automata; non-determinism; Borel sets; topological complexity; de- cidability

Domaines: Logique en informatique [cs.LO]

Michał Skrzypczak, Igor Walukiewicz. Deciding the topological complexity of Büchi languages *. ICALP, Jul 2016, Rome, Italy. pp.99:1--99:13, ⟨10.4230/LIPIcs.ICALP.2016.99⟩. ⟨hal-01394829⟩