Borel Ranks and Wadge Degrees of Omega Context Free Languages

Olivier Finkel (1)

1 ELM - Équipe de Logique Mathématique

We show that, from a topological point of view, considering the Borel and the Wadge hierarchies, 1-counter Büchi automata have the same accepting power than Turing machines equipped with a Büchi acceptance condition. In particular, for each recursive non null ordinal alpha, there exist some Sigma^0_alpha-complete and some Pi^0_alpha-complete omega languages accepted by Büchi 1-counter automata.

Domaines: Logique en informatique [cs.LO]; Informatique et théorie des jeux [cs.GT]; Complexité [cs.CC]; Logique [math.LO]

Olivier Finkel. Borel Ranks and Wadge Degrees of Omega Context Free Languages. 2005, pp.129-138. ⟨hal-00117508⟩