Borel ranks and wadge degrees of context free ω-languages

Authors:
Olivier Finkel
Affiliations:
Equipe de Logique Mathématique, U.F.R. de Mathématiques, Université Paris 7, Paris cedex 05, France
Venue:
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Year:
2005

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Abstract

We determine completely the Borel hierarchy of the class of context free ω-languages, showing that, for each recursive non null ordinal α, there exist some Σ$_{\alpha}^{\rm 0}$-complete and some Π$_{\alpha}^{\rm 0}$-complete ω-languages accepted by Büchi 1-counter automata.