Wadge hierarchy of omega context-free languages

On the Length of the Wadge Hierarchy of Omega-Context Free Languages

We prove in this paper that the length of the Wadge hierarchy of ω-context free languages is greater than the Cantor ordinal εω, which is the ω th fixed point of the ordinal exponentiation of base ω. We show also that there exist some Σ0ω-complete ω-context free languages, improving previous results on ω-context free languages and the Borel hierarchy.

[hal-00114310, v1] On the Wadge Hierarchy of Omega Context Free Languages

Topological Complexity of Context-Free omega-Languages: A Survey

We survey recent results on the topological complexity of context-free ω-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of non-deterministic or deterministic context-free ω-languages. We study also decision problems, the links with the notions of ambiguity and of degrees of amb...

Borel Ranks and Wadge Degrees of Context Free omega-Languages

We show that the Borel hierarchy of the class of context free ω-languages, or even of the class of ω-languages accepted by Büchi 1-counter automata, is the same as the Borel hierarchy of the class of ω-languages accepted by Turing machines with a Büchi acceptance condition. In particular, for each recursive non null ordinal α, there exist some Σ α -complete and some Π α -complete ω-languages ac...

J an 2 00 8 On the length of the Wadge hierarchy of ω - context free languages ∗

We prove in this paper that the length of the Wadge hierarchy of ω-context free languages is greater than the Cantor ordinal εω, which is the ω th fixed point of the ordinal exponentiation of base ω. We show also that there exist some Σ0ω-complete ω-context free languages, improving previous results on ω-context free languages and the Borel hierarchy.