Fine hierarchies and m-reducibilities in theoretical computer science
Theoretical Computer Science
Linear game automata: decidable hierarchy problems for stripped-down alternating tree automata
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
On the accepting power of 2-tape büchi automata
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
The expressive power of analog recurrent neural networks on infinite input streams
Theoretical Computer Science
There exist some ω-powers of any Borel rank
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
On the topological complexity of ω-languages of non-deterministic Petri nets
Information Processing Letters
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We show that the Borel hierarchy of the class of context free $\omega$-languages, or even of the class of $\omega$-languages accepted by Büchi 1-counter automata, is the same as the Borel hierarchy of the class of $\omega$-languages accepted by Turing machines with a Büchi acceptance condition. In particular, for each recursive non-null ordinal $\alpha$, there exist some ${\bf \Sigma}^0_\alpha$-complete and some ${\bf \Pi}^0_\alpha$-complete $\omega$-languages accepted by Büchi 1-counter automata. And the supremum of the set of Borel ranks of context free $\omega$-languages is an ordinal $\gamma_2^1$ that is strictly greater than the first non-recursive ordinal $\omega_1^{\mathrm{CK}}$. We then extend this result, proving that the Wadge hierarchy of context free $\omega$-languages, or even of $\omega$-languages accepted by Büchi 1-counter automata, is the same as the Wadge hierarchy of $\omega$-languages accepted by Turing machines with a Büchi or a Muller acceptance condition.