Wadge Degrees of Infinitary Rational Relations - ENS de Lyon - École normale supérieure de Lyon Access content directly
Journal Articles Mathematics in Computer Science Year : 2008

Wadge Degrees of Infinitary Rational Relations


We show that, from the topological point of view, 2-tape Büchi automata have the same accepting power as Turing machines equipped with a Büchi acceptance condition. The Borel and the Wadge hierarchies of the class RAT_omega of infinitary rational relations accepted by 2-tape Büchi automata are equal to the Borel and the Wadge hierarchies of omega-languages accepted by real-time Büchi 1-counter automata or by Büchi Turing machines. In particular, for every non-null recursive ordinal $\alpha$, there exist some $\Sigma^0_\alpha$-complete and some $\Pi^0_\alpha$-complete infinitary rational relations. And the supremum of the set of Borel ranks of infinitary rational relations is an ordinal $\gamma^1_2$ which is strictly greater than the first non-recursive ordinal $\omega_1^{CK}$. This very surprising result gives answers to questions of Simonnet (1992) and of Lescow and Thomas (1988,1994).
Fichier principal
Vignette du fichier
Wadge-degrees-rat-relations.pdf (246.19 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

ensl-00274931 , version 1 (21-04-2008)



Olivier Finkel. Wadge Degrees of Infinitary Rational Relations. Mathematics in Computer Science, 2008, 2 (1), pp.85-102. ⟨10.1007/s11786-008-0045-7⟩. ⟨ensl-00274931⟩
155 View
253 Download



Gmail Facebook X LinkedIn More