Skip to Main content Skip to Navigation
New interface
Journal articles

Wadge Degrees of Infinitary Rational Relations

Abstract : 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).
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download
Contributor : Olivier Finkel Connect in order to contact the contributor
Submitted on : Monday, April 21, 2008 - 9:11:14 PM
Last modification on : Thursday, September 29, 2022 - 2:58:07 PM
Long-term archiving on: : Friday, May 21, 2010 - 1:55:31 AM


Files produced by the author(s)



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⟩



Record views


Files downloads