Borel Ranks and Wadge Degrees of Context Free Omega Languages

Abstract : We show that, from a topological point of view, considering the Borel and the Wadge hierarchies, 1-counter Büchi automata have the same accepting power than Turing machines equipped with a Büchi acceptance condition. In particular, for every non null recursive ordinal alpha, there exist some Sigma^0_alpha-complete and some Pi^0_alpha-complete omega context free languages accepted by 1-counter Büchi automata, and the supremum of the set of Borel ranks of context free omega languages is the ordinal gamma^1_2 which is strictly greater than the first non recursive ordinal. This very surprising result gives answers to questions of H. Lescow and W. Thomas [Logical Specifications of Infinite Computations, In:"A Decade of Concurrency", LNCS 803, Springer, 1994, p. 583-621].
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https://hal.archives-ouvertes.fr/hal-00139169
Contributeur : Olivier Finkel <>
Soumis le : dimanche 9 décembre 2007 - 20:59:04
Dernière modification le : vendredi 4 janvier 2019 - 17:32:32
Document(s) archivé(s) le : lundi 23 mai 2011 - 16:53:08

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  • HAL Id : hal-00139169, version 2
  • ARXIV : 0712.1359

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Olivier Finkel. Borel Ranks and Wadge Degrees of Context Free Omega Languages. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2006, 16 (5), pp.813-840. ⟨hal-00139169v2⟩

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