Borel Ranks and Wadge Degrees of Context Free Omega Languages - Archive ouverte HAL
Article Dans Une Revue Mathematical Structures in Computer Science Année : 2006

Borel Ranks and Wadge Degrees of Context Free Omega Languages

Olivier Finkel
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Résumé

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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Dates et versions

hal-00139169 , version 1 (29-03-2007)
hal-00139169 , version 2 (09-12-2007)

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