Topological Complexity of Locally Finite omega-Languages

Abstract : Locally finite omega-languages were introduced by Ressayre in [Formal Languages defined by the Underlying Structure of their Words, Journal of Symbolic Logic, 53 (4), December 1988, p. 1009-1026]. These languages are defined by local sentences and extend omega-languages accepted by Büchi automata or defined by monadic second order sentences. We investigate their topological complexity. All locally finite omega languages are analytic sets, the class LOC_omega of locally finite omega-languages meets all finite levels of the Borel hierarchy and there exist some locally finite omega-languages which are Borel sets of infinite rank or even analytic but non-Borel sets. This gives partial answers to questions of Simonnet [Automates et Théorie Descriptive, Ph. D. Thesis, Université Paris 7, March 1992] and of Duparc, Finkel, and Ressayre [Computer Science and the Fine Structure of Borel Sets, Theoretical Computer Science, Volume 257 (1-2), 2001, p.85-105].
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00160798
Contributor : Olivier Finkel <>
Submitted on : Sunday, July 8, 2007 - 10:39:15 AM
Last modification on : Friday, April 20, 2018 - 3:44:24 PM
Long-term archiving on : Thursday, April 8, 2010 - 6:43:11 PM

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Olivier Finkel. Topological Complexity of Locally Finite omega-Languages. 2007. ⟨ensl-00160798v1⟩

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