Topological Complexity of Locally Finite omega-Languages

Olivier Finkel (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

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].

Mots clés: Local sentences; Locally finite omega-languages; Topological complexity; Borel hierarchy; Analytic sets

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]; Informatique et langage [cs.CL]; Logique [math.LO]

Olivier Finkel. Topological Complexity of Locally Finite omega-Languages. Archive for Mathematical Logic, 2008, 47 (6), pp.625-651. ⟨ensl-00160798v2⟩