Fragments of First-Order Logic over Infinite Words (Extended Abstract)

Abstract : We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for ω-languages: Σ_2 , ∆_2 , FO^2∩ Σ_2 (and by duality FO^2∩ Π_2 ), and FO^2. These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke [20] and Bojanczyk [2] and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties.
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Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.325-336, 2009, Proceedings of the 26th Annual Symposium on the Theoretical Aspects of Computer Science
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  • HAL Id : inria-00359319, version 1

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Volker Diekert, Manfred Kufleitner. Fragments of First-Order Logic over Infinite Words (Extended Abstract). Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.325-336, 2009, Proceedings of the 26th Annual Symposium on the Theoretical Aspects of Computer Science. 〈inria-00359319〉

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