eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2009-02-19
325
336
10.4230/LIPIcs.STACS.2009.1818
article
Fragments of First-Order Logic over Infinite Words
Diekert, Volker
Kufleitner, Manfred
We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic $\mathrm{FO}[<]$ for $\omega$-languages: $\Sigma_2$, $\Delta_2$, $\mathrm{FO}^2 \cap \Sigma_2$ (and by duality $\mathrm{FO}^2 \cap \Pi_2$), and $\mathrm{FO}^2$. 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 (1998) and Boja{\'n}czyk (2008) and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol003-stacs2009/LIPIcs.STACS.2009.1818/LIPIcs.STACS.2009.1818.pdf
Infinite words
Regular languages
First-order logic
Automata theory
Semigroups
Topology