When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2009.1818
URN: urn:nbn:de:0030-drops-18185
URL: http://drops.dagstuhl.de/opus/volltexte/2009/1818/
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### Fragments of First-Order Logic over Infinite Words

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### Abstract

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.

### BibTeX - Entry

@InProceedings{diekert_et_al:LIPIcs:2009:1818,
author =	{Volker Diekert and Manfred Kufleitner},
title =	{{Fragments of First-Order Logic over Infinite Words}},
booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
pages =	{325--336},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-09-5},
ISSN =	{1868-8969},
year =	{2009},
volume =	{3},
editor =	{Susanne Albers and Jean-Yves Marion},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},