Fragments of First-Order Logic over Infinite Words

Authors Volker Diekert, Manfred Kufleitner

Thumbnail PDF


  • Filesize: 184 kB
  • 12 pages

Document Identifiers

Author Details

Volker Diekert
Manfred Kufleitner

Cite AsGet BibTex

Volker Diekert and Manfred Kufleitner. Fragments of First-Order Logic over Infinite Words. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 325-336, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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.
  • Infinite words
  • Regular languages
  • First-order logic
  • Automata theory
  • Semigroups
  • Topology


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail