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First-order logics: some characterizations and closure properties

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Abstract

The characterization of the class of FO[+]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to word bounded languages, this class coincides with the class of semilinear languages. We also study the closure properties of the classes of languages definable in FO[+1], FO[<], FO[+] and FOC[+] under the main classical operations.

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Authors and Affiliations

  1. LIAFA, UMR 7089, 175 Rue du Chevaleret, Paris 13, France

    Christian Choffrut

  2. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Andreas Malcher

  3. Dipartimento di Informatica, Università degli Studi di Milano, via Comelico 39/41, 20135, Milano, Italy

    Carlo Mereghetti & Beatrice Palano

Authors
  1. Christian Choffrut
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  2. Andreas Malcher
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  3. Carlo Mereghetti
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  4. Beatrice Palano
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Corresponding author

Correspondence to Carlo Mereghetti.

Additional information

This work was partially supported by the Italian MURST under the project “PRIN: Aspetti matematici e applicazioni emergenti degli automi e dei linguaggi formali: metodi probabilistici e combinatori in ambito di linguaggi formali”, and by CRUI/DAAD under the project “Programma Vigoni: Reducing complexity by introducing structure”.

A preliminary version has been published in the Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010).

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Choffrut, C., Malcher, A., Mereghetti, C. et al. First-order logics: some characterizations and closure properties. Acta Informatica 49, 225–248 (2012). https://doi.org/10.1007/s00236-012-0157-z

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