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Interval Logics and ωB-Regular Languages

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Language and Automata Theory and Applications (LATA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7810))

Abstract

In the recent years, interval temporal logics are emerging as a workable alternative to more standard point-based ones. In this paper, we establish an original connection between these logics and ωB-regular languages. First, we provide a logical characterization of regular (resp., ω-regular) languages in the interval logic \(A\mspace{-0.3mu}B\bar{B}\) of Allen’s relations meets, begun by, and begins over finite linear orders (resp., ℕ). Then, we lift such a correspondence to ωB-regular languages by substituting \(A\mspace{-0.3mu}B\bar{B}\bar{A}\) for \(A\mspace{-0.3mu}B\bar{B}\) (\(A\mspace{-0.3mu}B\bar{B}\bar{A}\) is obtained from \(A\mspace{-0.3mu}B\bar{B}\) by adding a modality for Allen’s relation met by). In addition, we show that new classes of extended (ω-)regular languages can be naturally defined in \(A\mspace{-0.3mu}B\bar{B}\bar{A}\).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Udine, Italy

    Angelo Montanari

  2. Department of Pharmacology, University of Verona, Italy

    Pietro Sala

Authors
  1. Angelo Montanari
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  2. Pietro Sala
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Fakultät für Informatik, Institut für Wissens- und Sprachverarbeitung, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Bianca Truthe

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Montanari, A., Sala, P. (2013). Interval Logics and ωB-Regular Languages. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_38

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  • DOI: https://doi.org/10.1007/978-3-642-37064-9_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37063-2

  • Online ISBN: 978-3-642-37064-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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