Interval Logics and ωB-Regular Languages

  • Angelo Montanari
  • Pietro Sala
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7810)


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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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Angelo Montanari
    • 1
  • Pietro Sala
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversity of UdineItaly
  2. 2.Department of PharmacologyUniversity of VeronaItaly

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