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Timed Temporal Logics

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Models, Algorithms, Logics and Tools

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10460))

Abstract

Since the early 1990’s, classical temporal logics have been extended with timing constraints. While temporal logics only express contraints on the order of events, their timed extensions can add quantitative constraints on delays between those events. We survey expressiveness and algorithmic results on those logics, and discuss semantic choices that may look unimportant but do have an impact on the questions we consider.

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Notes

  1. 1.

    Zero-delay transitions are not allowed here, but could be included without affecting the presented results.

  2. 2.

    Rational bounds could be considered at the expense of scaling all constants by an appropriate factor.

  3. 3.

    That is, for every \(a \in \varSigma \), \(f_{\text {inter}}(a,\bullet ) = a_1\) and \(f_{\text {inter}}(\bullet ,a)=a_2\).

  4. 4.

    As shown in [30] this property fails without the assumption of finite variability.

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Author information

Authors and Affiliations

  1. LSV, CNRS & ENS Paris-Saclay, Cachan, France

    Patricia Bouyer

  2. IRIF, CNRS & Université Paris Diderot, Paris, France

    François Laroussinie

  3. IRISA, CNRS & INRIA & Université Rennes 1, Rennes, France

    Nicolas Markey

  4. Max Planck Institute for Software Systems, Saarbrücken, Germany

    Joël Ouaknine

  5. Department of Computer Science, Oxford University, Oxford, UK

    Joël Ouaknine & James Worrell

Authors
  1. Patricia Bouyer
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  2. François Laroussinie
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  3. Nicolas Markey
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  4. Joël Ouaknine
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  5. James Worrell
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Correspondence to Patricia Bouyer .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Luca Aceto

  2. Aalborg University, Aalborg, Denmark

    Giorgio Bacci

  3. Aalborg University, Aalborg, Denmark

    Giovanni Bacci

  4. Reykjavík University, Reykjavik, Iceland

    Anna Ingólfsdóttir

  5. Inria Campus Beaulieu, Rennes, France

    Axel Legay

  6. Aalborg University, Aalborg, Denmark

    Radu Mardare

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Bouyer, P., Laroussinie, F., Markey, N., Ouaknine, J., Worrell, J. (2017). Timed Temporal Logics. In: Aceto, L., Bacci, G., Bacci, G., Ingólfsdóttir, A., Legay, A., Mardare, R. (eds) Models, Algorithms, Logics and Tools. Lecture Notes in Computer Science(), vol 10460. Springer, Cham. https://doi.org/10.1007/978-3-319-63121-9_11

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