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Distance on Timed Words and Applications

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Formal Modeling and Analysis of Timed Systems (FORMATS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11022))

Abstract

We introduce and study a new (pseudo) metric on timed words having several advantages:

  • it is global: it applies to words having different number of events;

  • it is realistic and takes into account imprecise observation of timed events; thus it reflects the fact that the order of events cannot be observed whenever they are very close to each other;

  • it is suitable for quantitative verification of timed systems: we formulate and solve quantitative model-checking and quantitative monitoring in terms of the new distance, with reasonable complexity;

  • it is suitable for information-theoretical analysis of timed systems: due to its pre-compactness the quantity of information in bits per time unit can be correctly defined and computed.

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Notes

  1. 1.

    Generally, shared clocks could be considered, but they are not needed in this paper.

  2. 2.

    As usual in information theory, all logarithms are base 2.

  3. 3.

    when \(T<b\), the set of interest \(F^\varSigma _{b,T}\) is empty.

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Acknowledgements

The authors thank James Worrell and François Laroussinie for their valuable advice on complexity analysis.

Author information

Authors and Affiliations

  1. IRIF, University Paris Diderot and CNRS, Paris, France

    Eugene Asarin & Aldric Degorre

  2. VERIMAG, University Grenoble Alpes and CNRS, Grenoble, France

    Nicolas Basset

Authors
  1. Eugene Asarin
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  2. Nicolas Basset
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  3. Aldric Degorre
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Corresponding author

Correspondence to Aldric Degorre .

Editor information

Editors and Affiliations

  1. Institute of Software, Chinese Academy of Sciences, Beijing, China

    David N. Jansen

  2. Kansas State University, Manhattan, Kansas, USA

    Pavithra Prabhakar

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Asarin, E., Basset, N., Degorre, A. (2018). Distance on Timed Words and Applications. In: Jansen, D., Prabhakar, P. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2018. Lecture Notes in Computer Science(), vol 11022. Springer, Cham. https://doi.org/10.1007/978-3-030-00151-3_12

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  • DOI: https://doi.org/10.1007/978-3-030-00151-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00150-6

  • Online ISBN: 978-3-030-00151-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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