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Timed Symbolic Dynamics

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Formal Modeling and Analysis of Timed Systems (FORMATS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9268))

Abstract

We introduce a theory of timed symbolic dynamics unifying results from timed automata theory and symbolic dynamics. The timed sofic shift spaces we define are a way of seeing timed regular languages as shift spaces on general alphabets (in classical symbolic dynamics, sofic shift spaces correspond to regular languages). We show that morphisms of shift spaces on general alphabets can be approximated by sliding block codes resulting in a generalised version of the so-called Curtis-Hedlund-Lyndon Theorem. We provide a new measure for timed languages by characterising the Gromov-Lindenstrauss-Weiss metric mean dimension for timed shift spaces and illustrate it on several examples. We revisit recent results on volumetry of timed languages in terms of timed symbolic dynamics. In particular we explain the discretisation of timed shift spaces and their entropy.

This research is supported in part by ERC Advanced Grant VERIWARE and was also supported by the ANR project EQINOCS (ANR-11-BS02-004). The present article is an improved and shortened version of Chapter 5 of the PhD thesis [10]. Omitted proofs and extra details can be found in the technical report [12].

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Author information

Authors and Affiliations

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

    Nicolas Basset

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  1. Nicolas Basset
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Correspondence to Nicolas Basset .

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Editors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    Sriram Sankaranarayanan

  2. University of Florence, Florence, Italy

    Enrico Vicario

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Basset, N. (2015). Timed Symbolic Dynamics. In: Sankaranarayanan, S., Vicario, E. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2015. Lecture Notes in Computer Science(), vol 9268. Springer, Cham. https://doi.org/10.1007/978-3-319-22975-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-22975-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22974-4

  • Online ISBN: 978-3-319-22975-1

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