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A Uniform Framework for Timed Automata

Authors Tomasz Brengos, Marco Peressotti

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Tomasz Brengos
Marco Peressotti

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Tomasz Brengos and Marco Peressotti. A Uniform Framework for Timed Automata. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CONCUR.2016.26

Abstract

Timed automata, and machines alike, currently lack a general mathematical characterisation. In this paper we provide a uniform coalgebraic understanding of these devices. This framework encompasses known behavioural equivalences for timed automata and paves the way for the extension of these notions to new timed behaviours and for the instantiation of established results from the coalgebraic theory as well. Key to this work is the use of lax functors for they allow us to model time flow as a context property and hence offer a general and expressive setting where to study timed systems: the index category encodes "how step sequences form executions" (e.g. whether steps duration get accumulated or kept distinct) whereas the base category encodes "step nature and composition" (e.g. non-determinism and labels). Finally, we develop the notion of general saturation for lax functors and show how equivalences of interest for timed behaviours are instances of this notion. This characterisation allows us to reason about the expressiveness of said notions within a uniform framework and organise them in a spectrum independent from the behavioural aspects encoded in the base category.

Subject Classification

Keywords
  • coalgebras
  • lax functors
  • general saturation
  • timed behavioural equivalence
  • timed language equivalence

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