The Compound Interest in Relaxing Punctuality

  • Thomas FerrèreEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10951)


Imprecision in timing can sometimes be beneficial: Metric interval temporal logic (MITL), disabling the expression of punctuality constraints, was shown to translate to timed automata, yielding an elementary decision procedure. We show how this principle extends to other forms of dense-time specification using regular expressions. By providing a clean, automaton-based formal framework for non-punctual languages, we are able to recover and extend several results in timed systems. Metric interval regular expressions (MIRE) are introduced, providing regular expressions with non-singular duration constraints. We obtain that MIRE are expressively complete relative to a class of one-clock timed automata, which can be determinized using additional clocks. Metric interval dynamic logic (MIDL) is then defined using MIRE as temporal modalities. We show that MIDL generalizes known extensions of MITL, while translating to timed automata at comparable cost.


Metric Interval Temporal Logic (MITL) Timed Automata Elementary Decision Procedure MITL Formula Integer-bounded Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I thank Eugene Asarin, Tom Henzinger, Oded Maler, Dejan Ničković, and anonymous reviewers of multiple conferences for their helpful feedback.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IST AustriaKlosterneuburgAustria

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