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Online Timed Pattern Matching Using Derivatives

  • Dogan Ulus
  • Thomas Ferrère
  • Eugene Asarin
  • Oded Maler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9636)

Abstract

Timed pattern matching consists in finding all segments of a dense-time Boolean signal that match a pattern defined by a timed regular expression. This problem has been formulated and solved in [17] via an offline algorithm that takes the signal and expression as inputs and produces the set of all matches, represented as a finite union of two-dimensional zones. In this work we develop an online version of this approach where the input signal is presented incrementally and the matching is computed incrementally as well.

Naturally, the concept of derivatives of regular expressions due to Brzozowski [6] can play a role in defining what remains to match after having read a prefix of the signal. However the adaptation of this concept is not a straightforward for two reasons: the dense infinite-state nature of timed behaviors and the fact that we are interested in matching, not only in prefix acceptance. To resolve these issues we develop an alternative theory of signals and expressions based on absolute time and show how derivatives are defined and computed in this setting. We then implement an online timed pattern matching algorithm based on these results.

Keywords

Temporal Logic Regular Expression Constant Signal Propositional Variable Empty Word 
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.

Notes

Acknowledgement

This work was partially supported by the French ANR projects EQINOCS and CADMIDIA and benefitted from useful comments made by anonymous referees.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Dogan Ulus
    • 1
  • Thomas Ferrère
    • 1
  • Eugene Asarin
    • 2
  • Oded Maler
    • 1
  1. 1.VERIMAG Université Grenoble-Alpes/CNRSGrenobleFrance
  2. 2.IRIF, Université Paris Diderot/CNRSParisFrance

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