Refinements and abstractions of signal-event (timed) languages

  • Authors:
  • Béatrice Bérard;Paul Gastin;Antoine Petit

  • Affiliations:
  • LAMSADE, Université Paris Dauphine & CNRS, Paris, France;LSV, ENS de Cachan & CNRS, Cachan, France;LSV, ENS de Cachan & CNRS, Cachan, France

  • Venue:
  • FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
  • Year:
  • 2006

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Abstract

In the classical framework of formal languages, a refinement operation is modeled by a substitution and an abstraction by an inverse substitution. These mechanisms have been widely studied, because they describe a change in the specification level, from an abstract view to a more concrete one, or conversely. For timed systems, there is up to now no uniform notion of substitutions. In this paper, we study the timed substitutions in the general framework of signal-event languages, where both signals and events are taken into account. We prove that regular signal-event languages are closed under substitutions and inverse substitutions.