Realizability of Real-Time Logics

  • Laurent Doyen
  • Gilles Geeraerts
  • Jean-Francois Raskin
  • Julien Reichert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5813)

Abstract

We study the realizability problem for specifications of reactive systems expressed in real-time linear temporal logics. The logics we consider are subsets of MITL (Metric Interval Temporal Logic), a logic for which the satisfiability and validity problems are decidable, a necessary condition for the realizability problem to be decidable. On the positive side, we show that the realizability of LTL extended with past real-time formulas is decidable in 2EXPTIME, with a matching lower bound. On the negative side, we show that a simple extension of this decidable fragment with future real-time formulas leads to undecidability. In particular, our results imply that the realizability problem is undecidable for ECL (Event Clock Logic), and therefore also for MITL.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Laurent Doyen
    • 1
  • Gilles Geeraerts
    • 1
  • Jean-Francois Raskin
    • 1
  • Julien Reichert
    • 2
  1. 1.Département d’InformatiqueUniversité Libre de Bruxelles (U.L.B.)Belgium
  2. 2.École Normale Supérieure de CachanFrance

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