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)


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.


Temporal Logic Realizability Problem Time Stamp Linear Temporal Logic Winning Strategy 
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.


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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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