Realizability of Real-Time Logics

Authors:
Laurent Doyen;Gilles Geeraerts;Jean-Francois Raskin;Julien Reichert
Affiliations:
Département d'Informatique, Université Libre de Bruxelles (U.L.B.),;Département d'Informatique, Université Libre de Bruxelles (U.L.B.),;Département d'Informatique, Université Libre de Bruxelles (U.L.B.),;École Normale Supérieure de Cachan,
Venue:
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
Year:
2009

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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.