A New Modality for Almost Everywhere Properties in Timed Automata

  • Houda Bel Mokadem
  • Béatrice Bérard
  • Patricia Bouyer
  • François Laroussinie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3653)


The context of this study is timed temporal logics for timed automata. In this paper, we propose an extension of the classical logic TCTL with a new Until modality, called “Until almost everywhere”. In the extended logic, it is possible, for instance, to express that a property is true at all positions of all runs, except on a negligible set of positions. Such properties are very convenient, for example in the framework of boolean program verification, where transitions result from changing variable values. We investigate the expressive power of this modality and in particular, we prove that it cannot be expressed with classical TCTL modalities. However, we show that model-checking the extended logic remains PSPACE-complete as for TCTL.


Action Transition Temporal Logic Atomic Proposition Extended Logic Linear Time Temporal Logic 
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 2005

Authors and Affiliations

  • Houda Bel Mokadem
    • 1
  • Béatrice Bérard
    • 2
  • Patricia Bouyer
    • 1
  • François Laroussinie
    • 1
  1. 1.LSV, CNRS & ENS de CachanCachan CedexFrance
  2. 2.LAMSADE, CNRS & Université Paris-DauphineParis Cedex 16France

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