Lower and Upper Bounds in Zone Based Abstractions of Timed Automata

  • Gerd Behrmann
  • Patricia Bouyer
  • Kim G. Larsen
  • Radek Pelánek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2988)


Timed automata have an infinite semantics. For verification purposes, one usually uses zone based abstractions w.r.t. the maximal constants to which clocks of the timed automaton are compared. We show that by distinguishing maximal lower and upper bounds, significantly coarser abstractions can be obtained. We show soundness and completeness of the new abstractions w.r.t. reachability. We demonstrate how information about lower and upper bounds can be used to optimise the algorithm for bringing a difference bound matrix into normal form. Finally, we experimentally demonstrate that the new techniques dramatically increases the scalability of the real-time model checker Uppaal.


Normal Form Simulation Relation Successor Computation Time Automaton Maximal Bound 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Gerd Behrmann
    • 1
  • Patricia Bouyer
    • 2
  • Kim G. Larsen
    • 1
  • Radek Pelánek
    • 3
  1. 1.BRICSAalborg UniversityDenmark
  2. 2.LSV, CNRS & ENS de Cachan, UMR 8643France
  3. 3.Masaryk University BrnoCzech Republic

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