Discrete Event Dynamic Systems

, Volume 17, Issue 2, pp 133–158

Reachability Problems and Abstract State Spaces for Time Petri Nets with Stopwatches

  • Bernard Berthomieu
  • Didier Lime
  • Olivier H. Roux
  • François Vernadat
Article

DOI: 10.1007/s10626-006-0011-y

Cite this article as:
Berthomieu, B., Lime, D., Roux, O.H. et al. Discrete Event Dyn Syst (2007) 17: 133. doi:10.1007/s10626-006-0011-y

Abstract

Several extensions of Time Petri nets (TPNs) have been proposed for modeling suspension and resumption of actions in timed systems. We first introduce a simple class of TPNs extended with stopwatches (SwTPNs), and present a semi-algorithm for building exact representations of the behavior of SwTPNs, based on the known state class method for Time Petri nets. Then, we prove that state reachability in SwTPNs and all similar models is undecidable, even when bounded, which solves an open problem. Finally, we discuss overapproximation methods yielding finite abstractions of their behavior for a subclass of bounded SwTPNs, and propose a new one based on a quantization of the polyhedra representing temporal information. By adjusting a parameter, the exact behavior can be approximated as closely as desired. The methods have been implemented, experiments are reported.

Keywords

Time Petri nets Stopwatches State classes Reachability Decidability Approximation Real-time systems modeling and verification 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Bernard Berthomieu
    • 1
  • Didier Lime
    • 2
  • Olivier H. Roux
    • 2
  • François Vernadat
    • 1
  1. 1.LAAS-CNRSToulouseFrance
  2. 2.IRCCyN1, rue de la NoëNantesFrance