Robustness of Time Petri Nets under Guard Enlargement

  • S. Akshay
  • Loïc Hélouët
  • Claude Jard
  • Pierre-Alain Reynier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7550)


Robustness of timed systems aims at studying whether infinitesimal perturbations in clock values can result in new discrete behaviors. A model is robust if the set of discrete behaviors is preserved under arbitrarily small (but positive) perturbations. We tackle this problem for Time Petri Nets (TPNs for short) by considering the model of parametric guard enlargement which allows time-intervals constraining the firing of transitions in TPNs to be enlarged by a (positive) parameter.

We show that TPNs are not robust in general and checking if they are robust with respect to standard properties (such as boundedness, safety) is undecidable. We then extend the marking class timed automaton construction for TPNs to a parametric setting, and prove that it is compatible with guard enlargements. We apply this result to the (undecidable) class of TPNs which are robustly bounded (i.e., whose finite set of reachable markings remains finite under infinitesimal perturbations): we provide two decidable robustly bounded subclasses, and show that one can effectively build a timed automaton which is timed bisimilar even in presence of perturbations. This allows us to apply existing results for timed automata to these TPNs and show further robustness properties.


Discrete Move Time Automaton Time Automaton Robustness Problem Reachable Marking 
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 2012

Authors and Affiliations

  • S. Akshay
    • 1
    • 2
  • Loïc Hélouët
    • 1
  • Claude Jard
    • 1
    • 2
  • Pierre-Alain Reynier
    • 3
  1. 1.INRIA/IRISA RennesFrance
  2. 2.ENS Cachan BretagneRennesFrance
  3. 3.CNRS, LIF, UMRAix-Marseille UniversitéMarseilleFrance

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