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Robustness of Time Petri Nets under Guard Enlargement

Sundararaman Akshay 1 Loïc Hélouët 2 Claude Jard 3 Pierre-Alain Reynier 4
2 SUMO - SUpervision of large MOdular and distributed systems
Inria Rennes – Bretagne Atlantique , IRISA-D4 - LANGAGE ET GÉNIE LOGICIEL
LINA - Laboratoire d'Informatique de Nantes Atlantique
4 MOVE - Modélisation et Vérification
LIF - Laboratoire d'informatique Fondamentale de Marseille
Abstract : 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 behav- iors 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.
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Submitted on : Tuesday, October 11, 2016 - 3:01:43 PM
Last modification on : Friday, January 24, 2020 - 1:23:43 AM

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Sundararaman Akshay, Loïc Hélouët, Claude Jard, Pierre-Alain Reynier. Robustness of Time Petri Nets under Guard Enlargement . Fundamenta Informaticae, Polskie Towarzystwo Matematyczne, 2016, 143 (3-4), pp.207-234. ⟨10.3233/FI-2016-1312⟩. ⟨hal-01379431⟩



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