Affiliations: [a] Indian Institute of Technology, Bombay, India. [email protected] | [b] INRIA/IRISA, Rennes, France. [email protected] | [c] Université de Nantes, Nantes, France. [email protected] | [d] Aix Marseille Université, CNRS, LIF UMR 7279, F-13288, Marseille, France. [email protected]
Correspondence:
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Address for correspondence: Laboratoire d’Informatique Fondamentale de Marseille, Parc Scientifique et Technologique de Luminy, 163 avenue de Luminy - Case 901, F-13288 Marseille Cedex 9, France
Note: [*] This work was partly supported by ANR projects ImpRo (ANR-2010-BLAN-0317) and ECSPER (ANR-2009-JCJC-0069).
Note: [†] This work was partly supported by DST-INSPIRE award [IFA12-MA-17].
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 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.
Keywords: Time Petri nets, Robustness, Timed automata
