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Robustness of Time Petri Nets under Guard Enlargement

Akshay S., Jard C., Hélouët L., Reynier P.-A.

Fundamenta Informaticae

2016

Vol. 143, nr 3/4

207--234

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.

Blending Timed Formal Models with Clock Transition Systems

Jard C., Lime D., Roux O.H.

Fundamenta Informaticae

2014

Vol. 129, nr 1/2

85--100

Networks of Timed Automata (NTA) and Time Petri Nets (TPNs) are well-established formalisms used to model, analyze and control industrial real-time systems. The underlying theories are usually developed in different scientific communities and both formalisms have distinct strong points: for instance, conciseness for TPNs and a more flexible notion of urgency for NTA. The objective of the paper is to introduce a new model allowing the joint use of both TPNs and NTA for the modeling of timed systems. We call it Clock Transition System (CTS). This new model incorporates the advantages of the structure of Petri nets, while introducing explicitly the concept of clocks. Transitions in the network can be guarded by an expression on the clocks and reset a subset of them as in timed automata. The urgency is introduced by a separate description of invariants. We show that CTS allow to express TPNs (even when unbounded) and NTA. For those two classical models, we identify subclasses of CTSs equivalent by isomorphism of their operational semantics and provide (syntactic) translations. The classical state-space computation developed for NTA and then adapted to TPNs can easily be defined for general CTSs. Armed with these merits, the CTS model seems a good candidate to serve as an intermediate theoretical and practical model to factor out the upcoming developments in the TPNs and the NTA scientific communities.