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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.

Distributed Timed Automata with Independently Evolving Clocks

Akshay S., Bollig B., Gastin P., Mukund M., Kumar K. N.

Fundamenta Informaticae

2014

Vol. 130, nr 4

377--407

We propose a model of distributed timed systems where each component is a timed automaton with a set of local clocks that evolve at a rate independent of the clocks of the other components. A clock can be read by any component in the system, but it can only be reset by the automaton it belongs to. There are two natural semantics for such systems. The universal semantics captures behaviors that hold under any choice of clock rates for the individual components. This is a natural choice when checking that a system always satisfies a positive specification. To check if a system avoids a negative specification, it is better to use the existential semantics—the set of behaviors that the system can possibly exhibit under some choice of clock rates. We show that the existential semantics always describes a regular set of behaviors. However, in the case of universal semantics, checking emptiness or universality turns out to be undecidable. As an alternative to the universal semantics, we propose a reactive semantics that allows us to check positive specifications and yet describes a regular set of behaviors.