We define an extension of time Petri nets such that the time at which a transition can fire, also called its firing date, may be dynamically updated. Our extension provides two mechanisms for updating the timing constraints of a net. First, we propose to change the static time interval of a transition each time it is newly enabled; in this case the new time interval is given as a function of the current marking. Next, we allow to update the firing date of a transition when it is persistent, that is when a concurrent transition fires. We show how to carry the widely used state class abstraction to this new kind of time Petri nets and define a class of nets for which the abstraction is exact. We show the usefulness of our approach with two applications: first for scheduling preemptive task, as a poor man’s substitute for stopwatch, then to model hybrid systems with non trivial continuous behavior.
We have shown how to extend the construction to handle fickle transitions. The is certainly the most widely used state space abstraction for Time Petri nets: it is a convenient abstraction for LTL model checking; it is finite when the set of markings is bounded; and it preserves both the markings and traces of the net. The results are slightly different with dynamic , even for the restricted class of translation nets. In particular, we may have an infinite even when the net is bounded. This may be the case, for instance, if we have a transition that can stay persistent infinitely and that is associated to the fickle function @math . This entails that our construction may not terminate, even if the set of markings is bounded. This situation is quite comparable to what occurs with @cite_12 and, like in this model, it is possible to prove that the model-checking problem is undecidable in the general case. This does not mean that our construction is useless in practice, as we show in our examples of Sect. .
@cite_12
1513999490 2109613468 1841167015 2091676842
We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decidability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separations between seemingly related problems. Our main theorem is the very surprising fact that boundedness is undecidable for Petri nets with Reset arcs. We propose a technique for verification of mobile systems. We translate finite control processes, a well-known subset of π-Calculus, into Petri nets, which are subsequently used formodel checking. This translation always yields bounded Petri nets with a small bound, and we develop a technique for computing a non-trivial bound by static analysis. Moreover, we introduce the notion of safe processes, a subset of finite control processes, for which our translation yields safe Petri nets, and show that every finite control process can be translated into a safe one of at most quadratic size. This gives a possibility to translate every finite control process into a safe Petri net, for which efficient unfolding-based verification is possible. Our experiments show that this approach has a significant advantage over other existing tools for verification of mobile systems in terms of memory consumption and runtime. We also demonstrate the applicability of our method on a realistic model of an automated manufacturing system. This paper is concerned with construction of some state space abstractions for Time Petri nets. State class spaces were introduced long ago by Berthomieu and Menasche as finite representations for the typically infinite state spaces of Time Petri nets, preserving their linear time temporal properties. This paper proposes a similar construction that preserves their branching time temporal properties. The construction improves a previous proposal by Yoneda and Ryuba. The method has been implemented, computing experiments are reported. Automata-theoretic representations have proven useful in the automatic and exact analysis of computing systems. We propose a new semantical mapping of π-Calculus processes into place transition Petri nets. Our translation exploits the connections created by restricted names and can yield finite nets even for processes with unbounded name and unbounded process creation. The property of structural stationarity characterises the processes mapped to finite nets. We provide exact conditions for structural stationarity using novel characteristic functions. As application of the theory, we identify a rich syntactic class of structurally stationary processes, called finite handler processes. Our Petri net translation facilitates the automatic verification of a case study modelled in this class.