On Reachability in Autonomous Continuous Petri Net Systems

Fluidification is a common relaxation technique used to deal in a more friendly way with large discrete event dynamic systems. In Petri nets, fluidification leads to continuous Petri nets systems in which the firing amounts are not restricted to be integers. For these systems reachability can be interpreted in several ways. The concepts of reachability and lim-reachability were considered in [7]. They stand for those markings that can be reached with a finite and an infinite firing sequence respectively. This paper introduces a third concept, the δ-reachability. A marking is δ-reachable if the system can get arbitrarily close to it with a finite firing sequence. A full characterization, mainly based on the state equation, is provided for all three concepts for general nets. Under the condition that every transition is fireable at least once, it holds that the state equation does not have spurious solutions if δ-reachability is considered. Furthermore, the differences among the three concepts are in the border points of the spaces they define. For mutual lim-reachability and δ-reachability among markings, i.e., reversibility, a necessary and sufficient condition is provided in terms of liveness.