Reachability analysis for a class of Petri nets

In this paper, we study the reachability problem for the class of (strictly) monotone Petri nets that we define based on algebraic conditions. More specifically, given a (strictly) monotone Petri net, an initial marking and a final target marking, we devise an algorithm that verifies if there is a firing sequence that leads the net from the initial marking to the final target marking. The algorithm operates essentially by enumerating markings that are reachable by finite firing sequences of length less than or equal to a bound which we characterize exactly. We also establish that reachability of the final target marking is possible for the initial marking if and only if reachability is possible within this bounded number of transition firings. The algorithm is important and useful for a variety of applications including fault diagnosis and control. As an example, we discuss how the algorithm can be used to determine if certain faulty or undesirable states are possible given a sequence of observations in a labeled Petri net. In addition, the algorithm can be used to verify whether a given model is deadlock-free (deadlock checking is recursively equivalent to the reachability problem) as a deadlock-free system model is a typical assumption in many fault diagnosis methods.