Modeling and reachability analysis of synchronizing transitions bounded Petri net systems based upon semi-tensor product of matrices

Abstract

The reachability problem of synchronizing transitions bounded Petri net systems (BPNSs) is investigated in this paper by constructing a mathematical model for dynamics of BPNS. Using the semi-tensor product (STP) of matrices, the dynamics of BPNSs, which can be viewed as a combination of several small bounded subnets via synchronizing transitions, are described by an algebraic equation. When the algebraic form for its dynamics is established, we can present a necessary and sufficient condition for the reachability between any marking (or state) and initial marking. Also, we give a corresponding algorithm to calculate all of the transition paths between initial marking and any target marking. Finally, an example is shown to illustrate proposed results. The key advantage of our approach, in which the set of reachable markings of BPNSs can be expressed by the set of reachable markings of subnets such that the big reachability set of BPNSs do not need generate, is partly avoid the state explosion problem of Petri nets (PNs).