Modeling and reachability analysis of a class of Petri nets via semi-tensor product of matrices

This paper investigates the matrix expression of state equation and reachability of a class of Petri nets (PNs) by using the semi-tensor product of matrices (STP). First, we get the formula for the number of states of the PNs based on the combinatorial mathematics method. The states and transitions of the PNs are expressed as vector forms, respectively, then the state equation of the PNs is established by using STP. Second, the transition-state adjacency matrix (TSAM) of the PNs is proposed, several necessary and sufficient conditions are obtained for the reachability of the PNs by using this state equation and TSAM. An algorithm is also designed to find all the firing sequences of any two reachable states. Finally, an example is presented to illustrate the theoretical results in this paper and shows that the new results are very effective in investigating the reachability of the PNs.