Enumeration of reachable states for arbitrary marked graphs

This study develops the theory to enumerate the reachable states of marked graphs that are a simple subclass of Petri nets where every place has a single input and output transition without the construction of a reachability graph (RG), which, as far as the authors know, does not receive much attention in the previous studies. Usually, it is necessary to enumerate all the reachable states of a plant to be controlled. However, the construction of an RG suffers from the state explosion problem. This study tackles the problem for a special class of Petri nets by expressing and finding the number of reachable states in an algebraic way.