Closed form formula construction to enumerate control related states of K-th order S3PR system (with a Top Left side non-sharing resource place) of Petri nets

Earlier, Chao pioneered the very first closed-form solution of the number of reachable and other states for marked graphs (MG) and k-th order system which is the simplest class of S
³
PR (Systems of Simple Sequential Processes with Resources). This paper progresses one step further on enumerating reachable (forbidden, live and deadlock) states for top k-th order systems (one non-sharing resource place in the top position of the left-side process, below denoted as Top-Left ) with a formula depending on parameter k for a subclass of nets with k sharing resources.