Enumeration of reachable, forbidden, live, and deadlock states of bottom k-th order system (with a 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 S³PR (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 bottom position of the left-side process, below denoted as Bottom-Left ) with a formula depending on parameter k for a subclass of nets with k sharing resources.