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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.