Closed form formula construction to enumerate control related states of Bottom Left k-net S3PR system (with a Bottom 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 Bottom Left k-net systems (one non-sharing resource place in the Bottom position of the right-side process, below denoted as Bottom-Left-k-net) with a formula depending on parameter k for a subclass of nets with k sharing resources.