Closed Form Formula Construction to Enumerate Control Related States of Middle-Left K-Th Order S3PR System of Petri Nets

Earlier, we 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 Middle-Left k-th order systems (one non-sharing resource place in the middle position of the left-side process) with a formula depending on parameter k for a subclass of nets with k sharing resources.