Parameterized of control related states of Middle Left K-net system (with a nonsharing 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 and live states for Middle Left K-net systems (one nonsharing resource place in the middle position of the left-side process, below denoted as Middle-Left-K-net) with a formula depending on parameter k for a subclass of nets with k sharing resources and μ processes where u and k can be very large.