Enumeration of reachable, forbidden, live states of gen-left k-net system (with a 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 kth 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 general k-net systems (one non-sharing resource place in the general position of the Left-side process) with a formula depending on parameter k for a subclass of nets with k sharing resources. The results are also verified by Top-Left-k-net, Bottom-Left-k-net and Middle-Left-k-net system.