Enumeration of reachable, forbidden, live states of gen-left k-net system (with a non-sharing resource place) of Petri Nets

Abstract

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.