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

Abstract

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. © 2015 IEEE.