Recursive solution of number of reachable states of a simple subclass of FMS

This paper aims to compute the number of reachable (forbidden, live and deadlock) states for flexible manufacturing systems (FMS) without the construction of reachability graph. The problem is nontrivial and takes, in general, an exponential amount of time to solve. Hence, this paper focusses on a simple version of Systems of Simple Sequential Processes with Resources (S³PR), called kth-order system, where each resource place holds one token to be shared between two processes. The exact number of reachable (forbidden, live and deadlock) states can be computed recursively.