Earlier, Chao pioneered the very first closed-form solution of the number of reachable and other states for marked graphs and kth-order systems, which is the simplest class of systems of simple sequential processes with resources. This paper progresses one step further by enumerating reachable, forbidden, live and deadlock states for bottom kth-order systems, which have one non-sharing resource place in the bottom position of the right-side process, with a formula depending on parameter k for a subclass of nets with k sharing resources.
Transactions of the Institute of Measurement and Control, vol. 37 no. 3 382-395