Enumeration of reachable (forbidden, live and deadlock) states of kth order system of Petri nets

Abstract

So far, none (except the authors) in the literature proposes closed-form solutions of the number of reachable states for even the marked graphs, the simplest subclass of Petri nets, not to mention infinite systems (i.e. very large number of resources and process steps). This paper is the first one to tackle such issues by estimating reachable (forbidden, live and deadlock) states with a non-recursion and closed-form formula (depending on parameter k) for a subclass of nets with k resources. As a result, we can deal with even an infinite system with infinite resources which nobody can ever do it. Extension to more than two processes has been briefly presented. Application to large Gadara RAS (resource allocation system) is also mentioned. ©The authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.