Basis marking representation of Petri net reachability spaces and its application to the reachability problem

In this paper a compact representation of the reachability graph of a Petri net is proposed. The transition set of a Petri net is partitioned into the subsets of explicit and implicit transitions, in such a way that the subnet induced by implicit transitions does not contain directed cycles. The firing of implicit transitions can be abstracted so that the reachability set of the net can be completely characterized by a subset of reachable markings called basis makings. We show that to determine a max-cardinality-T_I basis partition is an NPhard problem, but a max-set-T_I basis partition can be determined in polynomial time. The generalized version of the marking reachability problem in a Petri net can be solved by a practically efficient algorithm based on the basis reachability graph. Finally this approach is further extended to unbounded nets

A method to verify the controllability of language specifications in Petri nets based on basis marking analysis

In this paper we propose an effective method based on basis marking analysis to verify the controllability of a given language specification in Petri nets. We compute the product, i.e., the concurrent composition, of the plant and of the specification nets and enumerate a subset of its reachable states, called basis markings. Each of these basis markings can be classified as controllable or uncontrollable by solving an integer programming problem. We show that the specification is controllable if and only if no basis marking is uncontrollable. The method can lead to practically efficient verification because it does not require an exhaustive enumeration of the state space