Marking Estimation in Labelled Petri nets by the Representative Marking Graph

In this paper a method to recognize the set of consistent markings in labelled Petri nets is proposed. In this method, the set of unobservable transitions are partitioned into pseudo-observable and strictly unobservable ones, and the subnet induced by the latter is acyclic. The unobservable reach of a marking can be characterized by the union of the strictly unobservable reach of several basis markings, called representative markings, in the unobservable subnet. The set of consistent markings can be characterized by a linear algebraic system based on those representative markings. Based on the representative marking graph, the current marking estimation problem for a labelled Petri net can be efficiently solved. This method does not require the assumption that the unobservable subnet is acyclic.