Marking estimation of Petri nets with silent transitions

In this paper we deal with the problem of estimating the marking of a labeled Petri net system based on the observation of transitions labels. In particular, we assume that a certain number of transitions are labeled with the empty string ε, while a different label taken from a given alphabet is assigned to all the other transitions. Transitions labeled with the empty string are called silent because their firing cannot be observed. Under some technical assumptions on the structure of the T_ε -induced subnet, where T_ε denotes the set of silent transitions, we formally prove that the set of markings consistent with the observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.