State estimation of λ-free labeled Petri nets with contact-free nondeterministic transitions

In this paper we deal with the problem of estimating the marking of a labeled Petri net with nondeterministic transitions. In particular, we consider the case in which nondeterminism is due to the presence of transitions that share the same label and that can be simultaneously enabled. Under the assumption that: the structure of the net is known, the initial marking is known, the transition labels can be observed, the nondeterministic transitions are contact-free, we present a technique for characterizing the set of markings that are consistent with the actual observation. More precisely, we show that the set of markings consistent with an observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.