Marking Estimation of Petri Nets with Λ-free Labeling

We present a technique for estimating the marking of a Petri net based on the observation of transition labels. In particular, the main contribution of the paper consists in deriving a methodology that can handle the case of nondeterministic transitions, i.e., transitions that share the same label. Under some technical assumptions, the set of markings consistent with an observation can be represented by a linear system with a fixed structure that does not depend on the length of the observed word. The validity of the proposed methodology is illustrated in detail through a numerical example.