State Estimation in Discrete Event Systems Modeled by Labeled Petri Nets

In this paper, we address the problem of state estimation in discrete event systems (DES) modeled by labeled Petri nets that may have nondeterministic transitions (i.e., transitions that share the same label) or unobservable transitions (i.e., transitions that are associated with the null label). More specifically, given knowledge of the initial Petri net state (or set of states), we show that the number of consistent markings in a Petri net with nondeterministic transitions is at most polynomial in the length of the observation sequence (i.e., in the number of labels observed) even though the set of possible firing sequences can be exponential in the length of the observation sequence. The result applies to general Petri nets without any specific assumption on the structure of the Petri net or the nature of the labeling function. By restricting attention to bounded Petri nets with acyclic unobservable subnets, this polynomial dependency of the number of consistent markings on the length of the observation sequence also applies to Petri nets with unobservable transitions