Observation Equivalence of Petri Net Generators

Abstract In the framework of discrete event systems, the observation of events is considered as outputs in most problem settings, such as state estimation and fault diagnosis, while only a few studies exploit the availability of partial state information. In this paper, equivalent relations between Petri nets with different observation structures, i.e., Petri net generators, are discussed. We focus on a model called labeled Petri nets with outputs (LPNO), i.e., labeled Petri nets endowed with an arbitrary observation function of the marking. It has been shown that any \LPNO\ can be converted into an adaptive labeled Petri net (ALPN) whose labeling function depends on the markings, if infinite labels are allowed. We propose an algorithm that converts a bounded \LPNO\ into an equivalent \ALPN\ with minimal alphabet, i.e., an alphabet of minimal cardinality, to avoid introducing a large number of unnecessary labels.