Computing observers from observation policies in discrete-event systems

Abstract

This paper considers partially-observed discrete-event systems modeled by finite-state automata. The observation of event occurrences is associated with the transitions of the automaton model. That is, whether or not an event occurrence is observed is state-dependent, i.e., it depends on the transition in which the event label appears. This is in contrast to the case when observations are static and an event is either observed or not observed at every state in which it can occur. We refer to the set of transitions whose associated events are observed as an observation policy. Given an automaton model and an observation policy, we consider the problem of computing a deterministic generator of the language of event sequences that are observed using the automaton model and observation policy (i.e., an observer). Such a generator is useful, e.g., in problems of sensor activation for providing a deterministic mapping from event observations to sensor activation decisions when the decision to activate an event’s sensor is initially modeled as an observation policy. We propose an abstraction of the automaton model that may be used to represent an observer in certain cases. We illustrate cases where this abstraction accurately represents an observer when there is no ambiguity as to which event occurrences are observed following two observationally-identical strings. For the most general case considered, we demonstrate that verifying if the case holds is PSPACE-complete.