Optimal sensor selection for discrete-event systems with partial observation

For discrete-event systems under partial observation, we study the problem of selection of an optimal set of sensors that can provide sufficient yet minimal events observation information. The sufficiency of the observed information is captured as the fulfillment of a desired formal property. Selection of sensors can be viewed as a selection of an observation mask and also of an equivalence class of events. A sensor set is called optimal if any coarser selection of the corresponding equivalence class of events results in some significant loss of the events observation information. We study an optimal selection of sensors over the set of general "nonprojection" observation masks. We show that this problem is NP hard in general. For mask-monotonic properties, we present a "top-down" and a "bottom-up" algorithm each of polynomial complexity. We show that observerness is not mask-monotonic. We show that the computational complexity can be further improved if the property is preserved under the projection via an intermediary observation mask that is an observer. Our results are obtained in a general setting so that they can be adapted for an optimal selection of sensors for a variety of applications.