In this paper we study sufficient observation and work spaces for supervisors of a class of discrete-event dynamical systems (DEDS). We use finite state automata to model a DEDS. The finite automata generates a formal language defined over the set of events in the DEDS. A supervisor is a feedback system that observes a generated trace of events and dynamically disables (or enables) a subset of controllable events such that the closed-loop system behaves as desired. We model the desired behavior of the DEDS by a sublanguage defined over the set of events. A sufficient observation space is a collection of events whose observation by a supervisor is enough to realize a given desired behavior. A sufficient work space is a sufficient observation space such that the control action of the supervisor is limited to only the controllable elements of the work space. We construct algorithms to evaluate a sufficient work (or observation) space. The reduction of work (or observation) spaces results in reducing the number of event detectors, communication, and command channels between the supervisor and the plant.
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