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Computational complexity results are obtained for decentralized discrete-event system problems. These results generalize the earlier work of Tsitsiklis, who showed that for centralized supervisory control problems under partial observation, solution existence is decidable in polynomial time for a special type of problem but becomes computationally intractable for the general class. As in the case of centralized control, there is no polynomial-time algorithm for producing supervisor solutions.

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Abstract-This paper deals with distributed discrete-event systems, in which agents (or local sites) are required to communicate in order to perform some specified tasks. Associated with each agent is a finite-state automaton that captures the required tasks to be performed at that site. The problem considered is that each agent must be able to distinguish between the states of its automaton. To help it disambiguate states, an agent uses a combination of direct observation (obtained from sensor readings available to that agent) and communicated information (obtained from sensor readings available to another agent). Since communication may be costly, a strategy to minimize communication between sites is developed. The complexity of the solution reflects the interdependence of the agents' communication protocols. That is, the decision to communicate the occurrence of an event relies on which event sequences are indistinguishable to an agent, which, in turn, is a result of what has already been communicated to that agent.

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The role of inference is added to the capabilities of decentralized supervisors in a modal logic setting for discrete-event systems. In previous work, a decentralized supervisor made a control decision through formal reasoning, using only information obtained from direct observation of a given system. The framework is extended so that when a supervisor cannot make a definitive control decision based on its own knowledge of the system, the supervisor may reason about whether other supervisors have sufficient knowledge to eventually make the correct control decision.

Abstract-Modal logic is introduced into the modeling of discrete-event systems. Analysis within this framework includes formal reasoning about what supervisors know or do not know about a given system. This model can be used to develop control strategies that solve decentralized discrete-event control problems. When a problem cannot be solved using fully decentralized supervisors, reasoning about knowledge may provide guidelines for incorporating communication and pooled information into the model.