Verification for the predictability of decentralized discrete event systems with a polynomial complexity

In this paper, the verification issue for the predictability of decentralized discrete event systems (DESs) is investigated, in which the detection information may be decentralized among physically separated sites. After the predictability for decentralized DESs is formalized by the notion of copredictability, which describes the ability of the involved system that the failure events can be predicted prior to their occurrences by at least one local observer, a nondeterministic automaton, namely coverifier, is constructed to achieve the performance of the prediction. Then a necessary and sufficient condition for verifying the copredictability of DESs based on the coverifier is proposed. In particular, the complexity for realization of failure prediction is analyzed. It is proved that for a given decentralized system, the coverifier can be constructed with a polynomial complexity, and the verification for its copredictability can be completed within polynomial time.