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A symbolic approach to decentralized set-valued state estimation and prediction for systems that admit a hybrid state machine representations is proposed. The decentralized computational scheme represents a conjunction of a finite number of distributed state machines, which are specified by an appropriate decomposition of the external signal space. It aims at a distribution of computational tasks into smaller ones, allocated to individual distributed state machines, leading to a potentially significant reduction in the overall space/time computational complexity. We show that, in general, such a scheme outerapproximates the state set estimates and predictions of the original monolithic state machine. By utilizing structural properties of the transition relation of the latter, in a next step, we propose constructive decomposition algorithms for a recovery of the exact state set outcomes.