In this paper, we investigate the supervisory control of discrete event systems for bisimulation equivalence, in which the plant and the specification are modeled as nondeterministic automata. A notion of synchronous simulation-based state controllability is introduced and is shown to be a sufficient condition for the existence of a bisimilarity enforcing supervisor. A polynomial algorithm is developed to check such a condition. When the existence condition holds, a bisimilarity enforcing supervisor is constructed. When the condition does not hold, the synthesis of feasible sub-specifications is further studied.
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