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Extended Finite Automata (EFA), i.e., finite automata extended with variables, are a suitable modeling framework for discrete event systems owing to their compactness, resulting from the use of variables. In this paper, we propose a symbolic algorithm that efficiently synthesizes a supervisor for a plant modeled by an EFA and a specification defined by another EFA. The principle of the algorithm is to iteratively strengthen the guards of the plant EFA so that forbidden or blocking states become unreachable in the controlled plant. As a consequence of the algorithm, the controlled behavior is modeled by an EFA having the same structure as the plant EFA, having stronger guards and is shown to be maximally permissive. We illustrate our algorithm via a simple manufacturing example.