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To solve the problem of deadlock prevention for flexible manufacturing systems (FMS), an effective approach based on the theory of regions was proposed previously in a framework of Petri nets. However, it needs to solve too many linear programming problems (LPP). This paper presents an improved algorithm to decrease the number of LPP and thus reduces the computational efforts. First, the theory of regions is applied. The concepts of marking/transition separation matrix and elementary marking/transition separation instances are presented. Then it is proved that, in order to obtain the maximally permissive behavior, the number of monitors to be added is less than the smaller of the number of separation instances and the number of transitions plus one. Therefore, the number of LPP to be solved is bounded by the net size. This result significantly advances the supervisory design methods based on the theory of regions.