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30 6 2013 6 DOI: 10.7641/CTA.2013.20881 Control Theory Applications Petri 2, 1?, 3, 3 (1. , 310012; 2. , 230031; 3. : S4R(systems of sequential systems with shared resources) Petri , S4R . S4R S4R , , S4R . P– , Petri , , . : Petri ; ;; ; : TP278 :A . Vol. 30 No. 6 Jun. 2013 , 310027) : . . Redundancy detection and structure simpli?cation for a class of liveness-enforcing Petri net supervisors XU Shan-shan2, DONG Li-da1?, ZHU Dan3, ZHU Cheng-cheng3 (1. Hangzhou Institute of Service Engineering, Hangzhou Normal University, Hangzhou Zhejiang 310012, China; 2. Department of Management Engineering, Army Of?cer Academy, PLA, Hefei Anhui 230031, China; 3. Institute of Electronic Circuit and Information System, Zhejiang University, Hangzhou Zhejiang 310027, China) Abstract: S4R (systems of sequential systems with shared resources) is an important subclass of Petri nets used in analyzing and solving deadlock problem of ?exible manufacturing systems (FMS). Control places and related arcs are usually added for all or some of the strictly minimal siphons (SMS) by the existing S4R-oriented deadlock prevention methods. The defect of such methods is that there are redundant control places in the generated liveness-enforcing supervisors. For a liveness-enforcing S4R supervisor in which each SMS has been controlled by its control place, this paper proposes an integer-programming-technique-based method to detect the redundancy for control places and simplify the structure for the system. Then, it can produce the liveness-enforcing S4R supervisor with simpler structure and more permissible behaviors. The main idea is that if there is already a P-invariant in the net which makes an SMS max-controlled, then the control place added for this SMS is redundant. Because this method doesn’t need the reachability analysis, it can avoid the state explosion problem, and therefore it brings about high feasibility and computational ef?ciency. Finally, the experiments validate the correctness and