Supervisor Synthesis for FMS Based on Critical Activity Places
研究如何通过减少Petri网监督控制器设计中需要考虑的库所数量来简化死锁预防，定义了关键变迁和关键活动库所，并证明只需考虑这些库所即可禁止所有首次遇到的不良标记并允许所有合法标记。
Solving states separation problems is an important technique to obtain liveness-enforcing and optimal or near-optimal supervisors for flexible manufacturing systems based on Petri nets. It first generates the model's reachability graph and partitions it into a live zone (LZ) and a deadlock zone (DZ). Then, first-met bad markings (FBMs), which exist in DZ and are the very first entries from LZ to DZ, are forbidden by some designed place invariants (PIs) to prevent the system from entering DZ. This paper studies the reduction of the number of places to be considered in such PI designs. First, the concepts of critical transitions and critical activity places are defined, and a fast algorithm is provided to compute them. Then, the proofs of that only critical activity places need to be considered in such PI designs to forbid all FBMs and/or permit all legal markings in LZ are established.