中文摘要：

研究了顺序资源共享分配系统的建模模型S^4PR（Systems of sequential systems with shared resources）网的活性问题．已有的研究成果表明，一个SOPR网在所有信标都满足max，max′或max″-controlled时能保持活性，但现有的活性条件对信标的限制严格且不适用于某些网系统，本文提出了一类名为max″-controlled的改进型条件，并证明了当一个S^4PR网的所有信标都满足max＊-controlled条件时，网系统能保持活性．与现有的其他条件相比，新的活性条件更加宽松，为设计更高允许度的死锁预防或者活性保持监控器提供了理论支撑．

英文摘要：

This paper studies the liveness problem for S4PR （systems of sequential systems with shared resources） nets, a class of Petri net models of flexible manufacturing systems. Current research indicates that an S4PR net is live if all its siphons are max, max′, or max″-controlled. However, these conditions tend to be overly restrictive and are not available to some net systems. This paper presents an improved condition called max＊-controlled condition and proves that an S4PR net is live if all its siphons are max＊-controlled. Compared with the preceding ones, this new condition is more general and can be a theoretical support for designing deadlock prevention or liveness-enforcing supervisor which is more permissive on system behavior.