Systems of sequential systems with shared resources ((SPR)-P-4) represent a class of Petri nets that have powerful modeling capability for resource allocation systems. Their efficient siphon computation is important. An open issue is how to determine whether a resource subset can generate a strict minimal siphon (SMS). This paper presents the answer. In particular, we propose a new concept called characteristic implicit resource-transition nets. By charactering such nets, we successfully establish a necessary and sufficient condition for a resource subset to generate an SMS.