Necessary and sufficient conditions for resultant siphons to be controlled

Based on key resource subsets, a necessary and sufficient condition is proposed under which a resultant siphon can be always marked if its strict minimal siphons (SMS) are optimally controlled. The proposed condition is established by analyzing the structural characteristics and markings of the resource subnets in a class of Petri nets called L-S3PR. When it is used in deadlock prevention policies, the number of monitors can be significantly reduced, thereby decreasing control implementation complexity and cost.