An algorithm for elementary siphons in PN

The importance of siphons is well recognized in the detection and analysis of deadlocks in a Petri net. Based on siphons, a variety of techniques are developed for the deadlock problems in concurrent systems. The major disadvantage of the existing approaches is that the number of siphons that have to be considered is large or grows fast as these methods proceed. This unavoidably leads to structurally complex deadlock-free Petri net supervisors. This research explores ways to minimize the number of siphons that have to be controlled. In this paper, siphons are distinguished by elementary and redundant ones. Conditions are developed, under which a redundant siphon can always be marked if its elementary siphons are controlled. This research is of significance to reduce the complexity of the analysis and design of liveness enforcing Petri net supervisors.