Sufficient conditions for loop resource subsets to derive strict minimal siphons in class of petri nets

As a structural object of Petri nets, the importance of strict minimal siphons (SMSs) is well recognised in the analysis and control of deadlocks for flexible manufacturing systems. For a class of Petri nets called systems of simple sequential processes with resources (S³PRs), the concepts of critical resource places and their related multi-way holder places are firstly proposed. Next, by analysing the structural properties of the critical resource places and their related loop resource subsets, sufficient conditions for loop resource subsets to derive SMSs are established. Finally, based on the proposed results, all SMSs can be obtained from their related loop resource subsets in an S³PR net.