Structural conditions of systems of simple sequential processes with resources nets without weakly dependent siphons

For the purpose of deadlock control, siphons in a Petri net (PN) can be divided into elementary and dependent ones; the latter can further be distinguished by strongly and weakly dependent siphons (WDS). The computation of the elementary siphons in a PN is essential but expensive since a complete siphon enumeration is needed. The results reported in the literature show that the control of WDS is quite conservative. Li et al. present two open problems. First, for what kinds of PN, we can definitely find a set of elementary siphons such that no WDS can be derived? Secondly, could we develop an algorithm to find a set of elementary siphons that can minimise the number of WDS in a net? The aim here is to answer the first problem for an systems of simple sequential processes with resources (S³PR) by investigating its structural conditions under which there are no WDS in it. The authors address such an issue by using an incremental approach for the synthesis of subnets (to compute an strict minimal siphon) of a strongly connected resource component. At each step, the authors add a PP-handle Hi with at least one interior resource place. The structural condition for the absence of WDS is derived and show that the maximal class of S³PR is a 2c⁺-system.