Calculating basis siphons of Petri nets based on semi-tensor product of matrices

Abstract

In this paper, we address the problem of calculating basis siphons in Petri nets (PNs) by resorting to the semi-tensor product (STP) of matrices. The proposed appraoch is based on our previous results on the calculation of siphons and minimal siphons in PNs, whose key notion is that of the siphon equation (SE) of PNs. First, we discuss the properties of the SE of PNs in the framework of STP. Second, an efficient recursion algorithm is proposed, which can be applied to computing all basis siphons for any PNs. Some results on the computational complexity of the proposed algorithm, in this paper, are also provided, as well as comparison with the existing approach. Last, an example is presented to illustrate the theoretical results. The proposed approach proved highly effective in calculating all basis siphons of PNs and only requires matrix manipulations.