Calculation of Siphons and Minimal Siphons in Petri Nets Based on Semi-Tensor Product of Matrices
利用矩阵半张量积建立虹吸方程，提出枚举普通Petri网中所有虹吸和极小虹吸的算法，并通过实例和实验证明其有效性。
In this paper, we address the problems of enumerating siphons and minimal siphons in ordinary Petri nets (PNs) by resorting to the semi-tensor product (STP) of matrices. First, a matrix equation, called the siphon equation (SE), is established by using STP. Second, an algorithm is proposed to calculate all siphons in ordinary PNs. An example is presented to illustrate the theoretical results and show that the proposed method is more effective than other existing methods in calculating all siphons of PNs. Third, an efficient recursion algorithm is also proposed, which can be applied to computing all minimal siphons for any ordinary PNs. Last, some results on the computational complexity of the proposed algorithms, in this paper, are provided, as well as experimental results.