Abstract:
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. ...Show MoreMetadata
Abstract:
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.
Published in: IEEE Transactions on Systems, Man, and Cybernetics: Systems ( Volume: 47, Issue: 3, March 2017)