A fast algorithm to find a set of elementary siphons for a class of petri nets

Elementary siphons are a special class of the strict minimal siphons (SMS), which play an important role in the deadlock prevention of Petri nets. The existing computation methods in the literature depend on the complete siphon enumeration of a net. Since the number of minimal siphons grows in general exponentially with respect to the size of a net, it is difficult to compute all the SMS. This paper proposes a fast algorithm to find a set of elementary siphons for an L-S³PR based on partial SMS from a structural perspective. We show an approach to obtain a minimal siphon from a resource circuit. The concepts of the complementary matrix and independent arcs in a resource directed graph are proposed, which are important in our method. We describe the method of computing independent arcs in details. Then an algorithm to find a set of elementary siphons for an L-S³PR is developed. Compared with the existing methods, our method is much efficient