An Algorithm for the Set of All Generators of an Arbitrary Firing Count Vector in Petri Nets

Abstract

In this paper, an effective method to obtain all nonnegative integer minimal support vectors (U4,V4) at level 4 for an arbitrary homogeneous / inhomogeneous solution of a matrix equation A x = b (A∈Zmxn, b∈Zmxl) starting from nonnegative rational number minimal support vectors (U3,V3) at level 3 is proposed. Although V4 has been derived from all minimal vectors (U5,V5) of level 5 which are obtained starting from vectors at levell, 2, or 3, so far, this proposed method for (U4,V4) gives us a big shortcut comparing with them. However, it is pointed out that obtaining (U5,V5) of level 5 from (U4,V4) of level 4 is difficult