Algorithm for the set of generators of an arbitrary firing count vector in Petri nets

In this paper, an effective method to obtain all nonnegative integer minimal support vectors (U-4,V-4) at level 4 for an arbitrary homogeneous / inhomogeneous solution starting from nonnegative rational number minimal support vectors (U-3, V-3) at level 3 is proposed. Although V, has been derived from all minimal vectors (U-5,V-5) of level 5 which are obtained starting from vectors at level 1, 2, or 3, so far. This proposed method for (U-4, V-4) gives us a big shortcut comparing with them. However, it is pointed out that obtaining (U-5,V-5) of level 5 from (U-4,V-4) of level 4 is not so wise.