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 (U₄,V₄) at level 4 for an arbitrary homogeneous/inhomogeneous solution 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 level 1, 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 not so wise.