Some algebraic properties of particular solutions for state equation in Petri nets

There are infinitely nonnegative integer inhomogeneous solutions for a state equation Ax=b (A/spl epsi/Z/sup m/spl times/n/,b/spl epsi/Z/sup m/spl times/1/) of Petri nets. But a nonnegative integer inhomogeneous solutions are decomposed and represented by a finite number of generators of both homogeneous and inhomogeneous solutions for Ax=b. The generators are divided into five levels. Algebraic properties of generators for T-invariants are simple and well known, but those for particular solutions are rather complicated and not well known. In this paper, characterization for the basic, but not elementary, particular solutions is done from nonnegative rational and elementary generators.