In: Proceedings of 10th Workshop Algorithms and Tools for Petri Nets, Eichstätt, Germany, September 26-27, 2003, pages 184-190. September 2003.
Abstract: The paper gives a formal grounding of known heuristic Toudic method for the solution of linear diophantine homogeneous systems of equations in nonnegative integer numbers. In particular nonnegative solutions are required for calculation of the invariants for Petri nets. At first we construct the solution for one equation. Then the solution is expanded to whole system of equations. To generate all solutions via the Toudic’s basis a linear combination was extended by special operation of reduction in common measure of vectors’ components.
Keywords: diophantine equation; linear system; nonegative solution; Petri net; invariant.