In: Proceedings of Donetsk State Technical University, series "Informatics, Cybernetics and Computer Science", Vol. 74, pages 286-293. 2004. In Russian.
Abstract: Paper gives a theoretical grounding of know 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; Nonnegative solution; Petri net; Invariant.