Abstract
We consider optimizing transformations of the algorithm for construction of minimal generating sets of solutions of systems of linear homogeneous equations (SLHE) over the set of natural numbers. The features of such SLHEs are described, optimization transforms are substantiated, and examples of algorithm operation before and after optimization transforms are given. The application of the algorithm is illustrated by examples of the analysis of the properties of Petri nets and the construction of a set of basic solutions in the fields of complex, real, and rational numbers and over finite fields. Keywords: systems of linear equations, algorithms, solutions, optimization, complexity.
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