An approach to the synthesis of adaptive structures represented by multi-level logic, Boolean network described as an acyclic graph with universal logical elements, is proposed. As a result of the synthesis of such structures are determined the type of logic function of the Boolean network of a given learning sample of binary vectors, which allows using of this structure for the problem of classification of input vectors. Unlike known methods for the synthesis of multilevel logic, method of the synthesis of such schemes proposed in this paper. It based on the description of a Boolean network by Zhegalkin's polynomials, starting from subnet (n = 3).

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