Effective methods for solving systems of nonlinear equations of the algebra of logic based on disjunctions of complex conjunctions

Abstract

In order to simplify logical statements and reduce the time for solving systems of non-linear Boolean equations, a criterion for the absorption of complex conjunctions by a first-order neighborhood of conjunctions of statements of a separate class of systems of non-linear Boolean equations above the second degree, given by Zhegalkin polynomials, is proposed. In the class of systems of nonlinear Boolean equations under study, the logical formulas of Zhegalkin polynomials are completely or partially divided into some linear factors. As a result, logical formulas are reduced to the disjunction of complex elementary conjunctions, consisting of the product of individual arguments, linear polynomials or their negations, on the basis of which a system of nonlinear Boolean equations is obtained. Some problems of minimizing special disjunctive normal forms obtained from the Zhegalkin polynomial above the second degree of special classes are considered.