Optimal Method for Solving Special Classes of Systems of Nonlinear Equations of the Second Degree

Abstract

In order to simplify the notation and reduce the time for solving systems of Boolean equations, a method is proposed that is optimal for solving a separate class of systems of nonlinear Boolean equations of the second degree. In the class of systems of non-linear Boolean equations under study, logical formulas are divided completely or partially into some linear factors. As a result, logical formulas are reduced to a product of linear polynomials, on the basis of which a system of linear Boolean equations is obtained, which is solved an order of magnitude easier than a system of second-order Boolean equations. It is considered some problems of minimization of special disjunctive normal forms obtained from the Zhegalkin polynomial of the second degree of a special class.