Algorithms for Minimizing Disjunctions of Complex Conjunctions Based on First-Order Neighborhood Information for Solving Systems of Boolean Equations

Abstract

The neighborhoods of the 1st order of disjunctions of complex conjunctions of logical statements of systems of nonlinear Boolean equations given by Zhegalkin polynomials are investigated. A method for minimizing disjunctions based on the absorption of complex conjunctions by a first-order neighborhood is proposed. For this, criteria for the absorption of complex conjunctions by a first-order neighborhood are proved, similarly to the theory of Y.I.Zhuravlev on the absorption of elementary conjunctions in the class of disjunctive normal forms of Boolean functions. An algorithm for minimizing the disjunctions of complex conjunctions based on a neighborhood of the 1st order is developed.