On the minimization of complexity and automation of efficient representation of boolean functions in classes of formulas and circuits

A method for synthesizing Boolean formulas intended for the efficient construction of circuit composed on functional elements, which is also suitable for minimal complexity circuits, is developed. Upper bounds on the implementation complexity of arbitrary Boolean functions in terms of the Zhegalkin basis are determined. A computational method for improving these bounds is proposed. A method for deriving certain countable classes of Boolean functions of minimal complexity is also recommended.