On the complexity of completeness recognition of systems of Boolean functions realized in the form of Zhegalkin polynomials

Abstract

The existence of an algorithm with polynomial time complexity which determines whether a system of Boolean functions realized in the form of Zhegalkin polynomial is complete is proved. It is also proved that if / is the length and r is the rank of the polynomial for a Boolean function, then / > \flJ -1 for a self-dual function and / > ^/2' : for an even function.

Properties of polynomials of periodic functions and the complexity of periodicity detection by the Boolean function polynomial

“…In this area of research some interesting results were obtained earlier by S.N. Selezneva [1], S.P. Gorshkov [2].…”

“…However, we shall not write out algorithms in the form of programs for the RAM, since such programs are rather long and unreadable. As in the works [1,2] we shall describe algorithms in terms of some simplest procedures for the RAM (such as the multiplication of monomials, search for the least monomial, and so on), which can be easily implemented by the reader if necessary.…”