On the variables of the conjunctively
polynomial-like Boolean functions

Abstract. Conjunctively polynomial-like Boolean functions form a class of the Boolean functions invariant with respect to a special transform of the linear space of the two-valued logical functions. In this article we prove that every variable of such functions — with the exception of the zero function of at least one variable — is essential.

Key words and phrases. Boolean function, conjunctive normal form, Zhegalkin polynomial, conjunctively polynomial-like Boolean function.