Symmetric polynomial-like Boolean functions

Abstract. 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. Another special set of the Boolean-functions are the set of the symmetric functions. In this article we introduce the class of the symmetric polynomial-like Boolean functions and investigate some elementary properties of such functions.

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