A new normal form of Boolean functions

AbstractA new normal form of Boolean functions based on the sum (mod 2), product and negation is presented. Let n = {1, 2,…, n}, let As be the family of s-element subsets of a set A and let πaϵφxa = 1. Then every Boolean function ƒ(x1,x2,…,xn) has a normal form ƒ(x1,x2,…,xn=∑s=0n ⊕ΠA∈ns1⊕dAΠa∈Axa with unique coefficients dA ϵ {0, 1}. A transformation of Galois normal form into the present normal form is also shown