A Conjecture About Sums of Disjoint Products

Abstract

A sum of disjoint products (SDP) representation of a Boolean function is useful because it provides readily available information about the function; however, a typical SDP contains many more terms than an equivalent ordinary sum of products. We conjecture the existence of certain particular SDP forms of $x_1+\cdots +x_t$, which could be used as patterns in creating relatively economical SDP forms of other Boolean functions.