A Conjecture About Sums of Disjoint Products

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.