Absolute Minimal Expressions of Boolean Functions

In this paper we make a beginning in the hitherto unexplored problem of finding absolute minimal expressions of Boolean functions. We shall adhere to the notations and terminology introduced in our previous paper,1 which will be referred to as S. In the present paper, we shall find absolute minimals for Boolean functions whose point set complex consists of either one or two points. The case of one point is in Theorem 1, Section I. The case when the two points form a 1-cell is covered by Theorem 4, Section I which discusses an arbitrary dimensional cell. The case when the cell complex consists of two isolated points, the main theme of this paper, is dealt with in Section II.