A Canonical Partition of the Primes of Logic Functions

f(x1, . . . , xn) → {0, 1}, xi ∈ {0, 1}, i = 1, . . . , n assigns a value of 1 (TRUE) or 0 (FALSE ) to each of the 2 n-tuples that make up its domain. A Boolean function can be represented by a formula built using AND, OR and NOT operations. In this paper, ‘∗’ represents AND, ‘+’ represents OR, and x represents the negation NOT x (also called the complement of x). An AND of variables (some of which may be negated) is called a product, and an OR of products is called a sum-of-products. Every Boolean function can in fact be represented by a sum-of-products formula, such as