Negation trees: a unified approach to Boolean function complementation

Boolean function complementation is a basic operation of Boolean algebra. For functions given in SOP form, the complementation methods include the DeMorgan's Law, sharp, disjoint sharp, unate complementation, recursive, and Sasao's method. This paper accomplishes three purposes: (1) It exposes an underlying unification of the existing complementation algorithms. It is proven that (a) unate-complementation and sharp are the same as the DeMorgan Law algorithm; (b) Sasao's algorithm is the same as disjoint sharp; (c) disjoint sharp is a special case of the recursive method. (2) It proposes negation trees for the representation of functions and their complements. (3) It gives faster algorithms for finding complements of functions in SOP form based on negation trees.