Blake canonical form


In Boolean logic, a formula for a Boolean function f is in Blake canonical form, also called the complete sum of prime implicants, the complete sum, or the disjunctive prime form, when it is a disjunction of all the prime implicants of f.

Relation to other forms

The Blake canonical form is a special case of disjunctive normal form.
The Blake canonical form is not necessarily minimal, however all the terms of a minimal sum are contained in the Blake canonical form. On the other hand, the Blake canonical form is unique, whereas there can be multiple minimal forms. Selecting a minimal sum from a Blake canonical form amounts in general to solving the set cover problem, so is NP-hard.

History

Archie Blake presented his canonical form at a meeting of the American Mathematical Society in 1932, and in his 1937 dissertation. He called it the "simplified canonical form"; it was named the "Blake canonical form" by Frank Markham Brown and Sergiu Rudeanu in 1986–1990.

Methods for calculation

Blake discussed three methods for calculating the canonical form: exhaustion of implicants, iterated consensus, and multiplication. The iterated consensus method was rediscovered by Edward W. Samson and Burton E. Mills, Willard Quine, and Kurt Bing.