Blake canonical form

In Boolean logic, a formula for a Boolean function f is in Blake canonical form (BCF),[1] also called the complete sum of prime implicants,[2] the complete sum,[3] or the disjunctive prime form,[4] when it is a disjunction of all the prime implicants of f.[1] The Blake canonical form is a 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.[3]

It was introduced in 1937 by Archie Blake, who called it the "simplified canonical form";[5][6] it was named in honor of Blake by Frank Markham Brown in 1990.[1]

Blake discussed three methods for calculating the canonical form: exhaustion of implicants, iterated consensus, and multiplication. The iterated consensus method was rediscovered by Samson and Mills, Quine, and Bing.[1]

See also

References

  1. 1 2 3 4 Brown, Frank Markham (2012) [2003, 1990]. "Chapter 4: The Blake Canonical Form". Boolean Reasoning - The Logic of Boolean Equations (reissue of 2nd ed.). Mineola, New York: Dover Publications, Inc. pp. 77ff. ISBN 978-0-486-42785-0. ISBN 0-486-42785-4.
  2. ↑ Sasao, Tsutomu (1996). "Ternary Decision Diagrams and their Applications". In Sasao, Tsutomu; Fujita, Masahira. Representations of Discrete Functions. p. 278. ISBN 0792397207.
  3. 1 2 Kandel, Abraham. Foundations of Digital Logic Design. p. 177.
  4. ↑ Donald E. Knuth, The Art of Computer Programming 4A: Combinatorial Algorithms, Part 1, 2011, p. 54
  5. ↑ Blake, Archie (1937). Canonical expressions in Boolean algebra (Dissertation). Department of Mathematics, University of Chicago: University of Chicago Libraries.
  6. ↑ McKinsey, J. C. C., ed. (June 1938). "Blake, Archie. Canonical expressions in Boolean algebra, Department of Mathematics, University of Chicago, 1937". The Journal of Symbolic Logic (Review). 3 (2:93). doi:10.2307/2267634. JSTOR 2267634.


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