In Boolean algebra, Petrick's method (also known as the branchandbound method) is a technique for determining all minimum sumofproducts solutions from a prime implicant chart. Petrick's method is very tedious for large charts, but it is easy to implement on a computer.
Example of Petrick's method (copied from http://www.mrc.uidaho.edu/mrc/people/jff/349/lect.10)
Following is the function we want to reduce:
The prime implicant chart from Quine–McCluskey algorithm is as follows:
 0 1 2 5 6 7  K (0,1) a'b'  X X L (0,2) a'c'  X X M (1,5) b'c  X X N (2,6) bc'  X X P (5,7) ac  X X Q (6,7) ab  X X
Based on the X marks in the table above, build a product of sums of the rows where each row is added, and columns are multiplied together:
(K+L)(K+M)(L+N)(M+P)(N+Q)(P+Q)
Use the distributive law to turn that expression into a sum of products. Also use the following equivalences to simplify the final expression: X + XY = X and XX = X and X+X=X
= (K+L)(K+M)(L+N)(M+P)(N+Q)(P+Q) = (K+LM)(N+LQ)(P+MQ) = (KN+KLQ+LMN+LMQ)(P+MQ) = KNP + KLPQ + LMNP + LMPQ + KMNQ + KLMQ + LMNQ + LMQ
Now use again the following equivalence to further reduce the equation: X + XY = X
= KNP + KLPQ + LMNP + LMQ + KMNQ
Choose products with fewest terms, in our example, there are two products with three terms:
KNP LMQ
Choose term or terms with fewest total literals. In our example, the two products both expand to 6 literals total each:
KNP expands to a'b'+ bc'+ ac LMQ expands to a'c'+ b'c + ab
So either one can be used. In general, application of Petricks method is tedious for large charts, but it is easy to implement on a computer.
