Petrick's method

Petrick's method, also called the Petrick function or the branch-and-bound method, is a technique described by Stanley R. Petrick in 1956 for finding all of the minimum sum-of-products solutions of a Boolean function from its prime implicant chart. After the essential prime implicants and the columns they cover are removed, each remaining column gives a sum of the rows that cover it, and the product of these sums is true when every column is covered. Expanding that product with the distributive law and simplifying with the absorption law X + XY = X gives a sum of products in which each term is a set of prime implicants that covers the function. The terms with the fewest prime implicants are kept, and among them the ones with the fewest total literals give the minimal expressions. The method is tedious by hand for large charts but easy to implement on a computer. Insley B. Pyne and Edward Joseph McCluskey improved it in 1962, and the worked example in the article starts from a prime implicant chart produced by the Quine-McCluskey algorithm.