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IBM Journal of Research and Development  
Volume 31, Number 2, Page 187 (1987)
Mathematics and Computing
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Factoring logic functions

by R. K. Brayton
A factored form is a representation of a logic function that is either a single literal or a sum or product of factored forms. Thus it is equivalent to a parenthesized algebraic expression. It is one of many possible representations of a logic function, but seems to be the most appropriate one for use in multilevel logic synthesis. We give a number of methods for obtaining different factored forms for a given logic function. These methods range from purely algebraic ones, which are quite fast, to so-called Boolean ones, which are slower but are capable of giving better results. One of the methods given is both fast and gives good results, and is useful in providing continuous estimates of area and delay as logic synthesis proceeds. In multilevel logic synthesis, each of the methods given has a use in a system where run-time and quality are traded off. We also formulate the problem of optimal algebraic factorization, and pose its solution as a rectangle-covering problem for which a heuristic method is given.
Related Subjects: Algorithms; Logic; Mathematics