Two-level logic minimization: an overview

Fourty years ago Quine noted that finding a procedure that computes a minimal sum of products for a given propositional formula is very complex, even though propositional formulas are fairly simple. Since this early work, this problem, known as two-level logic minimization, has attracted much attention. It arises in several fields of computer science, e.g., in logic synthesis, reliability analysis, and automated reasoning. This paper exposes the classical approach for two-level logic minimization, and presents the recent developments that overcome the limitations of the procedures proposed in the past. We show that these new techniques yield a minimizer that is 10 up to 50 times faster than the previously best known ones, and that is able to handle more complex functions.