Using SAT Checkers to Solve The Logic Minimization Problem

We investigate new techniques for solving the two-level logic minimization problem: Given a Boolean function, find the smallest OR-of-ANDs expression that represents it. This is a problem of both theoretical and practical interest. It arises in several fields of Computer Science, such as digital design, reliability analysis and automated reasoning. This project explores a new approach that involves the use of SAT checkers: programs that accept as input a Boolean formula f using only ANDs, ORs and NOTs, and determine whether the given formula f is satisfiable or not. To some, this approach might seem counter-intuitive; the SAT problem is NP-complete, and so it may appear inefficient to base our techniques on it. Thus, it is a surprise to learn that the SAT-based approach has shown considerable promise in our work. As a by-product, our research has yielded a number of ideas and observations that can be explored in other contexts, such as hardware verification, software verification, and QBF checking (satisfiability checking for a class of formulae that is ’harder’ than what SAT checkers can handle).