A New Exact Minimizer for Two - Level

We present a new algorithm for exact two-level logic optimization. It diiers from the classical approach; rather than generating the set of all prime implicants of a function, and then deriving a covering problem, we derive the covering problem directly and implicitly, and then generate only those primes involved in the covering problem. We represent a set of primes by the cube of their intersection. We then derive some properties of the sets of primes which form this set covering problem. We prove that the set of sets of primes which forms the covering problem for an incompletely-speciied logic function F is unique. Hence the corresponding set of cubes forms a minimum canonical cover for F. We give a successive reduction algorithm for nding the minimum canonical cover from any initial cover. Using the minimum canonical cover, we then generate only those primes involved in at least one minimal cover of F. We discuss two related heuris-tic minimization procedures; a relaxed form of the exact procedure, and then an improved form of the Espresso-II procedure. We give experimental results for the exact minimizer. The method is eeective; solutions for 10 of the 20 hard examples in the Espresso benchmark set are derived and proved minimum. In addition, for 5 of the remaining examples the minimum canonical cover is derived, but the covering problem remains to be solved exactly.