Fast computation of the prime implicants by exact direct-cover algorithm based on the new partial ordering operation rule

In this study, a novel OFF-set based direct-cover Exact Minimization Algorithm (EMA) is proposed for single-output Boolean functions represented in a sum-of-products form. To obtain the complete set of prime implicants covering the given Target Minterm (ON-minterm), the proposed method uses OFF-cubes (OFF-minterms) expanded by this Target Minterm. The amount of temporary results produced by this method does not exceed the size of the OFF-set. In order to achieve the goal of this study, which is to make faster computations, logic operations were used instead of the standard operations. Expansion OFF-cubes, commutative absorption operations and intersection operations are realized by logic operations for fast computation. The proposed minimization method is tested on several classes of benchmarks and then compared with the ESPRESSO algorithm. The results show that the proposed algorithm obtains more accurate and faster results than ESPRESSO does.