A new method based on cube algebra for the simplification of logic functions

In this study an Off-set based direct-cover minimization method for single-output logic functions is proposed represented in a sum-of-products form. To find the sufficient set of prime implicants including the given On-cube with the existing direct-cover minimization methods, this cube is expanded for one coordinate at a time. The correctness of each expansion is controlled by the way in which the cube being expanded intersects with all of K < 2(n) Off-cubes. If we take into consideration that the expanding of one cube has a polynomial complexity, then the total complexity of this approach can be expressed as O(n(p))O(2(n)), that is, the product of polynomial and exponential complexities. To obtain the complete set of prime implicants including the given On-cube, the proposed method uses Off-cubes expanded by this On-cube. The complexity of this operation is approximately equivalent to the complexity of an intersection of one On-cube expanded by existing methods for one coordinate. Therefore, the complexity of the process of calculating of the complete set of prime implicants including given On-cube is reduced approximately to O(n(p)) times. The method is tested on several different kinds of problems and on standard MCNC benchmarks, results of which are compared with ESPRESSO.