An algorithm for generating prime implicants

Of late, an iterative procedure for the generation of the prime implicants of switching functions by utilizing a new tabular mode of functional representation called clause-column table was developed by Das and Khabra. This approach of Das and Khabra generates all the prime implicants of the functions given either in the sum-of-products or in the product-of-sums forms, both canonical and noncanonical, and is computationally very efficient. The method can be applied for finding the prime implicants of functions having a large number of unspecified or don't care terms as well. In a clause-column table representation of a function, the set of literals or clauses defining a product or sum term in the sum-of-products or product-of-sums form, respectively, appears in a column, the total number of columns in the table being equal to the number of such product or sum terms. Although the basic principle utilized in the procedure is that of successive expansion around the literals as employed in some of the other existing methods, the manner the expansion is carried through is entirely different and greatly reduces the generation of the redundant terms. For a switching function specified in the product-of-sums form, the method produces all the prime implicants, while for a switching function given in the sum-of-products form, the procedure yields all the prime implicates first and is next applied to this set of prime implicates to obtain the prime implicants of the function. In the paper, an assessment of the performance of this prime implicant generation algorithm has been made by simulating it on a computer under conditions of different numbers of variables and different numbers of terms in the product-of-sums (sum-of-products) representations of the functions. The experimental outcome indicates that the algorithm performs quite elegantly with respect to the CPU time and memory usage.