Comments on " ANew Algorithm for Generating Prime Implicants"

One of the major areas in switching theory research has been concerned with obtaining suitable algorithrns for the minimization of Boolean functions in connection with the general problem of their economic realization. A solution of the minimization problem, in general, involves consideration of two distinct phases. In the first phase all the prime implicants of the function are found, while in the second phase, from this set of all the prime implicants, a minimal subset (according to some criterion of minimality) of prime implicants is selected such that their disjunction is equivalent to the function and from which none of the prime implicants can be dropped without sacrificing equivalence. Many different algorithms exist for solving both the first and the second phase of this minimization problem. In a recent paper,' Slagle et al. describe a new algorithm for the generation of all the prime implicants of a Boolean function. As claimed by the authors, this algorithm is different from those previously given in the literature. The algorithm is efficient, does not generate the same prime implicant more than once (though the algorithm sometimes generates some non-prime implicants), and does not need large capacity of memory for implementation on a digital computer. The algorithm works equally well with either the conjunctive or the disjunctive (both canonical and noncanonical) form of the function.