A new method is presented for computing irredundant normal forms which renders feasible the handling of ``large'' functions. The method is based on the concept of abbreviated presence function and incorporates techniques found in the methods of ratio function and iterated consensus of the prime implicants. The complete set of irredundant normal equivalents of a formula is shown to be obtainable from an ``abbreviated presence function'' consisting of the presence relations corresponding to the prime implicants occurring in any one irredundant normal equivalent of the formula. Several examples are included to illustrate the economy in labor which the method provides. A new set of necessary and sufficient conditions is also given which allows a direct determination of absolutely dispensable prime implicants from the set of presence relations. The notion of absolute dispensability as presented here is related to that of Urbano and Mueller in which a prime implicant is absolutely dispensable if and only if it does not belong to an essential star.

This paper describes a new algebraic way of determining irredundant forms from the prime implicants. The method does not require using the developed normal form, and it makes novel application of Quine's technique of iterative consensus-taking. Thus, by applying repeatedly the rule of consensus to the prime implicants, it is possible to derive alist of implication relations that express the necessary and sufficient conditions of eliminability of the prime implicants in terms of which the irredundant normal forms can be computed. The extension of Quine's technique to this phase of simplification serves to shorten considerably the logical machinery needed for complete solution of the simplification problem. By the same token, it renders the method suitable for use with a digital computer.