Computing irredundant normal forms from abbreviated presence functions

[5]-, Decision-Making Processes in Pattern Recogplying Quine's technique4 of iterated consential prime implicants occur and other nition. New York: Macmillan, 1962, Ch. 4. [6] 0. Firschein and M. Fischler, "Automatic subsensus-taking to the set of prime implicants, dominated columns, if any. The necessary class determination for pattern-recognition appliMott derived a set of implication relations and sufficient conditions of eliminability of cations," IEEE Trans. on Electronic Computers (Correspondence), vol. EC-12, pp. 137-141, April that determine for every originally elimina nonessential prime implicant have next 1963. F a J L able prime implicant the necessary and sufbeen found by considering from the minimiz[7J E. Fix and J. L. Hodges, "Discriminatory analysis: 6.... Non-parametric discrimination," USAF School of ficent conditions of its eliminability. The ing function6 corresponding to the reduced Aviation Medicine, Randolph AFB, Tex., Rept. different irredundant forms were than found, prime implicant table only the disjunction 4, 1951, and Rept. 11, 1952, as summarized below [81. on the basis of these implication relations, terms which contain the prime implicant [8] L. N. Kanal and K. K. Nambiar, "On the applicaby writing a conjunctive form, one conjunct whose eliminability conditions have to be tion of discriminant analysis to identification in aerial photography," Philco Sci. Lab., Blue Bell, for each prime implicant, and simplifying it found, deleting the appearance of that parPa., presented at the 7th Nat'l Convention on by the use of distributive laws of Boolean ticular prime implicant from these disjuncMilitary Electronics, Washington', D. C., Septem algebra. In the aforementioned paper by tion terms and then taking the conjunction her 1963. Chang and Mott, it has been shown that the of these reduced disjunction terms. This complete set of irredundant normal equiproduct of sums expression has been simvalents of a formula can be obtained by conplified by the applications of the laws sidering only an "abbreviated presence funcof Boolean algebra to yield the required sum tion"-an expression in conjunctive form in of products form which corresponds to the which the different conjuncts give the presset of irredundant consequents implied by ence relations (i.e., those involving eliminthe prime implicant in question. Due to the