2024 Volume E107.D Issue 8 Pages 913-921
This paper shows that sum-of-product expression (SOP) minimization produces the generalization ability. We show this in three steps. First, various classes of SOPs are generated. Second, minterms of SOP are randomly selected to generate partially defined functions. And, third, from the partially defined functions, original functions are reconstructed by SOP minimization. We consider Achilles heel functions, majority functions, monotone increasing cascade functions, functions generated from random SOPs, monotone increasing random SOPs, circle functions, and globe functions. As for the generalization ability, the presented method is compared with Naive Bayes, multi-level perceptron, support vector machine, JRIP, J48, and random forest. For these functions, in many cases, only 10% of the input combinations are sufficient to reconstruct more than 90% of the truth tables of the original functions.
