Abstract—We consider the problem of synthesizing multiple-valued logic functions by neural networks. A genetic algorithm (GA) which finds the longest strip in is described. A strip contains points located between two parallel hyperplanes. Repeated application of GA partitions the space into certain number of strips, each of them corresponding to a hidden unit. We construct two neural networks based on these hidden units and show that they correctly compute the given but arbitrary multiple-valued function. Preliminary experimental results are presented and discussed. Index Terms—Constructive algorithm, genetic algorithm, multiple-threshold perceptron, multiple-valued logic, neural network, partitioning. I.

A new upper bound is given on the number of ways in which a set of N points in R n can be partitioned by k parallel hyperplanes. This bound improves upon a result of Olafsson and Abu-Mostafa [IEEE Trans. Pattern Analysis and Machine Intelligence 10(2), 1988: 277-281]; it agrees with the known (tight) result for the case k = 1; and it is, for fixed k and n, tight to within a constant. A previously published claimed improvement to the bound of Olafsson and Abu-Mostafa is shown to be incorrect. 1