Learning with permutably homogeneous multiple-valued multiple-threshold perceptrons

The (k,s)-perceptrons partition the input space {0,..., k-1}ⁿ into s+1 regions using s parallel hyperplanes. Their learning abilities are examined in this paper. The previously studied homogeneous (k, k-1)-perceptron learning algorithm is generalized to the permutably homogeneous (k,s)-perceptron learning algorithm with guaranteed convergence property. We also introduce a powerful learning method that learns any permutably homogeneously separable k-valued logic function given as input