A note on realizing multiple-valued logic functions using Akers' cells-cell sizes and path lengths

We propose arrays with less cells and shorter path lengths for realizing any multiple-valued logic functions using the Akers' cells. To do so, first we define the operations for constructing arrays. Using those operations, we construct the arrays which have already been given by Kamiura et al. We will call those arrays vertical type arrays. Then we prove formally that they realize any multiple-valued logic functions. Next, we propose a building type array which consists of a pedestal array and vertical type arrays. Then we show that it realizes any multiple-valued logic functions. We compare the number of cells to be used and the path lengths of our arrays with those of arrays proposed by Kamiura et al. (1994) which have been so far considered to use the minimum number of cells.