Multiple Threshold Neural Logic

Abstract

We introduce a new Boolean computing element, related to the Boolean version of a neural element. Instead of the sign function in the Boolean neural element, (also known as an LT element), it computes an arbitrary (with polynomialy many transitions) Boolean function of the weighted sum of its inputs. We call the new computing element an LTM element, which stands for Linear Threshold with Multiple transitions. The paper consists of the following main contributions related to our study of LTM circuits: (i) the characterization of the computing power of LTM relative to LT circuits, (ii) a proof that the area of the VLSI layout, is reduced from O(n to the power of 2) in LT circuits to O(n) in LTM circuits, for n inputs symmetric Boolean functions, and (iii) the creation of efficient designs of LTM circuits for the addition of a multiple number of integers and the product, of two integers. In particular, we show how to compute the addition of m integers with a single layer of LTM elements.

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