Memcomputing Numerical Inversion with Self-Organizing Logic Gates

TL;DR

This paper introduces a memcomputing approach using self-organizing logic gates to perform numerical inversion efficiently, potentially in a single hardware step, with scalability for high precision and real-time applications.

Contribution

It presents a novel memcomputing method with self-organizing logic gates for fast, scalable numerical inversion, extending to linear systems and matrix inversion.

Findings

Successful simulation of scalar inversion with a 5-bit circuit

Method extends efficiently to higher precision levels

Hardware implementation can perform inversion in a single step

Abstract

We propose to use Digital Memcomputing Machines (DMMs), implemented with self-organizing logic gates (SOLGs), to solve the problem of numerical inversion. Starting from fixed-point scalar inversion we describe the generalization to solving linear systems and matrix inversion. This method, when realized in hardware, will output the result in only one computational step. As an example, we perform simulations of the scalar case using a 5-bit logic circuit made of SOLGs, and show that the circuit successfully performs the inversion. Our method can be extended efficiently to any level of precision, since we prove that producing n-bit precision in the output requires extending the circuit by at most n bits. This type of numerical inversion can be implemented by DMM units in hardware, it is scalable, and thus of great benefit to any real-time computing application.