Memcomputing Numerical Inversion With Self-Organizing Logic Gates

IEEE Transactions on Neural Networks and Learning Systems
Haik ManukianFabio L Traversa

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 -bit precision in the output requires extending the circuit by at most 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.

References

Nov 13, 2009·Physical Review Letters·Aram W HarrowSeth Lloyd
Jul 13, 2011·Frontiers in Neuroscience·Giacomo IndiveriKwabena Boahen
May 9, 2014·IEEE Transactions on Neural Networks and Learning Systems·Fabio Lorenzo TraversaMassimiliano Di Ventra
Dec 3, 2014·Neural Networks : the Official Journal of the International Neural Network Society·Jürgen Schmidhuber
Feb 11, 2015·IEEE Transactions on Neural Networks and Learning Systems·Fabio Lorenzo Traversa, Massimiliano Di Ventra
May 13, 2015·IEEE Transactions on Neural Networks and Learning Systems·Jiexiong TangGuang-Bin Huang
Nov 26, 2015·Science Advances·Fabio Lorenzo TraversaMassimiliano Di Ventra
Nov 3, 2017·Chaos·Massimiliano Di Ventra, Fabio L Traversa

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