A Survey and Discussion of Memcomputing Machines

TL;DR

This paper reviews memcomputing machines, discussing their theoretical models, capabilities, and limitations, concluding that current models are no more powerful than Turing machines and their potential for solving P vs. NP remains inconclusive.

Contribution

It provides a comprehensive review of memcomputing models, critically assesses their computational power, and clarifies misconceptions about their ability to resolve P vs. NP.

Findings

UMM is physically implausible

DMM is Turing-complete in simulations

Memcomputing is energy-efficient but not more powerful

Abstract

This paper serves as a review and discussion of the recent works on memcomputing. In particular, the $\textit{universal memcomputing machine}$ (UMM) and the $\textit{digital memcomputing machine}$ (DMM) are discussed. We review the memcomputing concept in the dynamical systems framework and assess the algorithms offered for computing $NP$ problems in the UMM and DMM paradigms. We argue that the UMM is a physically implausible machine, and that the DMM model, as described by numerical simulations, is no more powerful than Turing-complete computation. We claim that the evidence for the resolution of $P$ vs. $NP$ is therefore inconclusive, and conclude that the memcomputing machine paradigm constitutes an energy efficient, special-purpose class of models of dynamical systems computation.