A Survey and Discussion of Memcomputing Machines

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.