  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.
