A Survey and Discussion of Memcomputing Machines

This paper serves as a review and discussion of the recent works on memcomputing. In particular, the universal memcomputing machine (UMM) and the 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.