# A review of "Memcomputing NP-complete problems in polynomial time using polynomial resources" (arXiv: 1411.4798)

@article{Markov2014ARO, title={A review of "Memcomputing NP-complete problems in polynomial time using polynomial resources" (arXiv: 1411.4798)}, author={Igor L. Markov}, journal={ArXiv}, year={2014}, volume={abs/1412.0650} }

The reviewed paper describes an analog device that empirically solves small instances of the NPcomplete Subset Sum Problem (SSP). The authors claim that this device can solve the SSP in polynomial time using polynomial space, in principle, and observe no exponential scaling in resource requirements. We point out that (a) the properties ascribed by the authors to their device are insufficient to solve NPcomplete problems in poly-time, (b) runtime analysis offered does not cover the spectral…

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## References

SHOWING 1-9 OF 9 REFERENCES

Quantum Complexity Theory

- Computer ScienceSIAM J. Comput.
- 1997

This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.

Factoring Numbers in O(log n) Arithmetic Steps

- Mathematics, Computer ScienceInf. Process. Lett.
- 1979

Abstract : A non-trivial factor of a composite number n can be found by performing arithmetic steps in a number proportional to the number of bits in n, and thus there are extremely short…

On the Power of Random Access Machines

- Computer ScienceICALP
- 1979

We study the power of deterministic successor RAM's with extra instructions like +,*,⋎ and the associated classes of problems decidable in polynomial time. Our main results are NP ... PTIME (+,*,⋎)…

NP-complete Problems and Physical Reality

- Computer Science, PhysicsElectron. Colloquium Comput. Complex.
- 2005

Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms,…

The General and Logical Theory of Au-tomata

- Mathematics
- 1963

I have to ask your forbearance for appearing here, since I am an outsider to most of the fields which form the subject of this conference. Even in the area in which I have some experience, that of…

Quantum computation and quantum information

- Mathematics, Computer ScienceMathematical Structures in Computer Science
- 2007

This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…

Your Favorite Parallel Algorithms Might Not Be as Fast as You Think

- Computer ScienceIEEE Trans. Computers
- 1988

A problem that requires I inputs, K outputs and I computations is to be solved on a d-dimensional parallel processing machine (usually d > d) when the inputs, outputs and computations are all d.

The Church-Turing thesis and its look-alikes

- Mathematics, Computer ScienceSIGA
- 2005

"A function is mechanically computable (that is: computable by means of a machine) if and only if it is Turing-computable."

Cerebral Mechanisms in Behavior, The Hixon Symposium

- Psychology
- 1952

OW THE BR\I> functions has alwas been a great puzzle to both laymen and experts. It is interesting, therefore, to see what a group of 19 outstanding scientists had to say on this subject when they…