• Corpus ID: 16688352

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

  title={A review of "Memcomputing NP-complete problems in polynomial time using polynomial resources" (arXiv: 1411.4798)},
  author={Igor L. Markov},
  • I. Markov
  • Published 29 November 2014
  • Computer Science
  • ArXiv
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… 


Quantum Complexity Theory
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
  • A. Shamir
  • Mathematics, Computer Science
    Inf. 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
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
  • S. Aaronson
  • Computer Science, Physics
    Electron. 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
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
  • T. Paul
  • Mathematics, Computer Science
    Mathematical 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
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
"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
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