On the existence of polynomial-time algorithms to the subset sum problem
General Mathematics
2020-11-23 v4
Abstract
This paper proves that there does not exist a polynomial-time algorithm to the the subset sum problem. As this problem is in NP, the result implies that the class P of problems admitting polynomial-time algorithms does not equal the class NP of problems admitting nondeterministic polynomial-time algorithms.
Keywords
Cite
@article{arxiv.0809.4935,
title = {On the existence of polynomial-time algorithms to the subset sum problem},
author = {Jorma Jormakka},
journal= {arXiv preprint arXiv:0809.4935},
year = {2020}
}
Comments
The paper proves that P is not NP. This is a checked and revised version of the 2008 preprint. The paper is still correct and still unchecked. I did try to submit it to one journal two weeks ago, but as often happens on this particular field of mathematics, the journal editor did not take a proof of P not NP to a review. It was reviewed for 15 weeks in 2008 and no error was found at that time