English

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

R2 v1 2026-06-21T11:25:09.919Z