English

On P Versus NP

Computational Complexity 2026-05-14 v10

Abstract

It is shown that graph-theoretic problem CLIQUE can't be solved in polynomial time by any deterministic TM. This upgrades the well-known partial result that claims only monotone unsolvability thereof, and eventually implies P \neq NP as CLIQUE is NP-complete. This paper essentially simplifies my previous presentation that used more complex models of computation based on standard Boolean semantics while fixing technical errors spotted by a generic proof assistant Isabelle that has been implemented by Ren\'e Thiemann.

Keywords

Cite

@article{arxiv.2005.00809,
  title  = {On P Versus NP},
  author = {Lev Gordeev},
  journal= {arXiv preprint arXiv:2005.00809},
  year   = {2026}
}

Comments

This is a refined two-side version of arXiv:2104.07166

R2 v1 2026-06-23T15:15:38.888Z