On P Versus NP

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 $\ne$ 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 René Thiemann.

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