Critique of J. Kim's "P is not equal to NP by Modus Tollens"

TL;DR

This paper critically examines Joonmo Kim's proof claiming P ≠ NP, identifying logical inconsistencies and demonstrating that the proof's core argument does not hold under reasonable interpretations.

Contribution

It provides a detailed critique of Kim's proof, highlighting logical flaws and showing that the claim P ≠ NP is not convincingly established in his approach.

Findings

Kim's proof contains logical inconsistencies.

Under reasonable interpretations, P ≠ NP does not follow from Kim's argument.

The critique undermines the validity of Kim's proof.

Abstract

This paper is a critique of version three of Joonmo Kim's paper entitled "P is not equal to NP by Modus Tollens. [arXiv:1403.4143v3]" After summarizing Kim's proof, we note that the logic that Kim uses is inconsistent, which provides evidence that the proof is invalid. To show this, we will consider two reasonable interpretations of Kim's definitions, and show that "P is not equal to NP" does not seem to follow in an obvious way using any of them.