A Critique of Keum-Bae Cho's Proof that $\mathrm{P} \subsetneq \mathrm{NP}$

TL;DR

This paper critically examines Keum-Bae Cho's claimed proof that P is a strict subset of NP, arguing that the proof's key step is unjustified and does not establish the separation.

Contribution

The paper provides a detailed critique of Cho's proof, highlighting its logical flaws and clarifying why it does not resolve the P vs NP question.

Findings

Cho's proof contains a critical unjustified step.

The critique shows the proof does not establish P ≠ NP.

The paper clarifies the limitations of the original proof.

Abstract

In this paper we critique Keum-Bae Cho's proof that $\mathrm{P} \subsetneq \mathrm{NP}$. This proof relates instances of 3-SAT to indistinguishable binomial decision trees and claims that no polynomial-time algorithm can solve 3-SAT instances represented by these trees. We argue that their proof fails to justify a crucial step, and so the proof does not establish that $\mathrm{P} \subsetneq \mathrm{NP}$.