On Arroyo-Figueroa's Proof that $\mathrm{P} \neq \mathrm{NP}$

TL;DR

This paper critically analyzes Arroyo-Figueroa's claimed proof that P does not equal NP, demonstrating that the argument for the existence of certain one-way functions is flawed and does not establish the separation.

Contribution

It provides a detailed critique of Arroyo-Figueroa's proof attempt, clarifying why it does not succeed in proving P ≠ NP.

Findings

Arroyo-Figueroa's proof fails to establish the existence of one-way functions.

The critique clarifies misconceptions in the original argument.

The paper concludes P ≠ NP remains unproven by this approach.

Abstract

We critique Javier Arroyo-Figueroa's paper titled ``The existence of the Tau one-way functions class as a proof that $\mathrm{P} \neq \mathrm{NP}$,'' which claims to prove $\mathrm{P} \neq \mathrm{NP}$ by showing the existence of a class of one-way functions. We summarize our best interpretation of Arroyo-Figueroa's argument, and show why it fails to prove the existence of one-way functions. Hence, we show that Arroyo-Figueroa fails to prove $\mathrm{P} \neq \mathrm{NP}$.