Critique of Boyu Sima's Proof that ${\rm P}\neq{\rm NP}$

TL;DR

This paper critically reviews Boyu Sima's claimed proof that P does not equal NP, analyzing its argument, identifying its flaws, and providing a clear example to demonstrate the failure of the proof.

Contribution

It offers a detailed critique of Sima's proof attempt, clarifying where the argument fails and illustrating the issues with a simple example.

Findings

Sima's proof contains a fundamental flaw.

The critique clarifies the gap in the original argument.

A simple example demonstrates the proof's failure.

Abstract

We review and critique Boyu Sima's paper, "A solution of the P versus NP problem based on specific property of clique function," (arXiv:1911.00722) which claims to prove that ${\rm P}\neq{\rm NP}$ by way of removing the gap between the nonmonotone circuit complexity and the monotone circuit complexity of the clique function. We first describe Sima's argument, and then we describe where and why it fails. Finally, we present a simple example that clearly demonstrates the failure.