A Critique of Lin's "On $\text{NP}$ versus $\text{coNP}$ and Frege Systems"

Fuente: arXiv
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Main Authors: DeJesse, Nicholas, Lyudovyk, Spencer, Pai, Dhruv, Reidy, Michael
Format: Preprint
Published: 2025
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author DeJesse, Nicholas
Lyudovyk, Spencer
Pai, Dhruv
Reidy, Michael
author_facet DeJesse, Nicholas
Lyudovyk, Spencer
Pai, Dhruv
Reidy, Michael
contents In this paper, we examine Lin's "On NP versus coNP and Frege Systems" [Lin25]. Lin claims to prove that $\text{NP} \neq \text{coNP}$ by constructing a language $L_d$ such that $L_d \in \text{NP}$ but $L_d \notin \text{coNP}$. We present a flaw in Lin's construction of $D$ (a nondeterministic Turing machine that supposedly recognizes $L_d$ in polynomial time). We also provide a proof that $L_d \not\in \text{NP}$. In doing so, we demonstrate that Lin's claim that $\text{NP} \neq \text{coNP}$ is not established by his paper. In addition, we note that a number of further results that Lin claims are not validly established by his paper.
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id arxiv_https___arxiv_org_abs_2505_05658
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Critique of Lin's "On $\text{NP}$ versus $\text{coNP}$ and Frege Systems"
DeJesse, Nicholas
Lyudovyk, Spencer
Pai, Dhruv
Reidy, Michael
Computational Complexity
In this paper, we examine Lin's "On NP versus coNP and Frege Systems" [Lin25]. Lin claims to prove that $\text{NP} \neq \text{coNP}$ by constructing a language $L_d$ such that $L_d \in \text{NP}$ but $L_d \notin \text{coNP}$. We present a flaw in Lin's construction of $D$ (a nondeterministic Turing machine that supposedly recognizes $L_d$ in polynomial time). We also provide a proof that $L_d \not\in \text{NP}$. In doing so, we demonstrate that Lin's claim that $\text{NP} \neq \text{coNP}$ is not established by his paper. In addition, we note that a number of further results that Lin claims are not validly established by his paper.
title A Critique of Lin's "On $\text{NP}$ versus $\text{coNP}$ and Frege Systems"
topic Computational Complexity
url https://arxiv.org/abs/2505.05658