A Critique of Chen's "The 2-MAXSAT Problem Can Be Solved in Polynomial Time"
Tran Duy Anh Le, Michael P. Reidy, Eliot J. Smith
TL;DR
The paper critically examines Chen's claim of a polynomial-time solution to the $2$-MAXSAT problem, detailing a sequence of structural constructions (from converting $2$-CNF to $2$-DNF using fresh variables, to building $p$-graphs, a trie, and a layered graph) and two central algorithms. It provides concrete counterexamples showing that Algorithm 1 can produce incorrect results and questions the correctness and time guarantees of Algorithm 2, as well as the subsequent graph-improvement (Algorithm 3) and the overall complexity analysis. The critique emphasizes the lack of formal definitions and proofs, and argues that the presented analyses do not justify polynomial-time performance or correctness, thereby failing to establish $P=NP$. The work reinforces that $2$-MAXSAT remains NP-hard and that Chen's approach does not provide a credible polynomial-time algorithm, despite extensive use of illustrative examples. Overall, the paper highlights the necessity of rigorous formalism and worst-case proofs when making claims about fundamental complexity classes.
Abstract
In this paper, we examine Yangjun Chen's technical report titled ``The 2-MAXSAT Problem Can Be Solved in Polynomial Time'' [Che23], which revises and expands upon their conference paper of the same name [Che22]. Chen's paper purports to build a polynomial-time algorithm for the ${\rm NP}$-complete problem 2-MAXSAT by converting a 2-CNF formula into a graph that is then searched. We show through multiple counterexamples that Chen's proposed algorithms contain flaws, and we find that the structures they create lack properly formalized definitions. Furthermore, we elaborate on how the author fails to prove the correctness of their algorithms and how they make overgeneralizations in their time analysis of their proposed solution. Due to these issues, we conclude that Chen's technical report [Che23] and conference paper [Che22] both fail to provide a proof that ${\rm P}={\rm NP}$.