A Critique of Du's "A Polynomial-Time Algorithm for 3-SAT
Yumeng He, Matan Kotler-Berkowitz, Harry Liuson, Zeyu Nie
TL;DR
This critique targets Lizhi Du's claimed polynomial-time algorithm for $3$-SAT, focusing on the destroyed checking tree framework and Algorithm 1. It identifies a critical flaw in Step 3 of Algorithm 1 that can misclassify satisfiable instances as unsatisfiable, undermining the overall polynomial-time approach. A concrete counterexample supports the claim that the method may produce incorrect results, and the flaw propagates to the rest of the purported algorithm, invalidating the $P = NP$ conclusion. The work underscores the necessity of rigorous correctness in proposals for polynomial-time solutions to NP-complete problems and casts doubt on the viability of Du's approach.
Abstract
In this paper, we examine the claims made by the paper "A polynomial-time algorithm for 3-SAT" by Lizhi Du. The paper claims to provide a polynomial-time algorithm for solving the NP-complete problem 3-SAT. In examining the paper's argument, we find a flaw in one of the main sections of its algorithm. We argue that this flaw causes the paper's algorithm to incorrectly decide that an infinite family of satisfiable 3-CNF boolean formulas are not satisfiable. Therefore, the paper does not establish that P = NP.