On Salum's Algorithm for X3SAT

04/07/2021

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by   Arian Nadjimzadah, et al.

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This is a commentary on, and critique of, Latif Salum's paper titled "Tractability of One-in-three 3SAT: P = NP." Salum purports to give a polynomial-time algorithm that solves the NP-complete problem X3SAT, thereby claiming P = NP. The algorithm, in short, fixes the polarity of a variable, carries out simplifications over the resulting formula to decide whether to keep the value assigned or flip the polarity, and repeats with the remaining variables. One thing this algorithm does not do is backtrack. We give an illustrative counterexample showing why the lack of backtracking makes this algorithm flawed.