Barbosa, Uniform Polynomial Time Bounds, and Promises

Lane A. Hemaspaandra; Kyle Murray; Xiaoqing Tang

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arXiv · 1106.1150

Barbosa, Uniform Polynomial Time Bounds, and Promises

Lane A. Hemaspaandra·Kyle Murray·Xiaoqing Tang

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Abstract

This note is a commentary on, and critique of, Andre Luiz Barbosa's paper entitled "P != NP Proof." Despite its provocative title, what the paper is seeking to do is not to prove P \neq NP in the standard sense in which that notation is used in the literature. Rather, Barbosa is (and is aware that he is) arguing that a different meaning should be associated with the notation P \neq NP, and he claims to prove the truth of the statement P \neq NP in his quite different sense of that statement. However, we note that (1) the paper fails even on its own terms, as due to a uniformity problem, the paper's proof does not establish, even in its unusual sense of the notation, that P \neq NP; and (2) what the paper means by the claim P \neq NP in fact implies that P \neq NP holds even under the standard meaning that that notation has in the literature (and so it is exceedingly unlikely that Barbosa's proof can be fixed any time soon).

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BibTeX RIS

Lane A. Hemaspaandra, Kyle Murray, Xiaoqing Tang. 2011-06-06. Barbosa, Uniform Polynomial Time Bounds, and Promises. https://arxiv.org/abs/1106.1150

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