4 research outputs found
Barbosa, Uniform Polynomial Time Bounds, and Promises
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)