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> Intuitively, almost everyone assumes that P != NP

Donald Knuth believes P = NP.

Source: http://www.informit.com/articles/article.aspx?p=2213858&WT.m... (question 17). Also cf. https://www.quora.com/Why-does-Donald-Knuth-think-that-P-NP




But keep in mind that he (and just about everyone who believes P = NP) thinks any proof of it will be non-constructive and that we will never actually find a polynomial-time algorithm for NP problems.




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