I believe that P != NP in a theoretical sense, but that practically it will make less difference, as SAT solvers and related tools get better. I have no real basis for this, just a gut feeling based on seeing lots of failed P=NP proof attempts.
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Agreed. Basically I defer to experts, who mostly think P ≠ NP. But I also think it’s an academic question (which is not to say solving it wouldn’t be valuable!) NP is actually pretty “easy” these days in practice, because SAT solvers slice and dice the problems so well.
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Oh, I actually got disappointed for a minute until I looked at the date
You got me!
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Knuth suspects P = NP. The cardinality of P is uncountably infinite. So what are the odds that out of that immense infinity there exists no solution to NP-Complete problems?
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I don't know if that follows. The set of real numbers > 2 is uncountably infinite, but we can say with certainty that none of those numbers is <= 2.
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Best April Fools joke
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And then it'll be a question of whether a generalised version can be accelerated in hardware.
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We can just throw an unspecified number of Cores at it and prove that NC=P that way.
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Underrated tweet.
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