Couple of comments to the post below.
1. P=?NP is a purely mathematical problem, whereas the existence of an HPO
box is an emperical matter. If we had access to a purported HPO box while
P=?NP is still unsolved, we can use the box to exhaustively search for
proofs of either P=NP or PNP.
2. I
Wei Dai writes:
1. P=?NP is a purely mathematical problem, whereas the existence of an HPO
box is an emperical matter. If we had access to a purported HPO box while
P=?NP is still unsolved, we can use the box to exhaustively search for
proofs of either P=NP or PNP.
I've seen many speculations
Dear Hal and Wei Dai,
One question: Does it not make sense that if there did exist an instance
of a P=NP computation within our physical universe that Nature would not
have found a way to implement it widely? The fact that the folding of
proteins, a known NP complete problem, takes a
I want to describe in more detail how I see the Universal Distribution
(UDist) applying to the measure of observers and observer moments.
I apologize in advance for the length of this message; someday I will
collect this and my others on this topic into a set of web pages.
To briefly reiterate,
But I'm not sure what it would mean for an instance of P=NP
computation to exist in nature. What it would mean in computer
science is that there was an algorithm for translating any NP
algorithm into a P algorithm for the same problem. This refers
to classes of algorithms for classes of
Hi Brent,
Ok, I am rapidly loosing the connection that abstract models have with
the physical world, at least in the case of computations. If there is no
constraint on what we can conjecture, other than what is required by one's
choice of logic and set theory, what relation do mathematical
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