NP-complete Problems and Physical Reality · HackerPapers discussions

NP-complete Problems and Physical Reality — mentioned by hiddencost

Sun, 13 Aug 2023 05:27:14 GMT

https://arxiv.org/abs/quant-ph/0502072 Your comment reminded me of this classic of the genre. An extremely approachable read.

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NP-complete Problems and Physical Reality — mentioned by ScottAaronson

Fri, 29 Jun 2018 18:48:22 GMT

Yup. :-) Or better yet, we could bifurcate into: (1) Why is our universe apparently unable to solve the halting problem for Turing machines? The answer, presumably, is a combination of the physical Church-Turing Thesis (specifically, the apparent impossibility of Turing-uncomputable processes in our world), with Church and Turing and Post's theorem on the unsolvability of the halting problem. Of course one could then push back and ask why the Church-Turing Thesis should be true of our world: i.e., why shouldn't there be physical "hypercomputers"? That's an enormous question, but my old survey…

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NP-complete Problems and Physical Reality — mentioned by Rickasaurus

Thu, 24 Aug 2017 23:53:54 GMT

"NP-complete Problems and Physical Reality" by Scott Aaronson. It relates NP-complete problems to examples in nature. Excellent paper and a fun read. https://arxiv.org/abs/quant-ph/0502072

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NP-complete Problems and Physical Reality — HN submission

Tue, 29 Nov 2016 17:37:01 GMT

NP-Complete Problems and Physical Reality (2005)

5 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

NP-complete Problems and Physical Reality — mentioned by jessedhillon

Mon, 07 Nov 2016 17:16:08 GMT

Direct PDF link for the lazy (e.g. me): https://arxiv.org/pdf/quant-ph/0502072v2.pdf

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NP-complete Problems and Physical Reality — mentioned by nabla9

Mon, 07 Nov 2016 16:18:01 GMT

I like Scott Aaronsons approach: Using NP hardness asumption as a physical constraint and seeing what follows. https://arxiv.org/abs/quant-ph/0502072

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NP-complete Problems and Physical Reality — mentioned by evanpw

Thu, 03 Dec 2015 15:13:24 GMT

Related (amazing) paper by Scott Aaronson: "NP-complete Problems and Physical Reality" (http://arxiv.org/abs/quant-ph/0502072). He proposes "anthropic computing" as a way of solving NP-complete problems in polynomial time: guess an answer, then kill yourself if the answer is wrong.

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NP-complete Problems and Physical Reality — mentioned by chriswarbo

Wed, 11 Nov 2015 13:26:40 GMT

Reminds me of http://arxiv.org/abs/quant-ph/0502072 Also, as a Physicist and Computer Scientist, it explains my uneasiness when existence claims are made regarding infinite objects. For example, we can describe the trajectory of a particle using Feynman path integrals, which involve infinite sums over all possible paths. That's fine. Some will then treat this as a mechanism, i.e. claim that the reason particles have the trajectories they do, is because they literally are taking every possible path at once. This kind of reasoning sets my off my CS alarm bells, and articles like this provide…

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NP-complete Problems and Physical Reality — mentioned by ColinWright

Mon, 17 Aug 2015 17:01:57 GMT

OK, it says this: For example, the Steiner Tree problem (STP) is known to be NP-complete ... Nonetheless, a simple physical process (termed an analog computation) can apparently solve it quickly. No, it can't. Small, trivial cases can be solved, but I believe it's been shown that when you get to mildly interesting cases it's just as likely to find non-optimal solutions, and sometimes even more likely to find non-optimal solutions. This is at the top of page 2, and it doesn't bode at all well. Section 3 of Aaronson's paper[0] discusses this explicitly, and comes to the conclusion that, not to…

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NP-complete Problems and Physical Reality — HN submission

Tue, 14 Jul 2015 10:33:42 GMT

NP-Complete Problems and Physical Reality (2005)

88 points; 33 discussion replies on HN. Paper and source history. A submission is not an endorsement.

NP-complete Problems and Physical Reality — mentioned by ikeboy

Sun, 31 May 2015 18:54:44 GMT

See also NP-complete Problems and Physical Reality http://arxiv.org/abs/quant-ph/0502072

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NP-complete Problems and Physical Reality — HN submission

Mon, 25 May 2015 16:49:54 GMT

NP-Complete Problems and Physical Reality (2005) [pdf]

2 points; 1 discussion reply on HN. Paper and source history. A submission is not an endorsement.

NP-complete Problems and Physical Reality — mentioned by weinzierl

Mon, 25 May 2015 16:48:21 GMT

This is a good follow up read to the classic "NP-complete Problems and Physical Reality"[1] and has not been discussed here. [1] http://arxiv.org/pdf/quant-ph/0502072v2.pdf

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NP-complete Problems and Physical Reality — HN submission

Sun, 25 Jan 2015 06:30:11 GMT

NP-complete Problems and Physical Reality (2005)

94 points; 16 discussion replies on HN. Paper and source history. A submission is not an endorsement.

NP-complete Problems and Physical Reality — mentioned by jerf

Mon, 14 May 2012 12:34:13 GMT

Only for sufficiently small definitions of "solve": http://arxiv.org/pdf/quant-ph/0502072v2 Definitions which turn out to be very small indeed.

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NP-complete Problems and Physical Reality — HN submission

Tue, 27 Dec 2011 12:43:01 GMT

NP Complete Problems and Physical Reality

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

NP-complete Problems and Physical Reality — mentioned by alextp

Mon, 09 Aug 2010 00:58:15 GMT

This paper http://arxiv.org/pdf/quant-ph/0502072 explores what it means for physical reality. It's really interesting. There are many possible scenarios, however. This blog post http://rjlipton.wordpress.com/2009/07/03/is-pnp-an-ill-posed... describes some of them.

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