The halting problem is decidable on a set of asymptotic probability one · HackerPapers discussions

The halting problem is decidable on a set of asymptotic probability one — mentioned by Xcelerate

Wed, 31 Jan 2024 06:14:20 GMT

I see your pathological proof of existence and raise you an asymptotic probability of one: “The halting problem for Turing machines is perhaps the canonical undecidable set. Nevertheless, we prove that there is an algorithm deciding almost all instances of it.” https://arxiv.org/pdf/math/0504351.pdf

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The halting problem is decidable on a set of asymptotic probability one — mentioned by schoen

Fri, 18 Jun 2021 00:56:41 GMT

(2005) and I think the URL should be https://arxiv.org/abs/math/0504351 (that is, you forgot the path component "math")

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The halting problem is decidable on a set of asymptotic probability one — HN submission

Fri, 18 Jun 2021 00:47:45 GMT

The halting problem is decidable on a set of asymptotic probability one (2005)

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

The halting problem is decidable on a set of asymptotic probability one — mentioned by Xcelerate

Fri, 30 Nov 2018 10:29:43 GMT

Looks like the paper is a lot older than I thought it was: https://arxiv.org/abs/math/0504351 My code isn't public at the moment. It's written in Julia and rather messy so I'd have to clean it up a bit, but I wouldn't be opposed to putting it on Github. I really like your project idea btw. It never occurred to me that all that time and energy wasted on proofs of work could be spent approximating the universal distribution. That could be really valuable.

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The halting problem is decidable on a set of asymptotic probability one — mentioned by antidesitter

Sat, 04 Aug 2018 01:59:01 GMT

Well, obviously, the shortest program that outputs "0" is "0". And the shortest program that outputs "1" is "1". We're only interested in the general case, not specific cases. Just wanted to note that we have techniques for termination analysis that cover entire classes of programs of arbitrary length, not just specific short programs. See ranking function synthesis for an example. Hell, under some universal computational models, the halting problem is polynomial-time decidable for almost all programs: https://arxiv.org/abs/math/0504351.

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The halting problem is decidable on a set of asymptotic probability one — HN submission

Wed, 14 Sep 2016 21:36:24 GMT

The halting problem is decidable on a set of asymptotic probability 1

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