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I think this should be an AI problem.

Is there any algorithm that, given any number sequence, can find patterns?

And the patterns could be abstract as it can be...

For example:

12112111211112 ... ( increasing number of 1's separated by 2 )

1022033304440 ...

11114444333322221111444433332222.. (this can be either repetition of 1111444433332222

or

four 1's and 4's and 3's and 2's...)

and even some error might be corrected

1111111121111111111112111121111 (repetition of 1's with intermittent 2's)

TResponse
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KH Kim
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1 Answers1

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No, it's impossible, it's related to the halting problem and Gödels incompleteness theorem.

Furthermore some serious philosophical groundwork would need to be done to actually formalize the question. Firstly what is exactly meant by "recognizing a pattern". We should assume it identifies:

  • The most expressive true pattern. So "some numbers" is invalid as it is not expressive enough

The argument would go something like; assume the algo exists, and now consider a sequence of numbers that is a code for a sequence of programs. Now suppose we have a sequence of halting programs, by above it must know, it cannot just say "some programs" as that is not maximally expressive. So it must say "halting programs" Now given halting program P we can add it to the halting list and the algo should say "halting programs", which would conclude P halts, if it doesn't halt then the algo should say something else, like "some halting and one non halting". Therefore the algo can be used to define an algo that can decide if a program halts.

Not a formal proof now, but not a formal question :) Suggest you look up Gödel, Halting problem and Kolmogorov Complexity.

keyser
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samthebest
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    Thank you for answering. However my question is somewhat more practical. Yes I thought there could not be an alogrithm that catches all the possible patterns in a sequence. I am just wondering there might be some algorithm which can catch some patterns in a sequence. I heard some researcher in analogical thinking made those kind of programs, but I am not sure. Maybe AI researcher could have other implementation of that kind, I thought. – KH Kim Sep 16 '14 at 15:43