Le 26-oct.-07, à 16:21, Juergen Schmidhuber a écrit :
> Impressive result by Alex Smith!
Absolutely.
> Funny though how Wolfram's web sites on this
> print Wolfram's name in larger font and more
> frequently than Smith's, even trying to sell this
> as "New Kind Of Science" although it's just a
> continuation of a decades-old search for
> small universal Turing machines :-)
Yes.
>
> BTW, check out Marcus Hutter's older posting to
> the Kolmogorov Complexity mailing list on whether
> such machines should really count as UTMs or not:
> http://mailman.ti-edu.ch/pipermail/kolmogorov/2007/000245.html
Yes. And I agree with Marcus. The search of small UM in the context of
Kolmogorov Complexity is, imo, a red herring. All the interest in such
universal notion (of complexity, ...) is that there are equivalent up
to a constant. Wanting a special (little) constant cut the interest in
such theories at the start. Of course some existence theorem can be
made simpler, but that's all.
But small UM are interesting for many other reasons. The main one is
they put light on the nature of universality in math and computation
theory.
Wolfram says that the universality of its 2,3 UM adds evidences for the
CEP (comp equivalence principle). I don't see one. Idea?
Bruno
>
> JS
> http://www.idsia.ch/~juergen/computeruniverse.html
> http://www.idsia.ch/~juergen/wolfram.html
>
> On Oct 24, 2007, at 8:32 PM, Tom Caylor wrote:
>> We're excited to announce that the $25,000 Wolfram 2,3 Turing Machine
>> Research Prize has been won.
>> Alex Smith, a 20-year-old undergraduate in Birmingham, UK, has given a
>> 40-page proof that Wolfram's 2,3 Turing machine is indeed universal.
>> This result ends a half-century quest to find the simplest possible
>> universal Turing machine. It also provides strong further evidence for
>> Wolfram's Principle of Computational Equivalence. The official prize
>> ceremony is planned for November at Bletchley Park, UK, site of Alan
>> Turing's wartime work.
>> For more information about the prize and the solution, see:
>> http://www.wolframprize.org
>> Stephen Wolfram has posted his personal reaction to the prize at:
>> http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html
>
>
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Nov 02 2007 - 10:28:02 PDT