On 24 Aug 2012, at 19:23, meekerdb wrote:

On 8/24/2012 9:43 AM, Bruno Marchal wrote:

And those theorem are non constructive, meaning that in the world of inference inductive machine, a machine capable of being wrong is already non computably more powerful than an error prone machine.

There's something wrong with that sentence. An error prone machine one that is capable of being wrong, and hence non-computably more powerful than itself?

Yes. It makes sense because the identification criteria for the inductive inference has been weakened. A machine allowed to do one error (that is synthesizing a program giving a wrong output) will recognize a non computably vaster class of phenomena, even if wrong on some input. See the paper of Case and Smith reference in my url, or the book by Osherson, Stob, and Weinstein.



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