Hmm, can't we simply turn any coding into a prefix-free-coding by
prefacing each code for a GTM with a number of 1s indicating the
length of the following description, and then a 0 signaling the
beginning of the actual description? I am not especially familiar with
the prefix issue, so please forgive me if I am wrong...

Also, I do not understand why there would be reason to suspect that
the probability distribution, once properly defined, would turn out to
be equivalent to the S-L prior. GTMs can formally represent more
things than TMs, so why would those things not end up in the
probability distribution?

--Abram Demski

On Thu, Nov 27, 2008 at 5:18 AM, Russell Standish <[EMAIL PROTECTED]> wrote:
> On Wed, Nov 26, 2008 at 02:55:08PM -0500, Abram Demski wrote:
>> Russel,
>> I do not see why some appropriately modified version of that theorem
>> couldn't be proven for other settings. As a concrete example let's
>> just use Schmidhuber's GTMs. There would be universal GTMs and a
>> constant cost for conversion and everything else needed for a version
>> of the theorem, wouldn't there be? (I am assuming things, I will look
>> up some details this afternoon... I have the book you refer to, I'll
>> look at the theorem... but I suppose I should also re-read the paper
>> about GTMs before making bold claims...)
>> --Abram
> IIRC, Schmidhuber's machines were non-prefix Turing machines. As such
> there may or may not be a probability distribution in the first
> place. Solomonoff's original proposal using universal Turing machine
> didn't work because the probability distribution could not be defined.
> If, however, a probility distribution could be defined, then it would
> probably end up being equivalent to the S-L universal prior.
> Cheers
> --
> ----------------------------------------------------------------------------
> A/Prof Russell Standish                  Phone 0425 253119 (mobile)
> Mathematics
> UNSW SYDNEY 2052                         [EMAIL PROTECTED]
> Australia                      
> ----------------------------------------------------------------------------
> >

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