Russel, 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...

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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 http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---