On Mon, Apr 15, 2002 at 04:15:32PM +0200, Juergen Schmidhuber wrote:
> For example, suppose the process computing the universe is not optimally
> efficient for some reason. As long as the resource postulate holds the
> true prior cannot dominate the Speed Prior, and S-based predictions
> will be fine.
That reminds me, a while ago you wrote:
> Good point. Simulating a k-tape TM on a 1-tape TM may cause a quadratic
> slowdown indeed. Simulating a k-tape TM on a 2-tape TM, however, causes
> at most logarithmic slowdown. One should use a TM with several work tapes.
Isn't even a logarithmic slowdown enough to imply that a 2-tape TM based
Speed Prior does *not* dominate a 3-tape TM based Speed Prior? (Or at
least that we have no proof that it does?) It seems that we have no proof
that the set of Speed Priors based on k-tape TMs has a universal element.