Solomonoff Induction may require a trans-infinite level of complexity just to run each program. Suppose each program is iterated through the enumeration of its instructions. Then, not only do the infinity of possible programs need to be run, many combinations of the infinite programs from each simulated Turing Machine also have to be tried. All the possible combinations of (accepted) programs, one from any two or more of the (accepted) programs produced by each simulated Turing Machine, have to be tried. Although these combinations of programs from each of the simulated Turing Machine may not all be unique, they all have to be tried. Since each simulated Turing Machine would produce infinite programs, I am pretty sure that this means that Solmonoff Induction is, *by definition,*trans-infinite. Jim Bromer
On Thu, Jul 22, 2010 at 2:06 PM, Jim Bromer <jimbro...@gmail.com> wrote: > I have to retract my claim that the programs of Solomonoff Induction would > be trans-infinite. Each of the infinite individual programs could be > enumerated by their individual instructions so some combination of unique > individual programs would not correspond to a unique program but to the > enumerated program that corresponds to the string of their individual > instructions. So I got that one wrong. > Jim Bromer > ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
