Hi Tom,

Le Dimanche 11 Juin 2006 02:00, Tom Caylor a écrit :
> I've been wondering about this in the background for a while, so now I
> can ask this question.  OK, I think I understand everything so far.
> But...  if there are functions (in the list of *all* programmable
> functions) which will run forever, and you cannot (computably?) know
> which ones they are (otherwise you could solve the Halting problem?...
> or... at least by the digaonalization reasoning you've given), then
> isn't the Universal Dovetailer going to run into one of these programs
> and run forever?  Alternatively, if the UD executes the first
> instruction of each program, there are a (countably) infinite number of
> programs, so you would never get to the second instruction.

The UD doesn't work this way. The dovetailer dovetail ;) it means, first it 
generates the "first" program (programs are enumerated following the set N) 
and execute the first instruction of it, then it generate the second program, 
execute the first instruction of the second program, then the first 
instruction of the first program, then it generates the third one, executing 
its first instruction, the second instruction of the second program, the 
first of the first and so on ad infinitum.

This way the UD can't be stuck in a loop of one program it generates (even if 
the program itself will never halt).


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