Quote:
Originally Posted by Buffy
The Halting Problem requires *both* the function and a *finite* input. If as you suggest, you do an infinite regress of feeding the halting algorithm itself with the input to the algorithm itself, with the input to the algorithm itself, with the input to the algorithm itself, ad nauseum, then you've really only proved the theorem correct!
The Halting Problem theorem is only saying that a *general* algorithm cannot be developed that works for *all* function/finite-input pairs. You could feed the algorithm to itself with a *different* finite input, and it would halt. The fact that the infinite regress case does not work simply proves the theorem.
So,
is not at all an "assumption" its the fact that proves the theorem....
People seldom see the halting and painful steps by which the most insignificant success is achieved, 
Buffy |
Aww isn't that cute... I didn't say anything about feeding it anything infinite. I said that any halting machine which was fed a finite encoding of itself would cause an infinite regress instead of going through it's normal function.
Thus the only thing proven is that it cannot operate on itself. It could still very well exist and handle all other machine/input combos.
