Re: Can you find anything wrong with this solution to the Halting Problem?

From: Peter Olcott (olcott_at_att.net)
Date: 07/14/04 

Date: Wed, 14 Jul 2004 00:01:53 GMT

> The basis of your proof is that it's possible to construct
> situations in which A is not allowed to tell if B will exit
> or not. This is 100% true but 0% useful. It's not necessary
> for the above proof that _all_ programs A halt on input B
> where B is a program that infinite loops, etc., it's only
> necessary that it be possible to construct one program A
> under one set of circumstances for which the above is true.

This is a slippery point, that most fail to get. This point is crucial
to understand the meaning of my claim. I construct a program
that can correctly determine halting for the universal set of
programs, right there we are done, I have completely proven
my point.

For clarity I will continue, this is the place where most
people get lost. You are able to modify my original program
so that it no longer works. You claim that this is a basis
to show that my claim is not proven. YET and its a very
CRUCIAL ONE, my original program is still able to
correctly determine whether or not your modified version
halts. Also is is still able to determine if any element in the
universal set of programs halts.

All the modification of my program was (under the new
set of conditions) totally fruitless. The same pattern that
worked again, and again for fifty years, now all of a sudden
quits working, because one of the crucial requirements
has been eliminated.

> Then, under that circumstance, A cannot exist which means
> it is impossible to construct A for _ALL_ circumstances.
> That's what the proof says: There may well be cases of
> A and B where A will halt if B loops and A will loop if
> B halts, but it is impossible to construct a program A
> where A will _always_ halt if B loops and will _always_
> loop if B halts. Youre counterproof does not refute this,
> and therefore your counterproof is not a counterproof of
> the halting problem.
>
> I've now wasted far more time on this post than it was
> worth, thus proving that Kent was 100% right about invincible
> ignorance and timewasting morons, since the odds that you will accept
> the above as true are virtually 0%.
>
>
>

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