Re: Solution to the halting Problem?

From: David Hilsee (davidhilseenews_at_yahoo.com)
Date: 07/22/04 

Date: Wed, 21 Jul 2004 21:29:49 -0400

"Peter Olcott" <olcott@worldnet.att.net> wrote in message
news:GbELc.120889$OB3.11857@bgtnsc05-news.ops.worldnet.att.net...
>
> "Keith H Duggar" <duggar@mit.edu> wrote in message
news:b47de02.0407210829.69e99944@posting.google.com...
>
> > The authors misinterpretation of the halting problem seems to
> > come into play with his refute of objection (2) we he believes
> > it is sufficient to show that the proof does not apply to SOME
> > program. When it fact the opposite is true. The proof only
>
> There does not exist any program in the set of all possible
> programs a program that would cause my method to fail to
> provide the correct halting result.

This paragraph is contradictory:

"The possibility of creating one or more instances of WillHalt() that permit
LoopIfHalts() to function does not refute this method. In other words
defeating the security in less than every possible case does not prove that
this method does not work. One single case where the security is not
circumvented proves that the idea still works. Even a single case proves
that this method still works because this single case would form the
required single counter-example to refute the claim:
No program can ever be written to determine whether any arbitrary program
will halt"

This paragraph admits that it is possible to create a LoopIfHalts function
that causes the WillHalt() method to fail, and then says that this is not
proof that the method does not work. However, it is most certainly proof
that the method does not work in every case, which means that it fails to
meet the requirement, which is that it must work for "any arbitrary
program." One single case where the "security is not circumvented" only
proves that the method works for that single case, which is not proof that
it works for any program. That last sentence is confusing, because it
states that a program that can work for a single case is enough to refute
the claim that a program cannot work for every case. This is obviously
false.

BTW, I think the first link returned on my Google search
(http://www.cgl.uwaterloo.ca/~csk/halt/) had a more applicable description
and better source code than the one on halting-problem.com. 

-- 
David Hilsee

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