Re: What is the Result from Invoking this Halt Function?

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/24/04 

Date: Tue, 24 Aug 2004 02:51:34 GMT

"Simon G Best" <s.g.best@btopenworld.com> wrote in message news:4129238D.9010608@btopenworld.com...
> Marc Goodman wrote:
> >
> > Peter is talking about a TM that is extended to have access
> > to its own state transition table. Imagine, for example, a
> > TM with that extension that was calculating the MD5 checksum
> > of its own state transition table. Any "local transformation"
> > would be enough to change the result in such a case.
> >
> > So I don't believe that with the extension Peter is talking about,
> > it's necessarily true that TransmogrifiedWillHalt and
> > plain old WillHalt necessarily return the same values.
> >
> > Though I believe your proof below is reasonable for "plain old"
> > TMs.
>
> However, Olcott's augmented 'TM', P, is supposed to be run as a program
> on a special 'UTM', V, that /is/ an ordinary TM. We can therefore
> construct an ordinary TM that's equivalent to P-running-on-V, and then
> transmogrify :-)
>
> If Olcott's special 'UTM' isn't an ordinary TM, and if there can't be a
> computationally equivalent TM, then so what? That would leave the
> classic proof that no /TM/ could ever be a halt analyzer standing untouched.
>
> At some point, it's got to come down to a TM that either is a halt
> analyzer itself, or which runs a halt analyzer as a program. Either
> way, it's not really difficult to constuct a classic halt-analyzing TM.
> The classic proof of its nonexistence then applies for that
> constructed TM, and, by implication, also proves the nonexistence of
> Olcott's TM and/or program.
>
> Simon
>
The classic proof simply no longer applies. My method(s) have
permanently circumvented the classic proof. You can no longer
show that the Halting problem is undecidable. Since there is
at least one case where the Halting Problem is not undecidable,
it can not be proven to be undecidable.

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