Re: Refutation of the Halting Problem's Proof (Clarifications Wanted)

newstome_at_comcast.net
Date: 08/25/04 

Date: Wed, 25 Aug 2004 13:58:33 GMT

In comp.theory Peter Olcott <olcott@worldnet.att.net> wrote:
> www.halting-proiblem.com
> I want to make what I am saying as clear as possible. If anyone
> has any points that are still not clear, this is the thread to ask for
> clarifications.
>
> Also I would like to work towards a consensus of the best way
> to present the ideas that are mentioned on my website, and in
> these threads. This might require me to formalize some of these
> points. I would be happy to make my material easier to understand,
> and eliminate any ambiguities. I welcome all constructive critiques.

That's exactly what you need to do: Make clear definitions to remove
any ambiguities. While several of us have tried to lead you in this
direction and have helped try to make things clear, you have rebuffed
that at every turn.

> The end result of these discussions will be a website posting that most
> everyone can agree on the meaning of. In other words it should be
> clear to everyone what I am saying.

Hopefully if "everyone" includes you (just like a "for all" quantifier
includes your TMs), then you'll understand what you're saying too and
why it doesn't help in attacking the halting problem at all.

> If there seem to be any major gaps in what I am saying, please point
> these out.

Definitions, definitions, definitions.

> The most significant gap that I can see is exactly how to
> construct the augmented UTM without going beyond the capabilities
> of an regular TM. That this can be accomplished seems obvious.
> Exactly how this would be accomplished is less obvious.

Unlike some others here I have absolutely no problem with you defining
such a UTM. I've even proposed clear definitions on how it could work
(for example, giving the program that is running the capability of
requesting that the TM/UTM dump the entire state transition table to
the tape). Every time a clear definition is suggested, however, you
change the subject. If you want to make any progress toward
understanding this, then that has to stop.

It's clear (to everyone but you) that making such a UTM has absolutely
no effect on the halting problem -- you can't solve the halting
problem with such a special UTM any more than you can with a regular
TM (which can't be done). Convincing you of that fact would be a
whole lot easier if you'd give people a clear definition of what your
augmented TM actually is. 

-- 
That's News To Me!
newstome@comcast.net

Relevant Pages

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