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

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/13/04 

Date: Fri, 13 Aug 2004 00:46:16 GMT

"Kent Paul Dolan" <xanthian@well.com> wrote in message news:5396f249c0a76df409c6a009918fec1a.48257@mygate.mailgate.org...
> "Peter Olcott" <olcott@worldnet.att.net> wrote:

> > Alan Turing conclusively proved is that it is
> > impossible to construct a halt analyzer that
> > always returns a correct result back to the
> > program being analyzed.
>
> No, he didn't. He proved that it is impossible to
> produce a halt analyzer that returns a correct
> result from among the answer set "halts", "does not
> halt" in finite time, full stop.

Yet his proof fails to support this conclusion if you
remove the requirement that this return value must
be provided to each and every caller, including the
subject of the halt analysis.

All that it takes to refute the above statement is to
discern those times when the halt analyzer is not
being invoked within the context of another TM,
and in every other time refrain from returning results.

          1=TRUE=HALTS
          0=FALSE=DOES NOT HALT
SPACE=NO ANSWER IS BEING PROVIDED

> The problem of construction of a Halting Problem
> Solver has nothing to do with "returning a result
> to a program", only to do with "returning a result",
> a distinction you repeatedly prove yourself
> incompetent to grasp.
>
> > his proof did not show that constructing a halt
> > analyzer that works correctly for all input is
> > impossible.
>
> Well, yes, it did. You've merely tried to redefine
> what a halt analyzer _is_, and then framed an
> argument around this entirely other entity, but
> the entirely other entity which you have defined is
> of absolutely no interest to computer theory, so
> you have wasted your time, and that of many others
> in the process.
>
> > I have proven this. If you don't accept this, then
> > you are in denial.
>
> No, I don't "accept this" because you have never
> produced anything proving anything at all related to
> a Halt Problem Solver, only to your broken version
> of that conceptual entity.
>
> > The method on my website specifically shows how to
> > refute the definition of the Halting Problem
> > listed below.
>
> How sad for you that "the definition of the Halting
> Problem listed below" is not the definition of the
> Halting Problem, then.
>
> > Definition of the Halting Problem
>
> > There does not exist a Turing Machine that can
> > correctly determine whether or not each and every
> > element in the universal set of Turing Machines
> > will execute in a finite number of steps.
>
> That is not even vaguely close to a definition of
> the Halting Problem. Perhaps if you bothered to
> understand the Halting Problem, so that you were not
> of the opinion that was its definition, you could
> begin for the first time to make intelligent
> comments about the Halting Problem?

Halting Problem according to Alan Turing:
The problem of finding out whether a given number is the D.N of a
circle-free machine,

Translation: (The problem of finding out whether a given Turing Machine
Description specifies a Turing Machine that fails to Halt).

The above translation was based on pages 5, 12 and 18 of the following
http://www.abelard.org/turpap2/tp2-ie.asp

Turing's words continued:
and we have no general process for doing this in a finite number of steps.
In fact, by applying the diagonal process argument correctly, we can show
that there cannot be any such general solution.

> > www.halting-problem.com
>
> > This is a whole new proof,
>
> No, it is the same tired nonsense tricked out in
> new words, and not a "proof" any more than all the
> non-proofs that preceded it.
>
> > the only thing that remains the same is the above
> > quick summary.
>
> Which is also incorrect.
>
> > I will be happy to explain any points that are
> > unclear.
>
> Okay, explain the point that you have tried to
> overturn many well founded and famous results in the
> sciences, failed miserably every single time, and
> yet continue your incompetent attempts as if
> learning from your failures were beyond your
> capacity. Answer to any question but this one, or
> answers to this one that attempt to evade the issue
> or deny the facts, will be considered non-responsive
> (and brand you a fool (yet again)).
>
> xanthian, in TWOT mode.
>
>
> --
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