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

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/10/04 

Date: Tue, 10 Aug 2004 06:18:54 GMT

"Marc Goodman" <marc.goodman@comcast.net> wrote in message news:U_XRc.277260$Oq2.198273@attbi_s52...
> Peter Olcott wrote:
> >>Isn't it about time you started to read Turing's proof so you can
> >>pinpoint the exact line which is in error?
> >
> > It looks like the error is in its application to the Halting Problem.
> > I did print it out. There is some material that is interesting and easy.
>
> So, Peter, just to make sure I understand...
> You now say that since your refutation of Turing's proof does
> not actually apply to Turing's proof, that it's because Turing's
> proof has been erroneously applyed to halting problem? Or, your

It looks like Turing's proof may be erroneously applied to the
Halting Problem. It looks like Turing might have assumed that
the Halt function must always return a result to all callers. I
don't think that the diagonalization process has the facility to
operate otherwise. It does not allow a choice to be made
whether or not to derive a result. Its more like a multiplication
table. So tentatively it looks just like what I have been saying
all along.

Quick Summary:
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.

Since returning the result back to the program being analyzed is not the
only way to construct a halt analyzer, his proof did not show that
constructing a halt analyzer that works correctly for all input is impossible.

> failure to find a failure in the proof is because of a failure
> in the proof you're failing to find a failure in?
>
> Just thought I'd make sure that's what you're saying...
>

Relevant Pages

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  • Re: What is the Result from Invoking this Halt Function?
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    (comp.theory)