Re: Alan Turing's Halting Problem is Incorrect (FINAL PART)

From: Martin Shobe (mshobe_at_sbcglobal.net)
Date: 07/08/04 

Date: Thu, 08 Jul 2004 03:31:31 GMT

On Thu, 08 Jul 2004 00:39:17 GMT, "Peter Olcott"
<olcott@worldnet.att.net> wrote:

>> Well of course the halting problem is artificially contrived, it's
>> about Turing machines, which are artificially contrived.
>>
>> Martin
>
>A TM is derived for the real purpose of determining the actual
>limits of computation. TM's are perfectly valid and useful. They
>provide an excellent means to study the foundations of computing
>with a model of minimal complexity.

I agree with you to this point.

The counter-example program
>that proposes to prove the case of the Halting Problem is another
>case entirely. It does not relate to anything real, or anything
>possibly real, or even a comparable measure of a possible real
>thing. It does not show the real limits of the potential capabilities
>of automated program validation. It is purely an artificial contrivance
>used to prove a pointless point.

The question of does a Turing Machine halt on a given input, is a
"real" question, as it applies, in a straight forward manner, to real
computer programs. It's an important question in that the vast
majority of the time, we want our programs to halt. The
counter-example program is important because it shows that any attempt
to let the computer do the work is going to fail for certain programs.
This is ended a real limit to what can be done with computers.

Martin

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