Re: Yet another Attempt at Disproving the Halting Problem

From: >parr\(*> (parr_at_btinternet.nospamcom)
Date: 08/17/04 

Date: Tue, 17 Aug 2004 19:33:30 +0000 (UTC)

"Will Twentyman" <wtwentyman@read.my.sig> wrote in message
news:41220388$1_2@newsfeed.slurp.net...
|
| Since your website is down, I can't check that. I thought I saw
| something about halting without a returned value.

So you didn't think it worth taking a copy ;)

Below is text content of:
http://www.halting-problem.com/
>From about 2 days ago 

--
)>==ss$$%HTH(º>   Parr
==== start copied text which is copyright of Peter L Olcott 2004 ===
Disproving the Halting Problem
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.
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 for a specific
input data.
Basis of this Informal Proof
Simply refrain from returning the results of the Halt function to any
other Turing Machines. In order to return results there must be a
calling convention. In this case the return value can be placed in a
certain fixed location on the Universal Turing Machine's tape. Many
other calling conventions are possible.
When the return value of boolean TRUE is indicated (that the TM will
halt) a ONE is placed in this fixed tape location. This leaves a ZERO
for FALSE (does not halt), and the SPACE can be used to indicate that
no value is being returned. Other values can be substituted if
desired.
The last step is the method by which the Halt function can determine
its calling context. In other words whether or not it was called by
another Turing Machine, or invoked independently of any other Turing
Machine.
This can be a very simple feature that is implemented in the
Universal Turing Machine. The Halt function would merely ask the UTM
whether or not its specifically indicated final state has any state
transition defined. This information is very easy for the UTM to
provide, it merely looks up the action associated with the state in
its state transition matrix table. If there is no state transition
defined out of the Halt function's final states, then the Halt
function can know with certainty that it was not invoked as a part of
another Turing Machine's execution. It can use this information to
determine whether or not it can safely return a result, or that it
must refrain fro returning a result.
If these steps are taken, then the counter-example Turing Machine
that has been used as the basis for contructing the Halting Problem
Proof can no longer have any effect of the Halt analyzer or its
ability to produce correct results for each element of the universal
set of Turing Machines.
============ end copied text ============

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