Re: Disproof of the Halting Problem's Conclusion

From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 07/21/04 

Date: Wed, 21 Jul 2004 12:05:58 -0400

Peter Olcott wrote:

> "Will Twentyman" <wtwentyman@read.my.sig> wrote in message news:40fdceb5_3@newsfeed.slurp.net...
>
>>Peter Olcott wrote:
>>
>>
>>>>>>But it does. Your method is founded on the idea that LoopIfHalts
>>>>>>cannot be constructed. As soon as it is shown that that is possible,
>>>>>>your method breaks down.
>>>>>
>>>>>
>>>>>No. as long as a single unmodified copy of the my original program exists
>>>>>then this single copy still represents the required single counter-example to
>>>>>disprove the statement:
>>>>>No program can ever be written to determine whether any arbitrary program will halt
>>>>
>>>>This is not correct.
>>>
>>>One programs is greater than no program, don't you agree?
>>>Only one more than none is required to refute this claim.
>>
>>You offer a function:
>>
>>void POWillHalt(string function, string input)
>>{
>> [do stuff to figure out if function(input) halts]
>> cout << result;
>>}
>
> If I can provide any means to refute the statement below, I have refuted the HAlting Problem.
> No program can ever be written to determine whether any arbitrary program will halt
>
> It does not matter what you do with this solution, after the fact. It has already
> been correctly refuted.

1) To refute it, there must be a program that *does* determine if a
given program and input results in halting or not halting.
2) My understanding of your proposal for the appearance of such a
program is outlined above.
3) It can be readily modified to the outline below.
4) The outline below leads to a contradiction as illustrated in the
standard proof that WillHalt() does not exist.
5) Therefore, the outline below does not operate as claimed.
6) If it doesn't operate as claimed, neither does the one above.
7) Therefore, your idea of protected memory and output to screen fails.

Where am I missing something? At what step is there an error in the logic?

>>I can change it to
>>
>>bool StandardWillHalt(string function, string input)
>>{
>> [do stuff to figure out if function(input) halts]
>> return result;
>>}
>>
>>If you can't offer the source code, you can't claim to have the
>>solution. If you can offer the source code, I can modify how it does
>>the output so that we can construct the standard contradiction. This
>>should strongly suggest that your code didn't work as advertised. 

-- 
Will Twentyman
email: wtwentyman at copper dot net

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