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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs VERIFIED FACT
Date: Wed, 30 Apr 2025 21:00:33 -0400
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In-Reply-To: <vuugq2$1aldv$3@dont-email.me>

On 4/30/2025 8:55 PM, olcott wrote:
> On 4/30/2025 7:07 PM, Mike Terry wrote:
>> On 30/04/2025 23:04, Keith Thompson wrote:
>>> olcott <polcott333@gmail.com> writes:
>>>> On 4/30/2025 2:46 PM, Keith Thompson wrote:
>>>>> olcott <polcott333@gmail.com> writes:
>>>>> [...]
>>>>>> Because you don't pay any attention at all
>>>>>> you did not bother to notice that I have never been
>>>>>> attacking the Halting Problem only the conventional
>>>>>> Halting Problem proof.
>>>>> [...]
>>>>> That's some interesting news, at least to me.
>>>>> I was under the impression that you had explicitly claimed to have
>>>>> solved the Halting Problem.  I don't read most of what you write,
>>>>> and I don't remember all of what I've read, so my impression may
>>>>> have been mistaken.
>>>>> Now you're saying that you're only attacking the conventional proof.
>>>>
>>>> That is ALL that I have been saying for several years.
>>>> Anyone can figure that out simply on the basis of
>>>> actually paying attention to my proof.
>>>>
>>>> HHH(DD) does correctly report that the halting problem
>>>> proof's impossible input DOES NOT HALT SO THE PROOF
>>>> IS WRONG.
>>>
>>> So your only claim is that the commonly known Halting Problem proof
>>> is flawed.  (Others who have paid more attention might choose to
>>> comment on that.)
>>
>> My recollection is that PO does not claim to have a solution to the 
>> halting problem.
>>
>> I made a recent post here (Wed, 30 Apr 2025 19:30:46 +0100) with some 
>> background, since another poster also seemed to think PO was claiming 
>> to have "solved the HP".
>>
>> Several people [starting years ago with Ben] have explained to PO that 
>> there are multiple alternative proofs, including one in the Linz book 
>> which PO might be expected to have read, but PO blanks such 
>> discussions.  He wouldn't understand those proofs, of course.
>>  and
> 
> A single minded focus of 22 years has correctly
> refuted the conventional halting problem proof.
> 
> This would have been fully acknowledged years ago if
> people understood that HHH/DD is analogous (thus isomorphic)
> to Linz and Functions 

Meaning that the following mapping is assumed to be computable and HHH 
computes it:


Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

A solution to the halting problem is an algorithm H that computes the 
following mapping:

(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly



> computed by Turing Machines are ONLY
> allowed to derive outputs by applying finite string transformations
> to inputs.
> 
> This requirement forbids HHH to report on DD(DD)
> because the mapping from the input to HHH(DD)
> specifies something else.

i.e. a contradiction is reached, therefore the assumption that an H 
exists that can compute the above mapping is proven false, as show by 
Linz and you have *explicitly* agreed is correct.

> 
> You can't simply guess the mapping that you want
> and then assume that it exists.
> 

All mappings exist.  Whether or not a mapping is computable is another 
matter.