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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 15:40:14 -0400
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On 4/30/2025 11:15 AM, olcott wrote:
> On 4/29/2025 5:03 PM, Richard Heathfield wrote:
>> On 29/04/2025 22:38, olcott wrote:
>>
>> <snip>
>>
>>>
>>> int DD()
>>> {
>>>    int Halt_Status = HHH(DD);
>>>    if (Halt_Status)
>>>      HERE: goto HERE;
>>>    return Halt_Status;
>>> }
>>>
>>> HHH is correct DD as non-halting BECAUSE THAT IS
>>> WHAT THE INPUT TO HHH(DD) SPECIFIES.
>>
>> You're going round the same loop again.
>>
>> Either your HHH() is a universal termination analyser or it isn't. 
> 
> The domain of HHH is DD.
> 
>> If it isn't, it's irrelevant to the Halting Problem, 
> 
> It correctly refutes the conventional proof of the
> Halting Problem proofs. 

False, as that starts with the assumption that HHH satisfies the 
following requirements:


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


But yours does not, so the prerequisites are not met.