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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs VERIFIED FACT
Date: Tue, 29 Apr 2025 16:38:49 -0500
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On 4/29/2025 3:06 PM, Richard Heathfield wrote:
> On 29/04/2025 20:56, olcott wrote:
>> On 4/29/2025 2:39 PM, Richard Heathfield wrote:
>>> On 29/04/2025 20:06, olcott wrote:
>>>> On 4/29/2025 8:46 AM, Richard Heathfield wrote:
>>>>> On 29/04/2025 14:11, olcott wrote:
>>>>>> On 4/29/2025 2:10 AM, Richard Heathfield wrote:
>>>>>>> On 29/04/2025 03:50, olcott wrote:
>>>>>
>>>>> <snip>
>>>>>
>>>>>>>> Yet it is H(P,D) and NOT P(D) that must be measured.
>>>>>>>
>>>>>>> Nothing /has/ to be measured. P's behaviour (halts, doesn't halt) 
>>>>>>> when given D as input must be /established/. 
>>>>>>
>>>>>> No H can possibly see the behavior of P(D)
>>>>>
>>>>> It doesn't have to. 
>>>>
>>>> IF IT CAN'T SEE IT THEN  IT CAN'T REPORT ON  IT.
>>>
>>> Yes, it can. There is no need to see the behaviour to establish 
>>> whether it halts. All the decider has to be able to see is the code.
>>>
>>
>> THE CODE THAT IT CAN SEE
>> unequivocally specifies that the INPUT DOES NOT HALT
> 
> Fine. Either it's right or it's wrong.
> 

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.

> If it's wrong, it's wrong. And if it's right we can use it to write a 
> program that it can't figure out. Turing proved this.
> 
> 
>>
>>> I, as a decider, do not need to see the following program's behaviour 
>>> to determine whether it halts...
>>>
>>> int main(void)
>>> {
>>>    while(1);
>>>    return 0;
>>> }
>>>
>>> ...because I can tell just by reading the code that it enters an 
>>> infinite loop and so will not halt. I can report on whether the 
>>> program halts without having to execute it.
>>>
>>
>> IT DOES NOT WORK THAT WAY WITH PATHOLOGICAL SELF-REFERENCE.
> 
> There's nothing in the rules to stop it. Reading the code is a perfectly 
> valid way of establishing whether a program halts, and Turing machines 
> are more than capable of reading and analysing code. Compilers do it all 
> the time.
> 

Because the input to HHH(DD) specifies pathological self-reference
IT CANNOT POSSIBLY HALT.

> What we /can't/ do by reading the code is devise a universally accurate 
> termination analyser, 

HHH(DD) correctly rejects its input as non-halting.
DD <is> the Halting Problem counter-example input to HHH.

> for the same reason we can't devise a universally 
> accurate termination analyser that executes the code to see what happens.
> 

There is no evidence of that.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer