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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: ChatGPT agrees that I have refuted the conventional Halting Problem proof technique --- Full 38 page analysis
Date: Sat, 28 Jun 2025 15:04:45 +0300
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On 2025-06-27 14:19:28 +0000, olcott said:

> On 6/27/2025 1:55 AM, Mikko wrote:
>> On 2025-06-27 02:58:47 +0000, olcott said:
>> 
>>> On 6/26/2025 5:16 AM, Mikko wrote:
>>>> On 2025-06-25 15:42:36 +0000, olcott said:
>>>> 
>>>>> On 6/25/2025 2:38 AM, Mikko wrote:
>>>>>> On 2025-06-24 14:39:52 +0000, olcott said:
>>>>>> 
>>>>>>> *ChatGPT and I agree that*
>>>>>>> The directly executed DDD() is merely the first step of
>>>>>>> otherwise infinitely recursive emulation that is terminated
>>>>>>> at its second step.
>>>>>> 
>>>>>> No matter who agrees, the directly executed DDD is mote than
>>>>>> merely the first step of otherwise infinitely recursive
>>>>>> emulation that is terminated at its second step. Not much
>>>>>> more but anyway. After the return of HHH(DDD) there is the
>>>>>> return from DDD which is the last thing DDD does before its
>>>>>> termination.
>>>>> 
>>>>> *HHH(DDD) the input to HHH specifies non-terminating behavior*
>>>>> The fact that DDD() itself halts does not contradict that
>>>>> because the directly executing DDD() cannot possibly be an
>>>>> input to HHH in the Turing machine model of computation,
>>>>> thus is outside of the domain of HHH.
>>>> 
>>>> The input in HHH(DDD) is the same DDD that is executed in DDD()
>>>> so the behaviour specified by the input is the behavour of
>>>> directly executed DDD, a part of which is the behaour of the
>>>> HHH that DDD calls.
>>>> 
>>>> If HHH does not report about DDD but instead reports about itself
>>>> or its own actions it is not a partial halt decideer nor a partial
>>>> termination analyzer, as those are not allowed to report on their
>>>> own behavour more than "cannot determine".
>>> 
>>> Functions computed by Turing Machines are required to compute
>>> the mapping from their inputs and not allowed to take other
>>> executing Turing machines as inputs.
>> 
>> There is no restriction on the functions.
> 
> counter factual.

That is not a magic spell to create a restriction on functions.

>> A Turing machine is required
>> to compute the function identified in its specification and no other
>> function. For the halting problem the specification is that a halting
>> decider must compute the mapping that maps to "yes" if the computation
>> described by the input halts when directly executed.
> 
> No one ever bothered to notice that because directly
> executed Turing machines cannot possibly be inputs to
> other Turing machines that these directly executed
> Turing machines have never been in the domain of any
> Turing machine.

Irrelevant. They are the domain of the halting problem. If your
decider cannot predict whether a computation halts it is not a
halting decider.

> This excludes every TM from reporting on the behavior
> of any directly executed TM. TM's can only report on
> the behavior that their finite string input specifies.

No Turing machine has a behaviour that cannot be specified with a
finite string.

-- 
Mikko