Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
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: Sun, 29 Jun 2025 12:27:52 +0300
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On 2025-06-28 13:54:19 +0000, olcott said:

> On 6/28/2025 7:04 AM, Mikko wrote:
>> 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.
> 
> That they are in the domain of the halting problem
> and not in the domain of any Turing machine proves
> that the requirement of the halting problem is incorrect.

The halting problem can be partially solved with partial halt deciders.
A computation that cannot be determined to halt or not to halt with
some partical halt decier can be determined with another partial halt
decider.

-- 
Mikko