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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: ChatGPT agrees that I have refuted the conventional Halting
 Problem proof technique --- Full 38 page analysis
Date: Fri, 27 Jun 2025 09:19:28 -0500
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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.

> 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.

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.

*Failing to understand this does not count as a rebuttal*

> A decider that
> computes any other mapping, for example depending on whether its
> simulation reaches the halt state, is not a halting decider and not
> even a partial halting decider.
> 
>> This means that every directly executed Turing machine is
>> outside of the domain of every function computed by any
>> Turing machine.
> 
> There are functions with a directly executed Turing macines in
> their domain. But some functions are not Turing computable.
> 

Counter-factual. Turing machines can only take finite string
inputs. Finite strings are never and cannot possibly be directly 
executing Turing Machines.

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