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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 14:57:50 -0500
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On 4/29/2025 10:33 AM, Fred. Zwarts wrote:
> Op 29.apr.2025 om 15:11 schreef olcott:
>> On 4/29/2025 2:10 AM, Richard Heathfield wrote:
>>> On 29/04/2025 03:50, olcott wrote:
>>>> On 4/28/2025 3:13 PM, Richard Heathfield wrote:
>>>>> On 28/04/2025 19:30, olcott wrote:
>>>>>> On 4/28/2025 11:38 AM, Richard Heathfield wrote:
>>>>>>> On 28/04/2025 16:01, olcott wrote:
>>>>>>>> On 4/28/2025 2:33 AM, Richard Heathfield wrote:
>>>>>>>>> On 28/04/2025 07:46, Fred. Zwarts wrote:
>>>>>>>>>
>>>>>>>>> <snip>
>>>>>>>>>
>>>>>>>>>> So we agree that no algorithm exists that can determine for 
>>>>>>>>>> all possible inputs whether the input specifies a program that 
>>>>>>>>>> (according to the semantics of the machine language) halts 
>>>>>>>>>> when directly executed.
>>>>>>>>>> Correct?
>>>>>>>>>
>>>>>>>>> Correct. We can, however, construct such an algorithm just as 
>>>>>>>>> long as we can ignore any input we don't like the look of.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The behavior of the direct execution of DD cannot be derived
>>>>>>>> by applying the finite string transformation rules specified
>>>>>>>> by the x86 language to the input to HHH(DD). This proves that
>>>>>>>> this is the wrong behavior to measure.
>>>>>>>>
>>>>>>>> It is the behavior THAT IS derived by applying the finite
>>>>>>>> string transformation rules specified by the x86 language
>>>>>>>> to the input to HHH(DD) proves that THE EMULATED DD NEVER HALTS.
>>>>>>>
>>>>>>> The x86 language is neither here nor there. 
>>>>>>
>>>>>> Computable functions are the formalized analogue
>>>>>> of the intuitive notion of algorithms, in the sense
>>>>>> that a function is computable if there exists an
>>>>>> algorithm that can do the job of the function, i.e.
>>>>>> *given an input of the function domain it*
>>>>>> *can return the corresponding output*
>>>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>>>
>>>>>> *Outputs must correspond to inputs*
>>>>>>
>>>>>> *This stipulates how outputs must be derived*
>>>>>> Every Turing Machine computable function is
>>>>>> only allowed to derive outputs by applying
>>>>>> finite string transformation rules to its inputs.
>>>>>
>>>>> In your reply to my article, you forgot to address what I actually 
>>>>> wrote. I'm not sure you understand what 'reply' means.
>>>>>
>>>>> Still, I'm prepared to give you another crack at it. Here's what I 
>>>>> wrote before:
>>>>>
>>>>> What matters is whether a TM can be constructed that can accept an 
>>>>> arbitrary TM tape P and an arbitrary input tape D and correctly 
>>>>> calculate whether, given D as input, P would halt. Turing proved 
>>>>> that such a TM cannot be constructed.
>>>>>
>>>>> This is what we call the Halting Problem.
>>>>>
>>>>
>>>> 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)
>> when-so-ever D has defined a pathological
>> relationship with H this 
> 
> makes it impossible for H to see the behaviour of P(D).
> The behaviour of P(D) does not change, but H does not see it.

H MUST REPORT ON THE BEHAVIOR THAT IT DOES SEE

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