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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: Mon, 28 Apr 2025 23:57:12 -0500
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On 4/28/2025 10:00 PM, dbush wrote:
> On 4/28/2025 10:50 PM, 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.
> 
> Not if it's the behavior of P(D) we want to know about, which it is.
> 

Wanting the square root of a rotten egg would do as well.
When P defines a pathological relationship with H it
is stupidly incorrect to expect the behavior of P to remain the same.

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