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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: Wed, 30 Apr 2025 10:01:43 -0500
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On 4/30/2025 4:04 AM, Fred. Zwarts wrote:
> Op 29.apr.2025 om 21:57 schreef olcott:
>> 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
>>
> 
> That is your error. H must report on the behaviour specified in the 
> input. 

HHH DOES APPLY the finite string transformations
specified by the x86 language TO ITS INPUT and this
DOES SPECIFY THAT DD DOES NOT HALT.

> Bugs in H do not change the behaviour specified in the input.
> H just fails to see it.


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