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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions MUST apply finite string
 transformations to inputs
Date: Wed, 30 Apr 2025 23:30:02 -0500
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On 4/30/2025 6:52 PM, Richard Damon wrote:
> On 4/30/25 6:09 PM, olcott wrote:
>> On 4/30/2025 2:55 PM, dbush wrote:
>>> On 4/30/2025 1:32 PM, olcott wrote:
>>>> On 4/30/2025 11:11 AM, Richard Heathfield wrote:
>>>>> On 30/04/2025 16:44, joes wrote:
>>>>>> Am Wed, 30 Apr 2025 10:09:45 -0500 schrieb olcott:
>>>>>>> On 4/29/2025 5:01 AM, Mikko wrote:
>>>>>>
>>>>>>>> Irrelevant. There is sufficient agreement what Turing machines are.
>>>>>>>
>>>>>>> Turing machine computable functions must apply finite string
>>>>>>> transformation rues to inputs to derive outputs.
>>>>>>>
>>>>>>> This is not a function that computes the sum(3,2):
>>>>>>> int sum(int x, int y) { return 5; }
>>>>>> Yes it is, for all inputs.
>>>>>
>>>>> Not much of a computation, though, is it?
>>>>>
>>>>
>>>> It IS NOT a Turing Computable function
>>>
>>> Lying by misuse of terms.
>>>
>>> A turing computable function is a mapping for which an algorithm 
>>> exists to compute it, not the algorithm itself.
>>>
>>> Further use of "turing computable function" when what is meant is 
>>> "algorithm" will result in the former being replaced with the later 
>>> in future responses to your posts to make it clear what you are 
>>> actually talking about.
>>>
>>>
>>>> because it does not ever apply any finite
>>>> string transformation  rules to its inputs.
>>>
>>> Sure it does.  It computes the mapping of all pairs of integers to 
>>> the number 5.
>>>
>>
>> int sum(int x, int y) { return 5; }
>> Does not apply transformations to its inputs
>> to derive its outputs thus is no kind of computable
>> function not even for sum(2,3).
>>
> 
> And there is no requirement that a Turing Machine, or a Function, 
> actually use its input.
> 

Computable functions are the basic objects of study in
computability theory. 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

Then the relation between the input and the output
is violated.



> Note sum(2,3) isn't a Function, it is an invocation of a Function.
> 
> You seem to have a lot of misunderstanding about the meaning of the 
> words you use.


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