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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 22:50:47 -0500
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On 4/30/2025 7:17 PM, André G. Isaak wrote:
> On 2025-04-30 16:09, 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).
> 
> You are still hopelessly confused about your terminology.
> 
> Computable functions are a subset of mathematical functions, and 
> mathematical functions are *not* the same thing as C functions. 
> Functions do not apply "transformations". They are simply mappings, and 
> a functions which maps every pair of natural numbers to 5 is a perfectly 
> legitimate, albeit not very interesting, function.
> 
> What makes this function a *computable function* is that fact that it is 
> possible to construct a C function (or a Turing Machine, or some other 
> type of algorithm) such as int foo(int x, int y) {return 5;} which 
> computes that particular function; but the C function and the computable 
> function it computes are entirely separate entities.

computes the sum of two integers
by transforming the inputs into an output.
int sum(int x, int y) { return x + y; }

Computes no function because it ignores its inputs.
int sum(int x, int y) { return 5; }

> [I won't call that 
> function 'sum()' because that would be misleading, but the the *name* 
> assigned to a C function has no necessary relation to the function it 
> computes. It's good programming practice to give functions descriptive 
> names but nothing in the C standard requires it).
> 
> You keep conflating C functions/Turing Machines with computable 
> functions and as a result come across as completely ignorant about the 
> topic you purport to be discussing. No C function or Turing Machine is a 
> computable function. They are ways of expressing algorithms.
> 
> André
> 

The complete ignorance is to expect HHH(DD)
to report on DD(DD). That is just not the way
that reality works.

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