Re: Turing Machine computable functions MUST apply finite string transformations to inputs

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:

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Irrelevant. There is sufficient agreement what Turing machines are.

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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.

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Not much of a computation, though, is it?
>

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It IS NOT a Turing Computable function

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Lying by misuse of terms.
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A turing computable function is a mapping for which an algorithm exists to compute it, not the algorithm itself.
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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.
>
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because it does not ever apply any finite
string transformation  rules to its inputs.

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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