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

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:

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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.
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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.
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 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. [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
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