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

On 4/30/25 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
because it does not ever apply any finite
string transformation  rules to its inputs.
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THE OUTPUTS MUST CORRESPOND TO THE INPUTS.
sum(4,3) returns 5 proving that sum is
not a Turing Computable function.
>

 Sure it is. You just don't know that that mean.
 

THe function given computes the Computable Function defined by the mapping of all pair (x, y) -> the value 5.
 That is a perfectly fine Function, and easily proved to be computable.
 It isn't a correct function for computing the addition function that maps the pair (x, y) -> x+y, but that wasn't what you said, because you don't know what you are talking about.
 You don't seem to understand that "Functions" are defined just by the input -> output mapping that they specify.
 They are Computable if some Turing Machine exists that can create that whole mapping (via some representation method for the inputs/outputs)
 But the "Computable Function" still isn't defined by the code fo that Turing Machine, but by the mapping.
 NO "Turing Machine" is a "Turing Computable Function" as they are different categories of things.
 Turing Machine as strictly defined by the rules that they are built on that create the mappings they compute.
 Functions (Computable or Not) are defined by the Mapping of Input to Output that they are.
  Turing Machine COMPUTE some Computable Function, they are not the Function itself.