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

On 4/30/2025 6:50 PM, Richard Damon wrote:

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.
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Sure it is. You just don't know that that mean.
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 Algorithms must apply finite string
transformations to inputs. sum does not do that.
 

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