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

Op 01.mei.2025 om 22:15 schreef olcott:

On 5/1/2025 10:14 AM, André G. Isaak wrote:

On 2025-04-30 21:50, olcott wrote:

On 4/30/2025 7:17 PM, André G. Isaak wrote:

>

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; }

>
All you're demonstrating here is that you have no clue what a function is, nor, apparently, do you have any desire to learn.
>
André
>

 What I am explaining is that a halt decider
must compute the mapping FROM THE INPUTS ONLY
by applying a specific set of finite string
transformations to the inputs.
 int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
 

A correct decider would use finite string transformations and conclude that the input describes a halting program. This is possible, because the direct execution and world-class simulators perform those transformations correctly. A program that is not able to do the correct finite string transformation is just an erroneous program, even if it does not crash by violations of the x86 code.
The input to HHH describes a halting program, but HHH has a bug so that it does not complete the finite string transformations, but it aborts them prematurely.