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

On 4/30/2025 1:28 PM, olcott wrote:

On 4/30/2025 10:46 AM, Richard Heathfield wrote:

On 30/04/2025 16:15, olcott wrote:

On 4/29/2025 5:03 PM, Richard Heathfield wrote:

On 29/04/2025 22:38, olcott wrote:
>
<snip>
>

>
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
>
HHH is correct DD as non-halting BECAUSE THAT IS
WHAT THE INPUT TO HHH(DD) SPECIFIES.

>
You're going round the same loop again.
>
Either your HHH() is a universal termination analyser or it isn't.

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The domain of HHH is DD.

>
Then it is attacking not the Halting Problem but the Olcott Problem, which is of interest to nobody but you.
>

 Because you don't pay any attention at all
you did not bother to notice that I have never been
attacking the Halting Problem only the conventional
Halting Problem proof.
>

Which starts with the assumption that an H exists that meets these requirements:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly