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

On 5/1/2025 2:51 AM, Richard Heathfield wrote:

On 30/04/2025 19:30, Mike Terry wrote:

On 30/04/2025 16:46, 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.

>
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.

>
It would be (if correct) attacking the common proof for HP theorem as it occurs for instance in the Linz book which PO links to from time to time.

 Yes. That's what I call the Olcott Problem.
 De gustibus non est disputandum, but I venture to suggest that (correctly) overturning Turing's proof would be of cosmos-rocking interest to the world of computer science, compared to which pointing out a minor flaw in a minor[1] proof would, even if correct, have no more effect on our field than lobbing a pebble into the swash at high tide.
 

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
DD correctly simulated by HHH according to the rules of
the x86 language CANNOT POSSIBLY REACH ITS FINAL HALT
STATE NO MATTER WHAT HHH DOES.
Unless we have DD correctly simulated by HHH we do
not have the actual correct mapping of the actual
input to the actual behavior of this actual input.
Unless we have DD correctly simulated by HHH we do
not have the actual correct mapping of the actual
input to the actual behavior of this actual input.
Unless we have DD correctly simulated by HHH we do
not have the actual correct mapping of the actual
input to the actual behavior of this actual input.
Unless we have DD correctly simulated by HHH we do
not have the actual correct mapping of the actual
input to the actual behavior of this actual input.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer