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

Op 29.apr.2025 om 23:38 schreef olcott:

On 4/29/2025 3:06 PM, Richard Heathfield wrote:

On 29/04/2025 20:56, olcott wrote:

On 4/29/2025 2:39 PM, Richard Heathfield wrote:

On 29/04/2025 20:06, olcott wrote:

On 4/29/2025 8:46 AM, Richard Heathfield wrote:

On 29/04/2025 14:11, olcott wrote:

On 4/29/2025 2:10 AM, Richard Heathfield wrote:

On 29/04/2025 03:50, olcott wrote:

>
<snip>
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Yet it is H(P,D) and NOT P(D) that must be measured.

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Nothing /has/ to be measured. P's behaviour (halts, doesn't halt) when given D as input must be /established/.

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No H can possibly see the behavior of P(D)

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It doesn't have to.

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IF IT CAN'T SEE IT THEN  IT CAN'T REPORT ON  IT.

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Yes, it can. There is no need to see the behaviour to establish whether it halts. All the decider has to be able to see is the code.
>

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THE CODE THAT IT CAN SEE
unequivocally specifies that the INPUT DOES NOT HALT

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Fine. Either it's right or it's wrong.
>

 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.
 

This part of the input is irrelevant. The code also includes Halt7.c, which specifies a conditional abort, which makes the program specified in the input halting.
That HHH aborts too soon, so that it does not even analyse a full cycle of the recursion and misses Halt7.c, does not change the specification in the input.