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

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>
>

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

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

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

>
It doesn't have to.

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

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.
I, as a decider, do not need to see the following program's behaviour to determine whether it halts...
int main(void)
{
   while(1);
   return 0;
}
...because I can tell just by reading the code that it enters an infinite loop and so will not halt. I can report on whether the program halts without having to execute it.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within