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

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>
>

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/.

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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.
>

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

 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.

If it's wrong, it's wrong. And if it's right we can use it to write a program that it can't figure out. Turing proved this.
 

>

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.
>

>
IT DOES NOT WORK THAT WAY WITH PATHOLOGICAL SELF-REFERENCE.

 There's nothing in the rules to stop it. Reading the code is a perfectly valid way of establishing whether a program halts, and Turing machines are more than capable of reading and analysing code. Compilers do it all the time.
 

Because the input to HHH(DD) specifies pathological self-reference
IT CANNOT POSSIBLY HALT.

What we /can't/ do by reading the code is devise a universally accurate termination analyser,

HHH(DD) correctly rejects its input as non-halting.
DD <is> the Halting Problem counter-example input to HHH.

for the same reason we can't devise a universally accurate termination analyser that executes the code to see what happens.
 

There is no evidence of that.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer