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

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>
>

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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.

 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.
I suspect that the only reason we bother to argue with Mr Olcott so much is because (even if he does so unwittingly) he manages to convey the appearance of attacking the Halting Problem, and arguing about the Halting Problem is a lot more fun than arguing about the Olcott Problem.
To be of any interest, solving the Olcott Problem would have to have important consequences. But does it? Let's see.
Dr Linz Theorem 12.1 (Halting Problem is Undecidable): There does not exist any Turing machine H that behaves as required by Linz Definition 12.1. Thus the halting problem is undecidable.
Dr Linz has a proof for this claim, which can be found here: <https://john.cs.olemiss.edu/~hcc/csci311/notes/chap12/ch12.pdf>
If the proof is flawless, the conclusion stands and Mr Olcott is simply wrong.
If the proof is flawed through some error of reasoning, *either* it merely fails to correctly support its conclusion *or* a duly corrected proof /overturns/ the conclusion.
The latter would be /extremely/ interesting, but it would also mean that we have two proofs proving opposite things, and so it would effectively be a cataclysmic sideways attack on Turing's reasoning.
If Mr Olcott claims that he's not attacking Turing's proof, he is not attacking Dr Linz's conclusion, and his attack on the Linz proof can /at worst/ point out a minor error, which might be of interest to Mr Olcott and possibly even to Dr Linz if he ever got to hear about it, but it's hard to see what wider interest it holds, because what matters is Dr Linz's /conclusion/, and the conclusion is that the Halting Problem is undecidable. Unless Mr Olcott can overturn /that/ (which of course he can't), he has nothing worth wasting a lifetime over.
[1] If by some strange chance Dr Linz ever reads this, I hope he won't be too upset by 'minor' when I compare his proof to Turing's ground-breaker.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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