Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs VERIFIED FACT
Date: Fri, 2 May 2025 11:01:04 +0200
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Op 02.mei.2025 om 02:07 schreef olcott:
> On 5/1/2025 10:32 AM, Ben Bacarisse wrote:
>> Richard Heathfield <rjh@cpax.org.uk> writes:
>>
>>> 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.
>>>
>>> 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.
>>
>> There is peculiar irony here.  The proof is /not/ flawless.  It has, in
>> fact, a flaw that PO pointed out (although in passing).  PO does not
>> care about the flaw because it is easily fixed, but it's there none the
>> less[1].
>>
>> Anyway, Linz only gives this argument because it is of historical
>> interest.  His "real" proof immediately follows this argument (in the
>> book) and is a trivial corollary of the fact, proved in chapter 11, that
>> not all recursively enumerable languages are recursive.  But no crank
>> ever addresses that proof.  I wonder why...
>>
> 
> You wasted fifteen years of my life by your change-the-subject
> form of rebuttal so I no longer tolerate that from an anyone.
> 
> The flaw in all of the conventional proofs is that the
> mapping they they DO specify IS NOT the direct execution
> of their input.
> 
> Everyone moronically ignores how the pathological relationship
> between the INPUT and its TERMINATION ANALYZER CHANGES the
> behavior OF THE INPUT.
> 
> *When HHH emulates DD correctly the emulated DD cannot possibly halt*
> THIS IS THE BEHAVIOR OF THE FREAKING INPUT.
> 
What you do not understand is that the finite string specifies the exact 
behaviour of the program described in the input. That behaviour does not 
change. That HHH cannot see that behaviour, does not change the 
behaviour, it is a failure of HHH. Thinking that what HHH cannot see 
tells something about the behaviour of the program specified in the 
input is an error of the programmer.
If I close my eyes and don't see the people around me (because I have a 
pathological relationship with them), it does not mean that they 
disappear. Only a child would think so. Similarly, if HHH is unable to 
see the full behaviour specified in the input, does not make the 
specification any different.