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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: How do computations actually work?
Date: Thu, 29 May 2025 07:04:08 -0400
Organization: i2pn2 (i2pn.org)
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On 5/28/25 10:31 AM, olcott wrote:
> On 5/28/2025 2:36 AM, Mikko wrote:
>> On 2025-05-27 15:40:33 +0000, olcott said:
>>
>>> On 5/27/2025 3:29 AM, Mikko wrote:
>>>> On 2025-05-26 16:40:25 +0000, olcott said:
>>>>
>>>>> On 5/25/2025 10:46 AM, Fred. Zwarts wrote:
>>>>>> Op 25.mei.2025 om 16:50 schreef olcott:
>>>>>>> On 5/25/2025 4:09 AM, Mikko wrote:
>>>>>>>> On 2025-05-24 15:25:21 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 5/24/2025 2:54 AM, Mikko wrote:
>>>>>>>>>> On 2025-05-23 16:04:49 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> On 5/23/2025 2:09 AM, Mikko wrote:
>>>>>>>>>>>> On 2025-05-23 02:47:40 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 5/22/2025 8:24 PM, Mike Terry wrote:
>>>>>>>>>>>>>> On 22/05/2025 06:41, Richard Heathfield wrote:
>>>>>>>>>>>>>>> On 22/05/2025 06:23, Keith Thompson wrote:
>>>>>>>>>>>>>>>> Richard Heathfield <rjh@cpax.org.uk> writes:
>>>>>>>>>>>>>>>>> On 22/05/2025 00:14, olcott wrote:
>>>>>>>>>>>>>>>>>> On 5/21/2025 6:11 PM, Richard Heathfield wrote:
>>>>>>>>>>>>>>>> [...]
>>>>>>>>>>>>>>>>>>> Turing proved that what you're asking is impossible.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> That is not what he proved.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Then you'll be able to write a universal termination 
>>>>>>>>>>>>>>>>> analyser that can
>>>>>>>>>>>>>>>>> correctly report for any program and any input whether 
>>>>>>>>>>>>>>>>> it halts. Good
>>>>>>>>>>>>>>>>> luck with that.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Not necessarily.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Of course not. But I'm just reflecting. He seemed to 
>>>>>>>>>>>>>>> think that my inability to write the kind of program 
>>>>>>>>>>>>>>> Turing envisaged (an inability that I readily concede) is 
>>>>>>>>>>>>>>> evidence for his argument. Well, what's sauce for the 
>>>>>>>>>>>>>>> goose is sauce for the gander.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Even if olcott had refuted the proofs of the
>>>>>>>>>>>>>>>> insolvability of the Halting Problem -- or even if he 
>>>>>>>>>>>>>>>> had proved
>>>>>>>>>>>>>>>> that a universal halt decider is possible
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> And we both know what we both think of that idea.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> -- that doesn't imply
>>>>>>>>>>>>>>>> that he or anyone else would be able to write one.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Indeed.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I've never been entirely clear on what olcott is claiming.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Nor I. Mike Terry seems to have a pretty good handle on 
>>>>>>>>>>>>>>> it, but no matter how clearly he explains it to me my 
>>>>>>>>>>>>>>> eyes glaze over and I start to snore.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Hey, it's the way I tell 'em!
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Here's what the tabloids might have said about it, if it 
>>>>>>>>>>>>>> had made the front pages when the story broke:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>   COMPUTER BOFFIN IS TURING IN HIS GRAVE!
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>   An Internet crank claims to have refuted Linz HP proof 
>>>>>>>>>>>>>> by creating a
>>>>>>>>>>>>>>   Halt Decider that CORRECTLY decides its own "impossible 
>>>>>>>>>>>>>> input"!
>>>>>>>>>>>>>>   The computing world is underwhelmed.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Better?  (Appologies for the headline, it's the best I 
>>>>>>>>>>>>>> could come up with.)
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Mike.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> There is a key detail about ALL of these proofs
>>>>>>>>>>>>> that no one has paid attention to for 90 years.
>>>>>>>>>>>>>
>>>>>>>>>>>>> It is impossible to define *AN INPUT* to HHH that
>>>>>>>>>>>>> does the opposite of whatever value that HHH returns.
>>>>>>>>>>>>
>>>>>>>>>>>> That is a key detail about HHH. Your HHH is not a part of 
>>>>>>>>>>>> those proofs.
>>>>>>>>>>>
>>>>>>>>>>> All of the proofs work this same way.
>>>>>>>>>>
>>>>>>>>>> No, they don't. Some proofs derive the same conclusion with an 
>>>>>>>>>> essentially
>>>>>>>>>> different approach.
>>>>>>>>>>
>>>>>>>>>> However, in spite of the differences, they do share a common 
>>>>>>>>>> fieature:
>>>>>>>>>> your HHH is not a part of any of the proofs.
>>>>>>>>>
>>>>>>>>> All of the conventional proofs of the HP assume that
>>>>>>>>> there is an *input D* that can actually do the opposite
>>>>>>>>> of whatever value that HHH returns.
>>>>>>>>
>>>>>>>> Depends on what you mean by "conventional". If you merely mean 
>>>>>>>> proofs
>>>>>>>> that apply ordinary logic then there are proofs with a different
>>>>>>>> strategy. If you mean only proofs that use the same strategy that
>>>>>>>> Turing used then you are closer to the truth. But there is no 
>>>>>>>> assumption
>>>>>>>> about the exstence of such D. Its existence is proven.
>>>>>>>>
>>>>>>>
>>>>>>> In seems that way until you pay much closer attention.
>>>>>>>
>>>>>>> int main()
>>>>>>> {
>>>>>>>    DDD(); // The HHH that DDD calls cannot report on the
>>>>>>> }        // behavior of its caller because it cannot see
>>>>>>>           // is caller.
>>>>>>>
>>>>>>> Even if HHH could see and report on the behavior of
>>>>>>> its caller because its caller is not its input this
>>>>>>> too is no good.
>>>>>>
>>>>>> It seems that way to you, until you pay somewhat closer attention.
>>>>>
>>>>> The HHH(DDD) must report on the behavior that its actual input
>>>>> actually specified CANNOT BE VIOLATED.
>>>>
>>>> Of course it can. In fact HHH does violate that. DDD specifies a 
>>>> halting
>>>> behaviour but HHH reports that DDD specifies a non-halting behaviour.
>>>> That is a violation of that rquirement.
>>>
>>> If DDD simulated by HHH stops running for any
>>> reason besides reaching its own "ret" instruction
>>> final halt state THEN DDD HAS NOT HALTED.
>>
>> Irrelevant. The requirement is that a halt decider predicts whether the
>> complete execution of the computation described by the input will halt.
>>
> 
> Halting is defined as reaching a final state and
> terminating normally.

In the behavior of the actual program.

And Non-Halting is thus defined as will never reach a final state after 
an unbounded number of steps.

> 
> int main()
> {
>    DDD(); // The HHH that DDD calls cannot
> }        // see the behavior of its caller
> 

That it can not see is irrelevent, it *IS* the behavior it is being 
asked to determine.

Lying is not a valid option in logic.

> *That is incorrect*
> A termination analyzer must report on the basis
> of the behavior that its input specifies and does
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