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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: The input to HHH(DDD) specifies a non-halting sequence of configurations +++
Date: Sun, 15 Jun 2025 12:32:39 +0300
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On 2025-06-14 14:07:49 +0000, olcott said:

> On 6/13/2025 6:02 AM, Mikko wrote:
>> On 2025-06-11 14:03:41 +0000, olcott said:
>> 
>>> On 6/11/2025 3:20 AM, Mikko wrote:
>>>> On 2025-06-10 15:41:33 +0000, olcott said:
>>>> 
>>>>> On 6/10/2025 6:41 AM, Mikko wrote:
>>>>>> On 2025-06-10 00:47:12 +0000, olcott said:
>>>>>> 
>>>>>>> On 6/9/2025 7:26 PM, Richard Damon wrote:
>>>>>>>> On 6/9/25 10:43 AM, olcott wrote:
>>>>>>>>> On 6/9/2025 5:31 AM, Fred. Zwarts wrote:
>>>>>>>>>> Op 09.jun.2025 om 06:15 schreef olcott:
>>>>>>>>>>> On 6/8/2025 10:42 PM, dbush wrote:
>>>>>>>>>>>> On 6/8/2025 11:39 PM, olcott wrote:
>>>>>>>>>>>>> On 6/8/2025 10:32 PM, dbush wrote:
>>>>>>>>>>>>>> On 6/8/2025 11:16 PM, olcott wrote:
>>>>>>>>>>>>>>> On 6/8/2025 10:08 PM, dbush wrote:
>>>>>>>>>>>>>>>> On 6/8/2025 10:50 PM, olcott wrote:
>>>>>>>>>>>>>>>>> void DDD()
>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>    HHH(DDD);
>>>>>>>>>>>>>>>>>    return;
>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> The *input* to simulating termination analyzer HHH(DDD)
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>> No it's not, as halt deciders / termination analyzers work with algorithms,
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> That is stupidly counter-factual.
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> That you think that shows that
>>>>>>>>>>>>> 
>>>>>>>>>>>>> My understanding is deeper than yours.
>>>>>>>>>>>>> No decider ever takes any algorithm as its input.
>>>>>>>>>>>> 
>>>>>>>>>>>> But they take a description/specification of an algorithm,
>>>>>>>>>>> 
>>>>>>>>>>> There you go.
>>>>>>>>>>> 
>>>>>>>>>>>> which is what is meant in this context.
>>>>>>>>>>> 
>>>>>>>>>>> It turns out that this detail makes a big difference.
>>>>>>>>>>> 
>>>>>>>>>>>> And because your HHH does not work with the description/ specification 
>>>>>>>>>>>> of an algorithm, by your own admission, you're not working on the 
>>>>>>>>>>>> halting problem.
>>>>>>>>>>>> 
>>>>>>>>>>> 
>>>>>>>>>>> HHH(DDD) takes a finite string of x86 instructions
>>>>>>>>>>> that specify that HHH simulates itself simulating DDD.
>>>>>>>>>> 
>>>>>>>>>> And HHH fails to see the specification of the x86 instructions. It 
>>>>>>>>>> aborts before it can see how the program ends.
>>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> This is merely a lack of sufficient technical competence
>>>>>>>>> on your part. It is a verified fact that unless the outer
>>>>>>>>> HHH aborts its simulation of DDD that DDD simulated by HHH
>>>>>>>>> the directly executed DDD() and the directly executed HHH()
>>>>>>>>> would never stop running. That you cannot directly see this
>>>>>>>>> is merely your own lack of sufficient technical competence.
>>>>>>>> 
>>>>>>>> And it is a verified fact that you just ignore that if HHH does in fact 
>>>>>>>> abort its simulation of DDD and return 0, then the behavior of the 
>>>>>>>> input, PER THE ACTUAL DEFINITIONS, is to Halt, and thus HHH is just 
>>>>>>>> incorrect.
>>>>>>>> 
>>>>>>> 
>>>>>>> void DDD()
>>>>>>> {
>>>>>>>    HHH(DDD);
>>>>>>>    return;
>>>>>>> }
>>>>>>> 
>>>>>>> How the f-ck does DDD correctly simulated by HHH
>>>>>>> reach its own "return" statement final halt state?
>>>>>> 
>>>>>> If HHH is not a decider the question is not interesting.
>>>>> 
>>>>> I switched to the term: "termination analyzer" because halt deciders
>>>>> have the impossible task of being all knowing.
>>>> 
>>>> The termination problem is in certain sense harder than the halting
>>>> problem.
>>> 
>>> Not at all
>> 
>> That's in another sense in which nothing is harder than impossible.
>> 
>>> void DDD()
>>> {
>>>    HHH(DDD);
>>>    return;
>>> }
>>> 
>>> If HHH only determines non-halting correctly for the
>>> above input and gets the wrong answer on everything
>>> else then HHH *is* a correct termination analyzer.
>> 
>> It is not a correct termination analyzer if if gives the wrong answer.
> 
> *Key verified facts such that disagreement is inherently incorrect*
> 
> (a) HHH(DDD) does not correctly report on the behavior of its caller.

True.

> (b) Within the theory of computation HHH is not allowed to report
>      on the behavior of its caller.

False. The theory of computation does not prohibit anything. More
generally, mathematical and scientific theories do not prohibit.

> (c) HHH(DDD) does correctly report on the behavior that its
>      input specifies.

False. The input specifies the behavior that is observed when DDD and
a main that calls DDD are complided and linked with your HHH and with
whatever HHH needs, and then executed. That behaviour is known to halt.

-- 
Mikko