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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: D correctly simulated by H proved for THREE YEARS --- rewritten
Date: Sat, 15 Jun 2024 16:37:15 +0200
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Op 15.jun.2024 om 16:13 schreef olcott:
> On 6/15/2024 9:06 AM, Fred. Zwarts wrote:
>> Op 15.jun.2024 om 14:12 schreef olcott:
>>> On 6/15/2024 4:03 AM, Fred. Zwarts wrote:
>>>> Op 14.jun.2024 om 22:46 schreef olcott:
>>>>> On 6/14/2024 3:03 PM, Fred. Zwarts wrote:
>>>>>> Op 14.jun.2024 om 21:18 schreef olcott:
>>>>>>> On 6/14/2024 2:00 PM, Fred. Zwarts wrote:
>>>>>>>> Op 14.jun.2024 om 14:49 schreef olcott:
>>>>>>>>> I ran the actual code to verify the facts.
>>>>>>>>> HH1(DD,DD) does not have a pathological relationship to its input
>>>>>>>>> thus this input terminates normally.
>>>>>>>>
>>>>>>>> Your terminology is confusing. What you call a "pathological 
>>>>>>>> relationship" is that H must simulate itself.
>>>>>>>>
>>>>>>>
>>>>>>> *CONVENTIONAL TERMINOLOGY*
>>>>>>> For any program H that might determine whether programs halt, a
>>>>>>> "pathological" program D, called with some input, can pass its own
>>>>>>> source and its input to H and then specifically do the opposite 
>>>>>>> of what
>>>>>>> H predicts D will do. No H can exist that handles this case.
>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>
>>>>>> The problem is that your simulator does not even reach the 
>>>>>> "pathological" part of D. 
>>>>>
>>>>> That is not the problem that is the criterion measure of a solution.
>>>>
>>>> You are using the wrong criterion, because this wrong criterion also 
>>>> also applies to other programs, without a "pathological" part.
>>>>
>>>>         int main()
>>>>         {
>>>>           return H(main, 0);
>>>>         }
>>>>
>>>> where you proved that H reports a false negative.
>>>>
>>>> So, your criterion has no relation with "pathological" programs.
>>>>
>>>
>>> This criteria works correctly for ALL input, including pathological
>>> main(). 
>>
>> You are twisting your own words,because main is not "pathological".
>> You do not even understand you own definition of "pathological":
>>
>> Op 14.jun.2024 om 21:18 schreef olcott:
>>>
>>> *CONVENTIONAL TERMINOLOGY*
>>> For any program H that might determine whether programs halt, a
>>> "pathological" program D, called with some input, can pass its own
>>> source and its input to H and then specifically do the opposite of what
>>> H predicts D will do. No H can exist that handles this case. 
>>
>> No high level programming skills are needed to see that there is no 
>> part where main 'then specifically do the opposite of what H predicts 
>> it will do'.
>>
>> It seems that you are changing the definition of "pathological" to 
>> 'any program for which H returns a false negative', which then becomes 
>> a tautology.
>>
> 
> Any function that calls H specifies recursive simulation.

Is this the new definition of "pathological"?
Again a change of definition. No words any more about doing the opposite 
of what H predicts. Words you used in the definition only a few lines 
above have disappeared.
So, with this new definition, we agree that the fact that D does the 
opposite of what H returns is irrelevant.
This means that you only prove that there are programs that halt, for 
which the simulation by H does not reach its final state, because H is 
unable to reach its own simulated final state. H then aborts and reports 
non-halting. A false negative.

Further, it is not the function that specifies recursive simulation. The 
function does not even know about recursion. It is H that starts the 
recursive simulation, with the effect that its must simulate itself.
More important, it does not specify infinite recursion. Only if H does 
not halt, as required, an infinite recursion happens.