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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: D correctly simulated by H proved for THREE YEARS --- rewritten
Date: Mon, 17 Jun 2024 08:39:38 -0500
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On 6/16/2024 2:08 PM, Fred. Zwarts wrote:
> Op 16.jun.2024 om 14:37 schreef olcott:
>> On 6/16/2024 1:21 AM, Fred. Zwarts wrote:
>>> Op 15.jun.2024 om 17:23 schreef olcott:
>>>> On 6/15/2024 10:12 AM, Fred. Zwarts wrote:
>>>>> Op 15.jun.2024 om 16:48 schreef olcott:
>>>>>> On 6/15/2024 9:37 AM, Fred. Zwarts wrote:
>>>>>>>
>>>>>>> Is this the new definition of "pathological"?
>>>>>>
>>>>>> *It is the same thing that I have been saying all along*
>>>>>>
>>>>>> 00   typedef void (*ptr)(); // pointer to void function
>>>>>> 01
>>>>>> 02   int HH(ptr P, ptr I);
>>>>>> 03
>>>>>> 04   void DDD(int (*x)())
>>>>>> 05   {
>>>>>> 06     HH(x, x);
>>>>>> 07     return;
>>>>>> 08   }
>>>>>> 09
>>>>>> 10   int main()
>>>>>> 11   {
>>>>>> 12     HH(DDD,DDD);
>>>>>> 13   }
>>>>>>
>>>>>> Line 12 main()
>>>>>>    invokes HH(DDD,DDD); that simulates DDD()
>>>>>>
>>>>>> *REPEAT UNTIL outer HH aborts*
>>>>>>    Line 06 simulated DDD()
>>>>>>    invokes simulated HH(DDD,DDD); that simulates DDD()
>>>>>>
>>>>>> DDD correctly simulated by HH never reaches its own "return"
>>>>>> instruction and halts.
>>>>>
>>>>> So, you agree that you are changing definitions. 
>>>>
>>>> Not at all. The original definition still applies when it
>>>> is made more generic.
>>>>
>>>> 01       int D(ptr p)
>>>> 02       {
>>>> 03         int Halt_Status = H(p, p);
>>>> 04         if (Halt_Status)
>>>> 05           HERE: goto HERE;
>>>> 06         return Halt_Status;
>>>> 07       }
>>>>
>>>> D correctly simulated by H has isomorphic behavior to DDD
>>>> correctly simulated by HH, both get stuck in recursive
>>>> simulation.
>>>>
>>>
>>> When asked what is a pathological program olcott replied:
>>> Op 14.jun.2024 om 21:18 schreef olcott:
>>>> 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 he defines a "pathological" program as a program that calls H.
>>> All words about doing the opposite of what H predicts, have disappeared.
>>> Everyone sees the difference, but he is stuck is rebuttal mode and 
>>> denies the change of definition.
>>>
>>
>> The code that "does the opposite" was never reachable by
>> a simulating halt decider thus does not change the problem
>> for a simulating halt decider when this code is removed.
> 
> So, there was never a relation with the Linz proof, where the part that 
> does the opposite of what H predicts plays the essential role.
> 

This is the key essence of the pathological relationship in all
of the halting problem counter-example proofs including the Linz proof.

void DDD()
{
   H0(DDD);
}

int main()
{
   H0(DDD);
}

> What remains is the fact that H is unable to simulate itself up to its 
> final state, which is called a "pathological" property of H.
> 

H is always correct to abort the simulation of any input
that would cause itself to not terminate normally.

When this is construed as non-halting criteria then H is
always correct to reject all of these inputs as non-halting.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer