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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: Mon, 17 Jun 2024 16:21:06 +0200
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Op 17.jun.2024 om 15:39 schreef olcott:
> 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.
> 

When! But that would be a big mistake to do. The inability of H0 to 
simulate itself does not tell us anything about the halting behaviour of 
the program.