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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Who here understands that the last paragraph is Necessarily true?
Date: Mon, 15 Jul 2024 21:05:37 +0200
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Op 15.jul.2024 om 14:48 schreef olcott:
> On 7/15/2024 6:09 AM, Richard Damon wrote:
>> On 7/14/24 10:33 PM, olcott wrote:
>>> On 7/14/2024 9:04 PM, Richard Damon wrote:
>>>> On 7/14/24 9:27 PM, olcott wrote:
>>>>>
>>>>> Any input that must be aborted to prevent the non termination
>>>>> of simulating termination analyzer HHH necessarily specifies
>>>>> non-halting behavior or it would never need to be aborted.
>>>>
>>>> Excpet, as I have shown, it doesn't.
>>>>
>>>> Your problem is you keep on ILEGALLY changing the input in your 
>>>> argument because you have misdefined what the input is.
>>>>
>>>
>>> _DDD()
>>> [00002163] 55         push ebp      ; housekeeping
>>> [00002164] 8bec       mov ebp,esp   ; housekeeping
>>> [00002166] 6863210000 push 00002163 ; push DDD
>>> [0000216b] e853f4ffff call 000015c3 ; call HHH(DDD)
>>> [00002170] 83c404     add esp,+04
>>> [00002173] 5d         pop ebp
>>> [00002174] c3         ret
>>> Size in bytes:(0018) [00002174]
>>>
>>> The input *is* the machine address of this finite
>>> string of bytes: 558bec6863210000e853f4ffff83c4045dc3
>>>
>>
>> Nope, the "input" needs to define everything that varies from one 
>> question to another, 
> 
> Any input that must be aborted to prevent the non termination
> of simulating termination analyzer HHH necessarily specifies
> non-halting behavior or it would never need to be aborted.

But the simulation of HHH does not need to be aborted. Because it aborts 
and halts by itself.

DDD has nothing to do with it. It is easy to eliminate DDD:

        int main() {
          return HHH(main);
        }

This has the same problem. This proves that the problem is not in DDD, 
but in HHH, which halts when it aborts the simulation, but it decides 
that the simulation of itself does not halt.

HHH is unable to decide about finite recursions.

void Finite_Recursion (int N) {
   if (N > 0) Finite_Recursion (N - 1);
}

It decides after N recursions that there is an infinite recursion, which 
is incorrect.

Your HHH is programmed to abort the simulation after N cycles of 
recursive simulations. Therefore, it is incorrect to abort the 
simulation of HHH when the simulated HHH has performed N-1 cycles, 
because that changes the behaviour of HHH.
Since the simulated HHH always runs one cycle behind the simulating HHH, 
it is clear that HHH can never simulate enough cycles for a correct 
simulation, as is required by the x86 language.
Therefore, the simulation is incorrect according to the criteria you 
stipulated.
The conclusion is simple:
HHH cannot possibly simulate itself correctly.

No matter how much you want it to be correct, or how many times you 
repeat that it is correct, it does not change the fact that such a 
simulation is incorrect, because it is unable to reach the end.

Sipser would agree that this incorrect simulation cannot be used to 
detect a non-halting behaviour.