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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD emulated by HHH cannot possibly terminate normally --- x86
 code
Date: Sat, 1 Mar 2025 18:44:11 -0600
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On 3/1/2025 4:39 PM, Fred. Zwarts wrote:
> Op 01.mrt.2025 om 22:11 schreef olcott:
>> On 3/1/2025 2:16 PM, Fred. Zwarts wrote:
>>> Op 01.mrt.2025 om 17:33 schreef olcott:
>>>> On 3/1/2025 9:39 AM, Fred. Zwarts wrote:
>>>>> Op 01.mrt.2025 om 15:41 schreef olcott:
>>>>>> On 3/1/2025 6:49 AM, Richard Damon wrote:
>>>>>>> On 2/28/25 7:47 PM, olcott wrote:
>>>>>>>> _DD()
>>>>>>>> [00002133] 55         push ebp      ; housekeeping
>>>>>>>> [00002134] 8bec       mov ebp,esp   ; housekeeping
>>>>>>>> [00002136] 51         push ecx      ; make space for local
>>>>>>>> [00002137] 6833210000 push 00002133 ; push DD
>>>>>>>> [0000213c] e882f4ffff call 000015c3 ; call HHH(DD)
>>>>>>>> [00002141] 83c404     add esp,+04
>>>>>>>> [00002144] 8945fc     mov [ebp-04],eax
>>>>>>>> [00002147] 837dfc00   cmp dword [ebp-04],+00
>>>>>>>> [0000214b] 7402       jz 0000214f
>>>>>>>> [0000214d] ebfe       jmp 0000214d
>>>>>>>> [0000214f] 8b45fc     mov eax,[ebp-04]
>>>>>>>> [00002152] 8be5       mov esp,ebp
>>>>>>>> [00002154] 5d         pop ebp
>>>>>>>> [00002155] c3         ret
>>>>>>>> Size in bytes:(0035) [00002155]
>>>>>>>>
>>>>>>>> When we hypothesize that the code at machine address
>>>>>>>> 0000213c is an x86 emulator then we know that DD
>>>>>>>> remains stuck in recursive emulation and cannot possibly
>>>>>>>> reach its own "ret" instruction and terminate normally.
>>>>>>>>
>>>>>>>> When we add the additional complexity that HHH also
>>>>>>>> aborts this sequence at some point then every level
>>>>>>>> of recursive emulation immediately stops. This does
>>>>>>>> not enable any DD to ever reach its "ret" instruction.
>>>>>>>>
>>>>>>>
>>>>>>> But then you just negated your first assumption, as a partial 
>>>>>>> emulator that aborts its emulation, then DD no longer gets stuck.
>>>>>>>
>>>>>>
>>>>>> Cannot possibly reach its own "ret" instruction and terminate 
>>>>>> normally
>>>>> proves failure of HHH to reach the end of a proven terminating 
>>>>> program.
>>>>
>>>> DD emulated by HHH according to the above x86 machine code of DD
>>>> cannot possibly reach its own "ret" instruction and terminate normally
>>>
>>>
>>> In other words, 
>>
>> The DD input to HHH unequivocally specifies a
>> non terminating computation.
>>
>>
> 
> What is the meaning of 'non terminating computation'? 

The finite string input DD to HHH emulated by HHH according
to the behavior that it species (which includes pathological
self-reference) cannot possibly reach its "ret" instruction
and terminate normally.

When we say that the finite string input to HHH halts
because some other instance that is not an input halts
that is the same as saying that the Liar Paradox
is true because IT IS TRUE WHEN IT IS APPLIED TO ITSELF.

This sentence is not true: "This sentence is not true" IS TRUE.


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer