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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD emulated by HHH cannot possibly terminate normally --- x86
 code
Date: Fri, 28 Feb 2025 21:07:28 -0500
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On 2/28/2025 9:05 PM, olcott wrote:
> On 2/28/2025 7:00 PM, dbush wrote:
>> On 2/28/2025 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.
>>>
>>
>> Likewise:
>>
>> 0000000000400534 <no_numbers_greater_than_10>:
>>    400534:    55                       push   rbp
>>    400535:    48 89 e5                 mov    rbp,rsp
>>    400538:    b8 34 05 40 00           mov    eax,0x400534 ; push 
>> no_numbers_greater_than_10
>>    40053d:    48 89 c7                 mov    rdi,rax
>>    400540:    e8 a8 ff ff ff           call   4004ed <F>   ; call F
>>    400545:    5d                       pop    rbp
>>    400546:    c3                       ret
>>
>> When we hypothesize that the code at machine address
>> 4004ed is an x86 emulator then we know that no_numbers_greater_than_10
>> remains stuck in recursive emulation and cannot possibly
>> reach its own "ret" instruction and terminate normally.
>>
>> When we add the additional complexity that F also
>> aborts this sequence at some point then every level
>> of recursive emulation immediately stops. This does
>> not enable any no_numbers_greater_than_10 to ever reach its "ret" 
>> instruction.
>>
> 
> So you and your code agrees with me.
> 

And likewise, you agree that there is no natural number greater than 10.