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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD specifies non-terminating behavior to HHH --- RECURSIVE CHAIN
 --- Saving Democracy
Date: Sun, 23 Feb 2025 20:04:10 -0600
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On 2/23/2025 7:22 PM, dbush wrote:
> On 2/23/2025 8:13 PM, olcott wrote:
>> On 2/23/2025 6:15 PM, dbush wrote:
>>> On 2/23/2025 7:10 PM, olcott wrote:
>>>> On 2/23/2025 11:57 AM, dbush wrote:
>>>>> On 2/23/2025 12:30 PM, olcott wrote:
>>>>>> On 2/22/2025 8:34 PM, dbush wrote:
>>>>>>> On 2/22/2025 7:33 PM, olcott wrote:
>>>>>>>> On 2/22/2025 4:59 PM, dbush wrote:
>>>>>>>>> On 2/22/2025 5:53 PM, olcott wrote:
>>>>>>>>>> On 2/22/2025 2:59 PM, dbush wrote:
>>>>>>>>>>> On 2/22/2025 3:53 PM, olcott wrote:
>>>>>>>>>>>> On 2/22/2025 2:09 PM, dbush wrote:
>>>>>>>>>>>>> On 2/22/2025 3:03 PM, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> 01 int F(int i)
>>>>>>>>>>>> 02 {
>>>>>>>>>>>> 03   if (i > 10)
>>>>>>>>>>>> 04     return 0;
>>>>>>>>>>>> 05   else
>>>>>>>>>>>> 06     return F(i+1);
>>>>>>>>>>>> 07 }
>>>>>>>>>>>> 08
>>>>>>>>>>>> 09 int no_numbers_greater_than_10()
>>>>>>>>>>>> 10 {
>>>>>>>>>>>> 11   return F(0);
>>>>>>>>>>>> 12 }
>>>>>>>>>>>> 13
>>>>>>>>>>>> 14 int main()
>>>>>>>>>>>> 15 {
>>>>>>>>>>>> 16   F((int)no_numbers_greater_than_10);
>>>>>>>>>>>> 17   return 0;
>>>>>>>>>>>> 18 }
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> So if the address of no_numbers_greater_than_10 is greater 
>>>>>>>>>>>>> than 10 then 0 is returned right away, otherwise as most 10 
>>>>>>>>>>>>> recursive calls will be made before the condition is 
>>>>>>>>>>>>> matched and 0 is returned.
>>>>>>>>>>>>>
>>>>>>>>>>>>> This doesn't change the fact that 
>>>>>>>>>>>>> no_numbers_greater_than_10 correctly
>>>>>>>>>>>>> simulated by F cannot possibly return so 
>>>>>>>>>>>>> F(no_numbers_greater_than_10)
>>>>>>>>>>>>> is correct to report non-halting, which means that there is 
>>>>>>>>>>>>> no natural
>>>>>>>>>>>>> number greater than 10.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Agreed?
>>>>>>>>>>>>
>>>>>>>>>>>> I think that you will find more bugs when you try to
>>>>>>>>>>>> provide the line number by line number execution trace.
>>>>>>>>>>>>
>>>>>>>>>>>> #1 bug F never simulates anything.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> It is a verified fact that 
>>>>>>>>>>
>>>>>>>>>> F never simulates anything when i > 10.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Remember, you agreed that the behavior of X simulated by Y is 
>>>>>>>>> defined by replacing the code of Y with an unconditional 
>>>>>>>>> simulator and running Y(X):
>>>>>>>>>
>>>>>>>>> On 2/22/2025 1:02 PM, olcott wrote:
>>>>>>>>>  > On 2/22/2025 11:10 AM, dbush wrote:
>>>>>>>>>  >> On 2/22/2025 11:43 AM, olcott wrote:
>>>>>>>>>  >>> The first point is DD correctly simulated by HHH cannot
>>>>>>>>>  >>> possibly terminate normally by reaching its own "return"
>>>>>>>>>  >>> instruction.
>>>>>>>>>  >>
>>>>>>>>>  >> In other words, if the code of HHH is replaced with an 
>>>>>>>>> unconditional simulator then it can be shown that DD is non- 
>>>>>>>>> halting and therefore HHH(DD)==0 is correct.
>>>>>>>>>  >>
>>>>>>>>>  >
>>>>>>>>>  > Wow finally someone that totally gets it.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> So the behavior of no_numbers_greater_than_10 simulated by F is 
>>>>>>>>> defined by replacing the code of F with an unconditional 
>>>>>>>>> simulated and running F(no_numbers_greater_than_10).
>>>>>>>>>
>>>>>>>>> The finite string input to F proves that there are no 
>>>>>>>>> instructions in no_numbers_greater_than_10 that can break the 
>>>>>>>>> recursive simulation.
>>>>>>>>>
>>>>>>>>> Try to show how no_numbers_greater_than_10 correctly simulated 
>>>>>>>>> by F can possibly halt.
>>>>>>>>
>>>>>>>> Then is ceases to be analogous to HHH(DD) because
>>>>>>>> no_numbers_greater_than_10() always terminates normally
>>>>>>>> by reaching its own "return" instruction.
>>>>>>>
>>>>>>> In other words, when we actually run no_numbers_greater_than_10() 
>>>>>>> it reaches its own "return" instruction.
>>>>>>>
>>>>>>> That means we've now established that the direct execution of a 
>>>>>>> program (which includes all the functions it calls UNMODIFIED) 
>>>>>>> defines whether or not it halts.
>>>>>>>
>>>>>>> Likewise, when we actually run DD() unmodified it also reaches 
>>>>>>> its own "return" instruction.
>>>>>>>
>>>>>>> Therefore HHH(DD)==0 is wrong.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> _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 DD is correctly simulated by HHH according to the behavior
>>>>>> that the above machine code specifies then the call from DD
>>>>>> to HHH(DD) cannot possibly return and this correctly simulated
>>>>>> DD cannot possibly terminate  normally by reaching its own machine
>>>>>> address 00002155.
>>>>>>
>>>>>
>>>>> Similarly:
>>>>>
>>>>> 0000000000400534 <no_numbers_greater_than_10>:
>>>>>    400534:    55                       push   %rbp
>>>>>    400535:    48 89 e5                 mov    %rsp,%rbp
>>>>>    400538:    b8 34 05 40 00           mov    $0x400534,%eax
>>>>>    40053d:    48 89 c7                 mov    %rax,%rdi
>>>>>    400540:    e8 a8 ff ff ff           callq  4004ed <F>
>>>>>    400545:    5d                       pop    %rbp
>>>>>    400546:    c3                       retq
>>>>>
>>>>>
>>>>> When no_numbers_greater_than_10 is correctly simulated by F 
>>>>> according to the behavior that the above machine code specifies 
>>>>> then the call from no_numbers_greater_than_10  to 
>>>>> F(no_numbers_greater_than_10) cannot possibly terminate normally by 
>>>>> reaching its own machine address 400545
>>>>>
>>>>> So F(no_numbers_greater_than_10)==0 is correct, and therefore no 
>>>>> natural number exists that is greater than 10
>>>>>
>>>>> Agreed?
>>>>
>>>> I Only understand Intel format assembly language.
>>>>
>>>
>>> It corresponds to the following C code:
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