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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD specifies non-terminating behavior to HHH --- RECURSIVE CHAIN
 --- Saving Democracy
Date: Sun, 23 Feb 2025 23:09:26 -0500
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On 2/23/2025 10:20 PM, olcott wrote:
> On 2/23/2025 9:15 PM, dbush wrote:
>> On 2/23/2025 9:04 PM, olcott wrote:
>>> 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.
>>>>>>>
>>>>>>
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