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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 22:42:10 -0600
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On 2/23/2025 10:09 PM, dbush wrote:
> 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
========== REMAINDER OF ARTICLE TRUNCATED ==========