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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 23:45:27 -0500
Organization: A noiseless patient Spider
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On 2/23/2025 11:42 PM, olcott wrote:
> 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 ==========