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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 23:01:47 -0600
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On 2/23/2025 10:45 PM, dbush wrote:
> 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
>>>>>>>>>>>
========== REMAINDER OF ARTICLE TRUNCATED ==========