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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 23:17:19 -0600
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On 2/23/2025 11:08 PM, dbush wrote:
> On 2/24/2025 12:01 AM, olcott wrote:
>> 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
>>>>>>>>>>>>>
>>>>>>>>>>>>>
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