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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: Mon, 24 Feb 2025 08:11:36 -0500
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On 2/24/2025 12:17 AM, olcott wrote:
> 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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