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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Proof that executed HH(DD,DD) and simulated HH(DD,DD) simulate DD
 correctly -- Mike Terry
Date: Thu, 6 Jun 2024 10:06:22 -0500
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On 6/6/2024 9:51 AM, Mikko wrote:
> On 2024-06-06 13:11:34 +0000, olcott said:
> 
>> On 6/6/2024 3:21 AM, Mikko wrote:
>>> On 2024-06-05 13:49:47 +0000, olcott said:
>>>
>>>> On 6/5/2024 2:59 AM, Mikko wrote:
>>>>> On 2024-06-04 16:46:21 +0000, Fred. Zwarts said:
>>>>>
>>>>>> Op 04.jun.2024 om 18:28 schreef olcott:
>>>>>>> Heh Mike Terry, please study this to see your mistaken
>>>>>>> conclusion of this post:
>>>>>>>
>>>>>>> On 5/30/2024 3:51 PM, Mike Terry wrote:
>>>>>>>> On 30/05/2024 17:55, olcott wrote:
>>>>>>> http://al.howardknight.net/?STYPE=msgid&MSGI=%3CS8CcnRadHexfe8X7nZ2dnZfqnPqdnZ2d%40brightview.co.uk%3E+
>>>>>>> Message-ID: <S8CcnRadHexfe8X7nZ2dnZfqnPqdnZ2d@brightview.co.uk>
>>>>>>>
>>>>>>> *Here is your mistaken conclusion*
>>>>>>> On 5/30/2024 3:51 PM, Mike Terry wrote:
>>>>>>>> On 30/05/2024 17:55, olcott wrote:
>>>>>>>>> That HH is not a pure function does not show that
>>>>>>>>> the simulation is incorrect because:
>>>>>>>>
>>>>>>>> It shows that the simulation is "rubbish" and any
>>>>>>>> trace produced by it can just be ignored.
>>>>>>>>
>>>>>>>> Err, that's it.
>>>>>>>>
>>>>>>>> Mike.
>>>>>>>
>>>>>>> Proof that executed HH(DD,DD) and simulated HH(DD,DD) simulate DD
>>>>>>> correctly. This proof requires expert knowledge of the C programming
>>>>>>> language and the x86 programming language.
>>>>>>>
>>>>>>> With this expertise it is easy to confirm that both the directly
>>>>>>> executed HH(DD,DD) and the simulated executed HH(DD,DD) simulate the
>>>>>>> steps of DD exactly the way that the x86 machine language specifies.
>>>>>>>
>>>>>>> *New Paragraph inserted*
>>>>>>> We can see that the pair of execution traces derived by the executed
>>>>>>> HH(DD,DD) and the simulated HH(DD,DD) (shown below) exactly match
>>>>>>> the x86 machine code of DD, (also shown below) thus are proven to be
>>>>>>> correct.
>>>>>>>
>>>>>>> If one also has expertise on the mapping from the C source code 
>>>>>>> to the
>>>>>>> x86 assembly language then one also confirms that the x86 version of
>>>>>>> DD is exactly what the C source-code specifies.
>>>>>>>
>>>>>>> 01   int DD(int (*x)())
>>>>>>> 02   {
>>>>>>> 03     int Halt_Status = HH(x, x);
>>>>>>> 04     if (Halt_Status)
>>>>>>> 05         HERE: goto HERE;
>>>>>>> 06     return Halt_Status;
>>>>>>> 07   }
>>>>>>> 08
>>>>>>> 09   int main()
>>>>>>> 10   {
>>>>>>> 11     Output("Input_Halts = ", HH(DD,DD));
>>>>>>> 12   }
>>>>>>>
>>>>>>> _DD()
>>>>>>> [00001db2] 55         push ebp
>>>>>>> [00001db3] 8bec       mov ebp,esp
>>>>>>> [00001db5] 51         push ecx
>>>>>>> [00001db6] 8b4508     mov eax,[ebp+08]
>>>>>>> [00001db9] 50         push eax        ; push DD
>>>>>>> [00001dba] 8b4d08     mov ecx,[ebp+08]
>>>>>>> [00001dbd] 51         push ecx        ; push DD
>>>>>>> [00001dbe] e8bff5ffff call 00001382   ; call HH
>>>>>>> [00001dc3] 83c408     add esp,+08
>>>>>>> [00001dc6] 8945fc     mov [ebp-04],eax
>>>>>>> [00001dc9] 837dfc00   cmp dword [ebp-04],+00
>>>>>>> [00001dcd] 7402       jz 00001dd1
>>>>>>> [00001dcf] ebfe       jmp 00001dcf
>>>>>>> [00001dd1] 8b45fc     mov eax,[ebp-04]
>>>>>>> [00001dd4] 8be5       mov esp,ebp
>>>>>>> [00001dd6] 5d         pop ebp
>>>>>>> [00001dd7] c3         ret
>>>>>>> Size in bytes:(0038) [00001dd7]
>>>>>>>
>>>>>>>  machine   stack     stack     machine    assembly
>>>>>>>  address   address   data      code       language
>>>>>>>  ========  ========  ========  =========  =============
>>>>>>> [00001de2][00103292][00000000] 55         push ebp
>>>>>>> [00001de3][00103292][00000000] 8bec       mov ebp,esp
>>>>>>> [00001de5][0010328e][00001db2] 68b21d0000 push 00001db2 ; push DD
>>>>>>> [00001dea][0010328a][00001db2] 68b21d0000 push 00001db2 ; push DD
>>>>>>> [00001def][00103286][00001df4] e88ef5ffff call 00001382 ; call HH
>>>>>>> New slave_stack at:103336
>>>>>>>
>>>>>>> Begin Local Halt Decider Simulation   Execution Trace Stored 
>>>>>>> at:11333e
>>>>>>> [00001db2][0011332a][0011332e] 55         push ebp         ; DD 
>>>>>>> line 01
>>>>>>> [00001db3][0011332a][0011332e] 8bec       mov ebp,esp      ; DD 
>>>>>>> line 02
>>>>>>> [00001db5][00113326][001032fa] 51         push ecx         ; DD 
>>>>>>> line 03
>>>>>>> [00001db6][00113326][001032fa] 8b4508     mov eax,[ebp+08] ; DD 
>>>>>>> line 04
>>>>>>> [00001db9][00113322][00001db2] 50         push eax         ; push DD
>>>>>>> [00001dba][00113322][00001db2] 8b4d08     mov ecx,[ebp+08] ; DD 
>>>>>>> line 06
>>>>>>> [00001dbd][0011331e][00001db2] 51         push ecx         ; push DD
>>>>>>> [00001dbe][0011331a][00001dc3] e8bff5ffff call 00001382    ; call HH
>>>>>>> New slave_stack at:14dd5e
>>>>>>> [00001db2][0015dd52][0015dd56] 55         push ebp         ; DD 
>>>>>>> line 01
>>>>>>> [00001db3][0015dd52][0015dd56] 8bec       mov ebp,esp      ; DD 
>>>>>>> line 02
>>>>>>> [00001db5][0015dd4e][0014dd22] 51         push ecx         ; DD 
>>>>>>> line 03
>>>>>>> [00001db6][0015dd4e][0014dd22] 8b4508     mov eax,[ebp+08] ; DD 
>>>>>>> line 04
>>>>>>> [00001db9][0015dd4a][00001db2] 50         push eax         ; push DD
>>>>>>> [00001dba][0015dd4a][00001db2] 8b4d08     mov ecx,[ebp+08] ; DD 
>>>>>>> line 06
>>>>>>> [00001dbd][0015dd46][00001db2] 51         push ecx         ; push DD
>>>>>>> [00001dbe][0015dd42][00001dc3] e8bff5ffff call 00001382    ; call HH
>>>>>>> Local Halt Decider: Infinite Recursion Detected Simulation Stopped
>>>>>>>
>>>>>>> [00001df4][00103292][00000000] 83c408     add esp,+08
>>>>>>> [00001df7][0010328e][00000000] 50         push eax
>>>>>>> [00001df8][0010328a][00000743] 6843070000 push 00000743
>>>>>>> [00001dfd][0010328a][00000743] e8a0e9ffff call 000007a2
>>>>>>> Input_Halts = 0
>>>>>>> [00001e02][00103292][00000000] 83c408     add esp,+08
>>>>>>> [00001e05][00103292][00000000] eb79       jmp 00001e80
>>>>>>> [00001e80][00103292][00000000] 33c0       xor eax,eax
>>>>>>> [00001e82][00103296][00000018] 5d         pop ebp
>>>>>>> [00001e83][0010329a][00000000] c3         ret
>>>>>>> Number of Instructions Executed(16829) == 251 Pages
>>>>>>>
>>>>>>
>>>>>> This is a perfect example of a false negative. It is explained by 
>>>>>> the following:
>>>>>>
>>>>>> Olcott defends a simulating halt decider H. The problem with it 
>>>>>> is, that it introduces another halting problem: The H itself does 
>>>>>> not halt when simulated by itself. This causes false negatives: 
>>>>>> many functions are now diagnosed by H to be non-halting only by 
>>>>>> the mere fact that they call H, even if their direct execution 
>>>>>> does halt.
>>>>>>
>>>>>> We see in olcott's example above that the simulation of H invokes 
>>>>>> a recursive simulation of H.
>>>>>>
>>>>>> H even diagnoses itself to be non-halting, which is illustrated in 
>>>>>> the following example (where the D that contradicts H is eliminated):
>>>>>>
>>>>>>         typedef int (*ptr)();  // ptr is pointer to int function in C
>>>>>>
>>>>>>         int H(ptr p, ptr i);
>>>>>>
>>>>>>         int main()
>>>>>>         {
>>>>>>           H(main, 0);
>>>>>>         }
>>>>>
>>>>> That program does not tell what H says. You should instead say
>>>>>
>>>>> int main()
>>>>> {
>>>>>  return H(main, 0);
>>>>> }
>>>>>
>>>>> so that the result is returned to the operating systems. Many 
>>>>> operating
>>>>> systems tell the value returned by main or they can be asked about it.
>>>>>
>>>>
>>>> *I was surprised that this worked correctly: here are the details*
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