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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Proof that executed HH(DD,DD) and simulated HH(DD,DD) simulate DD correctly -- Mike Terry
Date: Thu, 6 Jun 2024 11:21:50 +0300
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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*
> 
> int main()
> {
>    Output("Input_Halts = ", HH(main,(ptr)0));
> }
> 
>   machine   stack     stack     machine    assembly
>   address   address   data      code       language
>   ========  ========  ========  =========  =============
> [00001e42][00103375][00000000] 55         push ebp      ; begin main
> [00001e43][00103375][00000000] 8bec       mov ebp,esp
> [00001e45][00103371][00000000] 6a00       push +00
> [00001e47][0010336d][00001e42] 68421e0000 push 00001e42 ; push main
> [00001e4c][00103369][00001e51] e831f5ffff call 00001382 ; call HH
> New slave_stack at:103419
> 
> Begin Local Halt Decider Simulation   Execution Trace Stored at:113421
> [00001e42][0011340d][00113411] 55         push ebp      ; begin main
> [00001e43][0011340d][00113411] 8bec       mov ebp,esp
> [00001e45][00113409][00000000] 6a00       push +00
> [00001e47][00113405][00001e42] 68421e0000 push 00001e42 ; push main
> [00001e4c][00113401][00001e51] e831f5ffff call 00001382 ; call HH
> New slave_stack at:14de41
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