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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: Wed, 5 Jun 2024 08:49:47 -0500
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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
========== REMAINDER OF ARTICLE TRUNCATED ==========