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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is Correctly rejected as
 non-halting V2 ---woefully mistaken rebuttal
Date: Thu, 25 Jul 2024 16:27:33 +0200
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Op 25.jul.2024 om 15:56 schreef olcott:
> On 7/24/2024 10:29 PM, Mike Terry wrote:
>> On 23/07/2024 14:31, olcott wrote:
>>> On 7/23/2024 1:32 AM, 0 wrote:
>>>> On 2024-07-22 13:46:21 +0000, olcott said:
>>>>
>>>>> On 7/22/2024 2:57 AM, Mikko wrote:
>>>>>> On 2024-07-21 13:34:40 +0000, olcott said:
>>>>>>
>>>>>>> On 7/21/2024 4:34 AM, Mikko wrote:
>>>>>>>> On 2024-07-20 13:11:03 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 7/20/2024 3:21 AM, Mikko wrote:
>>>>>>>>>> On 2024-07-19 14:08:24 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> When we use your incorrect reasoning we would conclude
>>>>>>>>>>> that Infinite_Loop() is not an infinite loop because it
>>>>>>>>>>> only repeats until aborted and is aborted.
>>>>>>>>>>
>>>>>>>>>> You and your HHH can reason or at least conclude correctly about
>>>>>>>>>> Infinite_Loop but not about DDD. Possibly because it prefers to
>>>>>>>>>> say "no", which is correct about Infinte_loop but not about DDD.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> *Because this is true I don't understand how you are not simply 
>>>>>>>>> lying*
>>>>>>>>> int main
>>>>>>>>> {
>>>>>>>>>    DDD();
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> Calls HHH(DDD) that must abort the emulation of its input
>>>>>>>>> or {HHH, emulated DDD and executed DDD} never stop running.
>>>>>>>>
>>>>>>>> You are the lying one.
>>>>>>>>
>>>>>>>> If HHH(DDD) abrots its simulation and returns true it is correct 
>>>>>>>> as a
>>>>>>>> halt decider for DDD really halts.
>>>>>>>>
>>>>>>>
>>>>>>> (b) We know that a decider is not allowed to report on the behavior
>>>>>>> computation that itself is contained within.
>>>>>>
>>>>>> No, we don't. There is no such prohibition.
>>>>>>
>>>>>
>>>>> Turing machines never take actual Turing machines as inputs.
>>>>> They only take finite strings as inputs and an actual executing
>>>>> Turing machine is not itself a finite string.
>>>>
>>>> The definition of a Turing machine does not say that a Turing machine
>>>> is not a finite string. It is an abstract mathematical object without
>>>> a specification of its exact nature. It could be a set or a finite
>>>> string. Its exact nature is not relevant to the theory of computation,
>>>> which only cares about certain properties of Turing machines.
>>>>
>>>>> Therefore It is not allowed to report on its own behavior.
>>>>
>>>> Anyway, that does not follow. The theory of Turing machines does not
>>>> prohibit anything.
>>>>
>>>>> Another different TM can take the TM description of this
>>>>> machine and thus accurately report on its actual behavior.
>>>>
>>>> If a Turing machine can take a description of a TM as its input
>>>> or as a part of its input it can also take its own description.
>>>> Every Turing machine can be given its own description as input
>>>> but a Turing machine may interprete it as something else.
>>>>
>>> In this case we have two x86utm machines that are identical
>>> except that DDD calls HHH and DDD does not call HHH1.
>>>
>>> It is empirically proven that this changes their behavior
>>> and the behavior of DDD.
>>>
>>
>> You say a lot about things that are "empirically proven" and without 
>> exception they are never "proven" at all.
>>
> 
> It is empirically proven according to the semantics of the
> x86 machine code of DDD that DDD correctly emulated by HHH
> has different behavior than DDD correctly emulated by HHH1.

No, you have proven that the *simulation* is different, not that the 
behaviour of the simulated function is different.
The simulations differ, because one is correct and the other one is 
incorrect.
The one that skips x86 instructions (by aborting) does not follow the 
semantics of the x86 language. Its simulation is incomplete and 
therefore is wrong.

> 
> _DDD()
> [00002177] 55         push ebp
> [00002178] 8bec       mov ebp,esp
> [0000217a] 6877210000 push 00002177
> [0000217f] e853f4ffff call 000015d7
> [00002184] 83c404     add esp,+04
> [00002187] 5d         pop ebp
> [00002188] c3         ret
> Size in bytes:(0018) [00002188]
> 
> _main()
> [00002197] 55         push ebp
> [00002198] 8bec       mov ebp,esp
> [0000219a] 6877210000 push 00002177
> [0000219f] e863f3ffff call 00001507
> [000021a4] 83c404     add esp,+04
> [000021a7] 33c0       xor eax,eax
> [000021a9] 5d         pop ebp
> [000021aa] c3         ret
> Size in bytes:(0020) [000021aa]
> 
>   machine   stack     stack     machine    assembly
>   address   address   data      code       language
>   ========  ========  ========  =========  =============
> [00002197][001037fb][00000000] 55         push ebp
> [00002198][001037fb][00000000] 8bec       mov ebp,esp
> [0000219a][001037f7][00002177] 6877210000 push 00002177 ; push DDD
> [0000219f][001037f3][000021a4] e863f3ffff call 00001507 ; call HHH1
> New slave_stack at:10389f
> 
> Begin Local Halt Decider Simulation   Execution Trace Stored at:1138a7
> [00002177][00113897][0011389b] 55         push ebp
> [00002178][00113897][0011389b] 8bec       mov ebp,esp
> [0000217a][00113893][00002177] 6877210000 push 00002177 ; push DDD
> [0000217f][0011388f][00002184] e853f4ffff call 000015d7 ; call HHH
> New slave_stack at:14e2c7
> 
> Begin Local Halt Decider Simulation   Execution Trace Stored at:15e2cf
> [00002177][0015e2bf][0015e2c3] 55         push ebp
> [00002178][0015e2bf][0015e2c3] 8bec       mov ebp,esp
> [0000217a][0015e2bb][00002177] 6877210000 push 00002177 ; push DDD
> [0000217f][0015e2b7][00002184] e853f4ffff call 000015d7 ; call HHH
> New slave_stack at:198cef
> [00002177][001a8ce7][001a8ceb] 55         push ebp
> [00002178][001a8ce7][001a8ceb] 8bec       mov ebp,esp
> [0000217a][001a8ce3][00002177] 6877210000 push 00002177 ; push DDD
> [0000217f][001a8cdf][00002184] e853f4ffff call 000015d7 ; call HHH
> Local Halt Decider: Infinite Recursion Detected Simulation Stopped

There is no infinite recursion.
HEH is simply unable to decide about finite recursions.

void Finite_Recursion (nit N) {
   if (N > 0) Finite_Recursion (N - 1);
}

It decides after N recursions that there is an infinite recursion, which 
is incorrect.

> 
> [00002184][00113897][0011389b] 83c404     add esp,+04
> [00002187][0011389b][000015bc] 5d         pop ebp
> [00002188][0011389f][0003a980] c3         ret
> [000021a4][001037fb][00000000] 83c404     add esp,+04
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