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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: HHH maps its input to the behavior specified by it --- never
 reaches its halt state ---
Date: Wed, 14 Aug 2024 16:04:31 +0200
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Op 14.aug.2024 om 15:47 schreef olcott:
> On 8/14/2024 2:41 AM, Mikko wrote:
>> On 2024-08-13 13:21:32 +0000, olcott said:
>>
>>> On 8/13/2024 6:08 AM, Mikko wrote:
>>>> On 2024-08-11 11:45:18 +0000, olcott said:
>>>>
>>>>> On 8/11/2024 1:30 AM, Mikko wrote:
>>>>>> On 2024-08-10 11:30:34 +0000, olcott said:
>>>>>>
>>>>>>> On 8/10/2024 3:29 AM, Mikko wrote:
>>>>>>>> On 2024-08-09 14:51:51 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 8/9/2024 4:03 AM, Mikko wrote:
>>>>>>>>>> On 2024-08-08 13:18:34 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> void DDD()
>>>>>>>>>>> {
>>>>>>>>>>>    HHH(DDD);
>>>>>>>>>>>    return;
>>>>>>>>>>> }
>>>>>>>>>>>
>>>>>>>>>>> Each HHH of every HHH that can possibly exist definitely
>>>>>>>>>>> *emulates zero to infinity instructions correctly* In
>>>>>>>>>>> none of these cases does the emulated DDD ever reach
>>>>>>>>>>> its "return" instruction halt state.
>>>>>>>>>>
>>>>>>>>>> The ranges of "each HHH" and "every HHH" are not defined above
>>>>>>>>>> so that does not really mean anything.
>>>>>>>>>
>>>>>>>>> Here is something that literally does not mean anything:
>>>>>>>>> "0i34ine ir m0945r (*&ubYU  I*(ubn)I*054 gfdpodf["
>>>>>>>>
>>>>>>>> Looks like encrypted text that might mean something.
>>>>>>>>
>>>>>>>>> "Colorless green ideas sleep furiously"
>>>>>>>>
>>>>>>>> This could be encrypted text, too, or perhaps refers to some
>>>>>>>> inside knowledge or convention.
>>>>>>>>
>>>>>>>>> I defined an infinite set of HHH x86 emulators.
>>>>>>>>
>>>>>>>> Maybe somewnete but not in the message I commented.
>>>>>>>>
>>>>>>>>> I stipulated that each member of this set emulates
>>>>>>>>> zero to infinity instructions of DDD.
>>>>>>>>
>>>>>>>> That doesn't restrict much.
>>>>>>>>
>>>>>>>>> *I can't say it this way without losing 90% of my audience*
>>>>>>>>> Each element of this set is mapped to one element of the
>>>>>>>>> set of non-negative integers indicating the number of
>>>>>>>>> x86 instructions of DDD that it emulates.
>>>>>>>>
>>>>>>>> It is easier to talk about mapping if is given a name.
>>>>>>>>
>>>>>>>>> *This one seems to be good*
>>>>>>>>> Each element of this set corresponds to one element of
>>>>>>>>> the set of positive integers indicating the number of
>>>>>>>>> x86 instructions of DDD that it emulates.
>>>>>>>>
>>>>>>>> That would mean that only a finite number (possibly zero) of
>>>>>>>> instructions is emulated. But the restriction to DDD does not
>>>>>>>> seem reasonable.
>>>>>>>>
>>>>>>>
>>>>>>> *The set of HHH x86 emulators are defined such that*
>>>>>>>
>>>>>>> Each element of this set corresponds to one element of
>>>>>>> the set of positive integers indicating the number of
>>>>>>> x86 instructions of DDD that it correctly emulates.
>>>>>>
>>>>>> As we onece observed, this would be clearer with incdices.
>>>>>> No journal woth of consideration will accept an article
>>>>>> that uses the same name for a specific program and a set.
>>>>>>
>>>>>>
>>>>>
>>>>> void DDD()
>>>>> {
>>>>>    HHH(DDD);
>>>>>    return;
>>>>> }
>>>>>
>>>>> None-the-less it is clear that of the above specified infinite
>>>>> set DDD correctly emulated by each element of that set never
>>>>> reaches its own "return" instruction halt state.
>>>>
>>>> To emulate an infinite set of DDD by infintely manu emulators
>>>> is too much to actually do. However, one may pick a HHHᵤ and
>>>> DDDᵥ so that HHHᵤ(DDDᵥ) correctly determines that DDDᵥ halts.
>>>
>>> Through something like mathematical induction we can directly
>>> see that DDD correctly emulated by any HHH cannot possibly
>>> reach its "return" instruction final halt state.
>>
>> No, we don't see, at least as long as you don't show.
>>
> 
> _DDD()
> [00002172] 55         push ebp      ; housekeeping
> [00002173] 8bec       mov ebp,esp   ; housekeeping
> [00002175] 6872210000 push 00002172 ; push DDD
> [0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
> [0000217f] 83c404     add esp,+04
> [00002182] 5d         pop ebp
> [00002183] c3         ret
> Size in bytes:(0018) [00002183]
> 
> The impossibility of DDD emulated by HHH
> (according to the semantics of the x86 language)
> to reach its own machine address [00002183] is
> compete proof.
> 
> We don't even need an actual HHH we only need
> to imagine that HHH is a pure x86 emulator and
> then anyone with sufficient expertise in the x86
> language can see that DDD correctly emulated by
> HHH never reaches machine address [00002183].
> 

Which proves that the simulation is incomplete, because it aborted one 
cycle too soon. This makes the simulation incorrect.
HHH cannot possibly simulate *itself* correctly.