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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 ---natural number mapping
Date: Sat, 10 Aug 2024 16:00:36 +0200
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Op 10.aug.2024 om 15:37 schreef olcott:
> On 8/10/2024 8:21 AM, Fred. Zwarts wrote:
>> Op 10.aug.2024 om 14:06 schreef olcott:
>>> On 8/10/2024 6:57 AM, Richard Damon wrote:
>>>> On 8/10/24 7:30 AM, olcott wrote:
>>>>> 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*
>>>>
>>>> I thopught HHH was a deider?
>>>>
>>>>>
>>>>> 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.
>>>>
>>>> And only those element of the set that either reach the final state, 
>>>> or simulate forever are "correct" emulators of the whole program, 
>>>> suitable to show halting.
>>>>
>>>
>>> void DDD()
>>> {
>>>    HHH(DDD);
>>>    return;
>>> }
>>>
>>> In other words even though it is dead obvious to
>>> us that a complete simulation of DDD simulated by HHH
>>
>> is impossible, because HHH is programmed to abort and, therefore, it 
>> is unable to do a complete simulation.
> 
> A complete simulation of DDD by a pure x86 emulator
> named HHH cannot possibly reach its own "return"
> instruction halt state.

Indeed, HHH fails to reach its own halt state. HHH cannot possibly 
simulate itself up to its halt state.
Which proves that the simulation is incomplete and, therefore, incorrect.

> 
> We can see this. Do you think that an algorithm
> is much more stupid than we are?
> 
No, but the programmer may be so stupid to deny that that the simulation 
failed when it did not reach the halt state. That there is a halt state 
is proven by the direct execution, by the simulation with HHH1 and by 
the knowledge that H is programmed to abort and halt after N instructions.