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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: Sun, 11 Aug 2024 21:54:35 +0200
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Op 11.aug.2024 om 13:45 schreef olcott:
> 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.

Since no DDD is correctly simulated by HHH, we are talking about the 
properties of an empty set.
But, indeed, the simulation of DDD by HHH fails to reach the halt state. 
It aborts one cycle before the simulated HHH would reach its 'return' 
instruction, after which DDD would reach its halt state.

> 
> My words must be understandable by ordinary C programmers
> and computer scientists. The latter tend to conclude that
> my work is incorrect as soon as they know the subject matter
> before actually seeing what I said.
> 
Every C programmer understands that a simulation fails if it does not 
reach the end of a halting program.
Your own words are that HHH halts (that is why it aborts: it must halt). 
The direct execution of HHH halts. The simulation by another simulator 
(e.g. HHH1) halts. The trace shows that HHH halts. A lot of evidence 
that HHH halts.
Only HHH as a simulator fails to reach the end of the simulated HHH, 
which makes clear that it is not a property of HHH, or DDD, but a 
failure of this simulator.
HHH cannot possibly simulate itself correctly up to the end.

When HHH aborts after 100 cycles, the simulated HHH has done only 99 cycles.
We can try to abort one cycle earlier, after 99 cycles, so that the path 
for the simulation to the end is shorter, but then the simulator also 
aborts earlier, when the simulated HHH has done only 98 cycles, again 
one cycle too soon.
It is impossible to make the path short enough, because the simulation 
always aborts one cycle before the end of the simulated HHH.