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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: HHH maps its input to the behavior specified by it --- never reaches its halt state ---natural number mapping
Date: Wed, 14 Aug 2024 10:41:03 +0300
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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.

-- 
Mikko