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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: Tue, 13 Aug 2024 14:08:24 +0300
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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.

-- 
Mikko