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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H ###
Date: Mon, 27 May 2024 11:11:40 +0300
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On 2024-05-26 16:50:21 +0000, olcott said:

> On 5/26/2024 11:19 AM, Mikko wrote:
>> On 2024-05-26 13:32:08 +0000, olcott said:
>> 
>>> On 5/26/2024 3:57 AM, Mikko wrote:
>>>> On 2024-05-25 12:09:18 +0000, olcott said:
>>>> 
>>>>> On 5/25/2024 3:14 AM, Mikko wrote:
>>>>>> On 2024-05-24 17:13:05 +0000, olcott said:
>>>>>> 
>>>>>>> On 5/24/2024 3:58 AM, Mikko wrote:
>>>>>>>> On 2024-05-23 13:18:02 +0000, olcott said:
>>>>>>>> 
>>>>>>>>> On 5/23/2024 5:06 AM, Mikko wrote:
>>>>>>>>>> On 2024-05-22 14:51:50 +0000, olcott said:
>>>>>>>>>> 
>>>>>>>>>>> On 5/22/2024 2:39 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-05-21 13:54:09 +0000, olcott said:
>>>>>>>>>>>>> You are asking for the definition of correct simulation
>>>>>>>>>>>>> that I have been providing for quite a while recently.
>>>>>>>>>>>> 
>>>>>>>>>>>> That was not my main intent. I wanted to know why your
>>>>>>>>>>>> statement
>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>> No D simulated correctly by any H of every H/D pair specified
>>>>>>>>>>>>>>>>>>> by the above template ever reaches its own line 06 and halts.
>>>>>>>>>>>> 
>>>>>>>>>>>> exludes every unsimulated or incorrectly simulated D?
>>>>>>>>>>> 
>>>>>>>>>>> That sounds like Richard that assumed that incorrect answers are OK
>>>>>>>>>>> unless I specifically say that incorrect answers are not OK.
>>>>>>>>>> 
>>>>>>>>>> Maybe but I don't promise that the response to the incorrect answer
>>>>>>>>>> will sound the same.
>>>>>>>>>> 
>>>>>>>>>>> On 5/19/2024 12:17 PM, Richard Damon wrote:
>>>>>>>>>>>  > On 5/19/24 9:59 AM, olcott wrote:
>>>>>>>>>>>  >> Richard has stated that he thinks that an example of
>>>>>>>>>>>  >> {D never simulated by H} ∈ {every D simulated by H}
>>>>>>>>>>>  >
>>>>>>>>>>>  > No, the H that didn't simulate its input shows that
>>>>>>>>>>>  > *once you allow H to not be required to be correct*,
>>>>>>>>>>>  > that we can then have a trivial function that is
>>>>>>>>>>>  > "just as correct" (since wrong answers were allowed).
>>>>>>>>>>> 
>>>>>>>>>>>>> A c function is correctly simulated when its machine language
>>>>>>>>>>>>> instructions are emulated with an x86 emulator in the order
>>>>>>>>>>>>> that they are specified by the x86 machine language of this
>>>>>>>>>>>>> c function.
>>>>>>>>>>>> 
>>>>>>>>>>>> Does "its machine language instructions" mean all executed instructions
>>>>>>>>>>>> until the progam terminates? Or from the start of the program until
>>>>>>>>>>>> there is no reason to continue? Or from some point to some other point?
>>>>>>>>>>>> 
>>>>>>>>>>> 
>>>>>>>>>>> It means that 1 to N instructions of D are correctly simulated
>>>>>>>>>>> by pure function H. Because D correctly simulated by H remains
>>>>>>>>>>> stuck in recursive simulation D cannot possibly reach is own
>>>>>>>>>>> line 06 and halt.
>>>>>>>>>> 
>>>>>>>>>> If you mean that H cannot simulate D to the line 06 then say so.
>>>>>>>>>> A D that is simulated by H is D and so is a D that is not simulated
>>>>>>>>>> by H so both can do what a D can do. Saying "simulated by H" adds
>>>>>>>>>> nothing.
>>>>>>>>>> 
>>>>>>>>>>>>> For non-terminating functions we can only correctly
>>>>>>>>>>>>> simulate N machine language instructions.
>>>>>>>>>>>> 
>>>>>>>>>>>> But does you definition regard that partial simulation as "correct
>>>>>>>>>>>> simulation"?
>>>>>>>>>>> 
>>>>>>>>>>> When 1 to 2^64 instructions of D are correctly simulated by H
>>>>>>>>>>> it becomes clear that for every H/D pair of the infinite set
>>>>>>>>>>> of H/D pairs D correctly simulated by H remains stuck in recursive
>>>>>>>>>>> simulation.
>>>>>>>>>> 
>>>>>>>>>> If you think that the meaning of "correctly simulate" is not
>>>>>>>>>> important you should not use those words.
>>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> I must use those words or a standard of incorrect simulation
>>>>>>>>> is assumed.
>>>>>>>> 
>>>>>>>> There is no "standard of incorrect simulation".
>>>>>>>> 
>>>>>>>>> We have been going over the term "correct simulation"
>>>>>>>>> in these forums with dozens of people and hundreds of messages
>>>>>>>>> over several years.
>>>>>>>> 
>>>>>>>> That alone is a sufficient reaston to avoid the expression.
>>>>>>>> 
>>>>>>>>> CORRECT SIMULATION DEFINED
>>>>>>>>>    In the above case a simulator is an x86 emulator that correctly
>>>>>>>>>    emulates at least one of the x86 instructions of D in the order
>>>>>>>>>    specified by the x86 instructions of D.
>>>>>>>>> 
>>>>>>>>>    This may include correctly emulating the x86 instructions of H in the
>>>>>>>>>    order specified by the x86 instructions of H thus calling H(D,D) in
>>>>>>>>>    recursive simulation.
>>>>>>>> 
>>>>>>>> That is not a definition but perhaps a suffient substitute for paractical
>>>>>>>> purposes.
>>>>>>>> 
>>>>>>> 
>>>>>>> It provides a clear and correct criterion measure to utterly
>>>>>>> refute each and every reviewer that tries to get away with
>>>>>>> the incorrect emulation of the x86 instructions of H or D or
>>>>>>> emulating them in the wrong order.
>>>>>> 
>>>>>> You may call it a "diagnostic criterion" or just a "criterion" but
>>>>>> it does not define anything. Whether it is clear or sufficient is
>>>>>> another problem.
>>>>>> 
>>>>> 
>>>>> For over two years I had two dozen people unified in consensus
>>>>> continue to insist that a correct simulation of D by H did not
>>>>> require emulating the x86 machine language instructions of D
>>>>> correctly or in the correct order specified by D.
>>>> 
>>>> Is the disagreement about the meaning of "correct" or "simulation"
>>>> or some other word, or is the disagreement about correctness of the
>>>> simulation?
>>>> 
>>> 
>>>     A simulator is an x86 emulator that correctly emulates 1 to N of the
>>>     x86 instructions of D in the order specified by the x86 instructions
>>>     of D. This may include M recursive emulations of H emulating itself
>>>     emulating D.
>>> 
>>> People disagree with the above definition.
>> 
>> Then you may ask what other word would be better instead of "simulator".
>> 
>>> They believe that a correct
>>> simulation requires H to report on the computation that itself is
>>> contained within:
>> 
>> Why should the term "simulation" imply anything about reporting?
>> 
> 
> There you go an actual mistake that I made.
> I will phrase what I mean more accurately.
> 
> Everyone reviewing my work agrees that D correctly simulated by H should
> simulate the behavior of the directly executed  D(D) thus not the actual
> behavior of D correctly simulated by pure function H.

The part after "thus" it not necessary. It merely comments whether H
should do what it does, which it does anyway.

> When we see that D correctly simulated by pure simulator H would remain
> stuck in recursive simulation then we also know that D never reaches its
> own line 06 and halts in less than an infinite number of correctly
> simulated steps.

Which means that H never terminates. You said that by your definition
a function that never terminates is not a pure function. Therefore
H, if it exists, is not a pure function, and the phrase "pure function
H" does not denote.

> This means that D correctly simulated by pure function H also never
> reaches it own line 06 and halts.

Yes, if H never terminates then neither does D.

-- 
Mikko