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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: Fri, 24 May 2024 11:58:02 +0300
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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.

-- 
Mikko