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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: Sat, 25 May 2024 11:14:12 +0300
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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.

-- 
Mikko