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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H ###
Date: Wed, 22 May 2024 19:01:52 -0400
Organization: i2pn2 (i2pn.org)
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On 5/22/24 10:51 AM, olcott wrote:
> 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.

But you DID say that incorrect answers were ok, because you said that 
H(D,D) is corret to say that the machine represented by its input (whihc 
is D(D) ) even though D(D) halts.

My argument was about a "just as correct" decider, not a correct 
decider, which doesn't exist.

> 
> 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.

Which means NOTHING about the Halting status of ANY of the N Ds that 
were simulated.

> 
>>> 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.

Nope, unless you mean that all your H have aborted their simulation of 
the input before an ACTUALLY COMPLETE AND CORRECT simulation of the 
input would reach an end.

> 
>>> For the H/D pair we can simulate 1 to N instructions of D that
>>> results in 0 to M recursive simulations of H simulating itself
>>> simulating D.
>>
>> But is this kind of recursive simulation "correc"? Does "correct"
>> apply to ("correctly" or otherwise) simulated simulations? Does
>> correctness of simulation of simulation depend on the oorrectness
>> of simulated simulation?
>>
> 
> typedef int (*ptr)();  // ptr is pointer to int function in C
> 00       int H(ptr p, ptr i);
> 01       int D(ptr p)
> 02       {
> 03         int Halt_Status = H(p, p);
> 04         if (Halt_Status)
> 05           HERE: goto HERE;
> 06         return Halt_Status;
> 07       }
> 08
> 09       int main()
> 10       {
> 11         H(D,D);
> 12         return 0;
> 13       }
> 
> When talking about an infinite set of H/D pairs...
> 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.
> 
> For terminating inputs the input is simulated until termination.
> 
> This applies to every H/D pair of the infinite set of H/D pairs
> matching the above template:
> 
> Every D correctly simulated by pure by function H remains stuck in
> recursive simulation and can never reach its own line 06 and halt.
> 

Nope. It may not be able to be SIMULATED by the H, but the D can reach 
that state when it is run, or correctly and completely simulated by a 
simulator that doesn't halt (and D still calls the H that you used on it).


Since your "Topic" says "Non-Halting" we need to make that point clear.

Your Hs absolutely do NOT show non-halting behavior, because there 
criteria measure is just incorrect.