Re: Every D(D) simulated by H presents non-halting behavior to H ###

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