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

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