On 2021-11-05 13:32, olcott wrote:
On 11/5/2021 2:16 PM, André G. Isaak wrote:
On 2021-11-04 19:51, olcott wrote:
We have to stay focused on the one single point that I perfectly and
totally proved that H did act as a pure simulator of the 14 steps of
P before we can move on to any other point.
As far as I can tell you are more interested in *avoiding* critical
points. The crucial points are:
(1) P(P) halts when run as an independent computation.
(2) Your H(P, P) claims that P(P) does *not* halt.
What you are saying is that if the correct pure simulation of the
input to H(P,P) never halts it still halts anyway. AKA a black cat is
sometimes not a cat at all.
I'm not talking about what happens inside your simulation. I'm talking
about the *actual* computation P(P) which you yourself have acknowledged halts.
That's the computation H(P, P) is supposed to be answering about.
Go back and reread the definition of Halt Decider. A halt decider takes
a description of a computation, but the answer it gives describes the *actual* computation described, not the 'behaviour of the input" (which
is meaningless gibberish) or what goes on inside some simulating halt decider.
P(P) halts. Ergo a halt decider must decide that it halts.
It is a verified fact that the correct pure simulation of the input to
H(P,P) never halts therefore nothing in the universe can possibly
contradict this.
It is *not* a verified fact. It is simply an assertion on your part.
The
fact that P(P) halts and your simulation allegedly does not demonstrates
that your simulation is not a pure, faithful simulation.
Note that a trace merely shows *what* some program did. It does not
provide evidence for the correctness of that program. So you're never
going to convince anyone that your H is giving the correct answer simply
by providing traces. Its a waste of electrons.
The way to show that a program gives the correct answer is to compare
the answer it gives to the ACTUAL answer as defined by the problem which
the program is supposed to be solving.
André
On 2021-11-05 14:51, olcott wrote:
On 11/5/2021 3:37 PM, André G. Isaak wrote:
On 2021-11-05 13:32, olcott wrote:
On 11/5/2021 2:16 PM, André G. Isaak wrote:
On 2021-11-04 19:51, olcott wrote:
We have to stay focused on the one single point that I perfectly
and totally proved that H did act as a pure simulator of the 14
steps of P before we can move on to any other point.
As far as I can tell you are more interested in *avoiding* critical
points. The crucial points are:
(1) P(P) halts when run as an independent computation.
(2) Your H(P, P) claims that P(P) does *not* halt.
What you are saying is that if the correct pure simulation of the
input to H(P,P) never halts it still halts anyway. AKA a black cat
is sometimes not a cat at all.
I'm not talking about what happens inside your simulation. I'm
talking about the *actual* computation P(P) which you yourself have
acknowledged halts.
Ah so you fundamentally disagree with the concept of a UTM.
You don't *have* a UTM. You have a C program.
And even if you were working with actual Turing Machines, you wouldn't
have a UTM, you'd have a 'simulating halt decider'.
That's the computation H(P, P) is supposed to be answering about.
Go back and reread the definition of Halt Decider. A halt decider
takes a description of a computation, but the answer it gives
describes the *actual* computation described, not the 'behaviour of
the input" (which is meaningless gibberish) or what goes on inside
some simulating halt decider.
P(P) halts. Ergo a halt decider must decide that it halts.
P(P) halts and the pure simulation of the input to H1(P,P) halts
Which takes us back to the question which you keep ignoring. You claimed
that "an infinite number of different simulating halt deciders must have exactly the same behavior while they are doing a pure simulation of
their input. "
So why do H and H1 have *different* behaviours? They can't both be pure simulations and have different behaviours.
and the pure simulation of the input to H(P,P) never halts
conclusively proving that it is not computationally equivalent to the
above two.
What is not computationally equivalent to what?
Any halt decider which takes a description of P(P) as its input is
answering about P(P). Ergo the behaviour of P(P) is all that matters in determining whether a given halting decision is correct.
If your 'pure simulation' is not "computationally equivalent" to this
then you are not answering about the right computation (and your
simulator isn't a pure simulator).
It is a verified fact that the correct pure simulation of the input
to H(P,P) never halts therefore nothing in the universe can possibly
contradict this.
It is *not* a verified fact. It is simply an assertion on your part.
That the 14 lines shown below conclusively prove that H does perform a
pure simulation of its input in H(P,P) is no more a mere assertion
than the assertion that the decimal integer 5 is numerically greater
than the decimal integer 3 AND YOU KNOW IT !!!
As I said before, traces DO NOT PROVE ANYTHING. Have you ever actually
looked at a proof of correctness for a computer program? They don't
involve traces. Traces are used for debugging, not for proofs. And on
the rare occasions when people actually do look at traces they do so in
a debugging environment where one can inspect the contents of variables
and memory locations. A printout of a trace is WORTHLESS.
André
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