XPost: comp.theory, comp.software-eng, sci.math.symbolic

On 8/30/2021 5:00 PM, André G. Isaak wrote:

On 2021-08-30 11:15, olcott wrote:

On 8/30/2021 11:25 AM, André G. Isaak wrote:

On 2021-08-30 08:35, olcott wrote:

My point is fully proven on the basis of two other points:
(1) Verified as true entirely on the basis of the meaning of its words: >>>

Claiming that something is 'verified as true entirely on the basis of
the meaning of its words' isn't a valid substitute for a proof.

That all cats are animals and all animals are living things is a
perfectly sound deductive proof that all cats are living things.

Yes, that's a valid proof. It also contains identifiable premises and a conclusion which can be linked to those premises by accepted rules of
logic. It doesn't just say 'verified on the basis of the meaning of the words' which is *not* a valid proof.

We only know that a cat is an animal and that an animal is a living
thing on the basis of the meaning of those words. We don't know this by
any other means.

That you fail to comprehend that proofs can be entirely based on the
meaning of words is merely your error based on an incorrectly narrow
minded focus.

A simulating halt decider correctly decides that any input that
never halts unless the simulating halt decider aborts its simulation
of this input is an input that never halts.

(2) It can be verified that the input to H(P,P) never halts unless H
aborts it. This is verified on the basis that the execution trace of
P meets this criteria:

where H = X() and P = Y()

Infinite recursion detection criteria:
If the execution trace of function X() called by function Y() shows:
(a) Function X() is called twice in sequence from the same machine
address of Y().
(b) With the same parameters to X().
(c) With no conditional branch or indexed jump instructions in Y().
(d) With no function call returns from X().
then the function call from Y() to X() is infinitely recursive.

First off, you simply state the above criteria without actually
offering any *proof* that these criteria actually work.

They above criteria have been extensively reviewed and critiqued,
none-the-less for the point at hand it is quite obvious to every
honest person that has a sufficient understanding of x86 assembly
language that the simulation of P on input P by H never halts while H
is in pure simulation mode.

They have been critiqued, but they haven't been *accepted*. Again, you
need to provide a proof that these criteria are valid. You can't just
state them.

The criteria are self-evidently true.

And second, even if these criteria are valid, your trace *doesn't*
actually meet these criteria because you deliberately omit portions
of the code from your trace (i.e. everything that happens starting at
address 966).

This is explained on pages 3-4 of my updated paper. That people
continue to ignore sound reasoning is no actual rebuttal at all.

People don't merely ignore it. They actively reject it on the grounds
that it is not valid reasoning.

The actively reject on the presumption that it seems to be invalid
reasoning to them when they make sure not follow the details that prove
it is valid.

https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation

The claim that 'it can be verified that the input to H(P, P) never
halts unless H aborts it.' Is not verified at all, since it can
easily shown to be false by simply observing the fact that P(P) does,
in fact, halt.

Yet again you twist my words. This is the straw-man error. See pages
3-4 of my paper.

You try to get around this by claiming that when you call H(P, P) the
input magically changes to some *other* computation which isn't
equivalent to P(P) and that this *other* computation is non-halting,
but even if such a claim made sense, it means your H is answering
about the *wrong* computation.

int main() { P(P); } will not be discussed on this thread.
I will no longer tolerate dishonest dodges away from the the point.

int main() { P(P); } is *precisely* the computation which H(P, P) is
supposed to be evaluating.

int main() { P(P); } will not be discussed on this thread.
int main() { P(P); } will not be discussed on this thread.
int main() { P(P); } will not be discussed on this thread.
int main() { P(P); } will not be discussed on this thread.

Refusing to discuss this is like refusing to discuss the results of 2 +
2 = 4 when trying to justify that sum(2, 2) == 5.

H(P,P)==0 is correct is a necessary consequence of its two premises.
H(P,P)==0 is correct is a necessary consequence of its two premises.
H(P,P)==0 is correct is a necessary consequence of its two premises.
H(P,P)==0 is correct is a necessary consequence of its two premises.

Anything outside of this necessary consequence is a dishonest dodge.

Failure to pay enough attention to understand that this is a necessary consequence is a dishonest dodge.

And from your recent posts in a different thread, it appears you are
also claiming that it is not possible to even ask your H about the
real P(P), which is the case we're really concerned about.

int main() { P(P); } will not be discussed on this thread.
I will no longer tolerate dishonest dodges away from the the point.

int main() { P(P); } is what corresponds to Linz's H_Hat(H_Hat).

More precisely:

Ĥ.q0 ⟨Ĥ1⟩ ⊢* Ĥ.qx ⟨Ĥ1⟩ ⟨Ĥ2⟩ ⊢* Ĥ.qy ∞
if the simulated ⟨Ĥ1⟩ applied to ⟨Ĥ2⟩ halts, and

Ĥ.q0 ⟨Ĥ1⟩ ⊢* Ĥ.qx ⟨Ĥ1⟩ ⟨Ĥ2⟩ ⊢* Ĥ.qn
if the simulated ⟨Ĥ1⟩ applied to ⟨Ĥ2⟩ does not halt

Ĥ applied to ⟨Ĥ⟩ is
exactly analogous to int main() { P((u32)P); }

Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ is exactly analogous to
H(P,P) called from main() { P((u32)P); }

Ĥ applied to ⟨Ĥ⟩ is a different computation than
Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ because the latter is under the dominion of a
simulating halt decider

int main() { P((u32)P); } is a different computation than
H(P,P) because the latter is under the dominion of a simulating halt decider

This, according to you, is the *only* case you care about since if your
H can solve it you think it would refute Linz.

If P(P) magically represents some 'different' computation when it is
given as an input to H(P, P) then (putting aside the fact that this illustrates you don't understand what a computation is) it means that
H(P, P) is evaluating the *wrong* computation.

And the fact that you claim P(P) represents some 'different' computation
when it is given as an input to your simulating halt decider, this
rather clearly shows that the simulating portion of your decider is
*broken*. If it simulates P(P), it must behave as P(P) behaves, not as
some 'other' computation.

You can't simply ignore the elephant in the room, which is the behaviour
of main() { P(P); }.

If you think bring this up is a 'dodge', then it means you clearly don't understand what the halting problem is. At all.

A halt decider is a program which takes as its argument some other
program and the input to that program (whether it be a C program, a TM,
or whatever) and determines whether that program halts.

H(P, P) *needs* to determine whether the independent program P(P) (i.e
main() { P(P); } halts. If it instead answers about what happens when
P(P) is simulated by your H in a way that somehow changes the nature of
the computation, then it is not answering the the question a halt
decider is, by definition, supposed to answer.

If it simply reports on the behaviour of P(P) inside a broken simulator,
why would that result be of interest to *anyone*. It's a "computation"
which only exists inside some specific piece of software.

void Infinite_Loop()
{
HERE: goto HERE;
}

int main()
{
Output("Input_Halts = ", H0((u32)Infinite_Loop));
Infinite_Loop();
}

The simplest way to see that a computation under the dominion of a
simulating halt decider can be entirely different than direct execution
is that line 1 of main halts and line 2 of main never halts.

If your H can't even be asked about the real P(P), then it isn't even
answering the question a halt decider is supposed to answer. So
what's the point of your H?

André

The only thing that will be discussed on this thread is the
[Airtight proof that H(P,P)==0 is correct] on the basis that (1) and
(2) are true. Everything else will be construed as a dishonest dodge.

You can't dictate what other people discuss. You want to ignore the
elephant in the room. You can't reasonably expect others to go along
with your delusion and pretend it isn't there. It is. It needs to be discussed.

I will not tolerate dishonest dodges. I will only discuss that
H(P,P)==0 is correct is a necessary consequence of its two premises.

If H(P,P)==0 is a necessary consequence of its two premises and its two premises are true then it necessarily makes no difference what
int main() { P(P); } does. That you cannot understand this proves the deficiency of your reasoning.

If H(P,P)==0 is a necessary consequence of its two premises and its two premises are true then it necessarily makes no difference what
int main() { P(P); } does. That you cannot understand this proves the deficiency of your reasoning.

If H(P,P)==0 is a necessary consequence of its two premises and its two premises are true then it necessarily makes no difference what
int main() { P(P); } does. That you cannot understand this proves the deficiency of your reasoning.

If H(P,P)==0 is a necessary consequence of its two premises and its two premises are true then it necessarily makes no difference what
int main() { P(P); } does. That you cannot understand this proves the deficiency of your reasoning.

If H(P,P)==0 is a necessary consequence of its two premises and its two premises are true then it necessarily makes no difference what
int main() { P(P); } does. That you cannot understand this proves the deficiency of your reasoning.

André

(1) Verified as true entirely on the basis of the meaning of its words:
A simulating halt decider correctly decides that any input that never
halts unless the simulating halt decider aborts its simulation of this
input is an input that never halts.

(2) It can be verified that the input to H(P,P) never halts unless H
aborts it. This is verified on the basis that the execution trace of P
meets this criteria:

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

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