Re: H(D,D) cannot even be asked about the behavior of D(D)

Am Fri, 14 Jun 2024 08:15:52 -0500 schrieb olcott:

On 6/14/2024 6:39 AM, Richard Damon wrote:

On 6/14/24 12:13 AM, olcott wrote:

On 6/13/2024 10:44 PM, Richard Damon wrote:

On 6/13/24 11:14 PM, olcott wrote:

On 6/13/2024 10:04 PM, Richard Damon wrote:

On 6/13/24 9:39 PM, olcott wrote:

On 6/13/2024 8:24 PM, Richard Damon wrote:

On 6/13/24 11:32 AM, olcott wrote:

H cannot even be asked the question: Does D(D) halt?

No, you just don't understand the proper meaning of "ask" when applied
to a deterministic entity.

When H and D have a pathological relationship to each other then H(D,D)
is not being asked about the behavior of D(D). H1(D,D) has no such
pathological relationship thus D correctly simulated by H1 is the
behavior of D(D).

H is asked whether its input halts, and by definition should give the
(right) answer for every input.
D by construction is pathological to the supposed decider it is
constructed on. H1 can not decide D1. For every "decider" we can construct
an undecidable pathological program. No decider decides every input.

Can a correct answer to the stated question be a correct answer to the
unstated question?
H(D,D) is not even being asked about the behavior of D(D)

It can't be asked any other way.

When H is a simulating halt decider you can't even ask it about the
behavior of D(D). You already said that it cannot map its input to the
behavior of D(D). That means that you cannot ask H(D,D) about the
behavior of D(D).

OF course you can, becaue, BY DEFINITION, that is the ONLY thing it
does with its inputs.

That definition might be in textbooks,
yet H does not and cannot read textbooks.

That is very confusing. H still adheres to textbooks.

The only definition that H sees is the combination of its algorithm with
the finite string of machine language of its input.

H does not see its own algorithm, it only follows its internal
programming. A machine and input completely determine the behaviour,
whether that is D(D) or H(D, D).

It is impossible to encode any algorithm such that H and D have a
pathological relationship and have H even see the behavior of D(D).

H literally gets it as input.

You already admitted there there is no mapping from the finite string of
machine code of the input to H(D,D) to the behavior of D(D).

Which means that H can't simulate D(D). Other machines can do so.

And note, it only gives difinitive answers for SOME input.

It is my understanding is that it does this much better than anyone else
does. AProVE "symbolically executes the LLVM program".

Better doesn't cut it. H should work for ALL programs, especially for D.

H is just a "mechanical" computation. It is a rote algorithm that
does what it has been told to do.

H cannot be asked the question Does D(D) halt?
There is no way to encode that. You already admitted this when you
said the finite string input to H(D,D)
cannot be mapped to the behavior of D(D).

H answers that question for every other input.
The question "What is your answer/Is your answer right?" is pointless
and not even computed by H.

It is every time it is given an input, at least if H is a halt decider.

If you cannot even ask H the question that you want answered then this
is not an actual case of undecidability. H does correctly answer the
actual question that it was actually asked.

D(D) is a valid input. H should be universal.

That is what halt deciders (if they exist) do.

When H and D are defined to have a pathological relationship then H
cannot even be asked about the behavior of D(D).

H cannot give a correct ANSWER about D(D).

It really seems likem you just don't understand the concept of
deterministic automata, and Willful beings as being different.

You can not simply correctly wave your hands to get H to know what
question is being asked.

H doesn't need to know. It is programmed to answer a fixed question,
and the input completely determines the answer.

It can't even be asked. You said that yourself.
The input to H(D,D) cannot be transformed into the behavior of D(D).

It can, just not by H.

No, we can't make an arbitrary problem solver, since we can show there
are unsolvable problems.

That is a whole other different issue.
The key subset of this is that the notion of undecidability is a ruse.

A ruse for what?

Nothing says we can't encode the Halting Question into an input.

If there is no mapping from the input to H(D,D) to the behavior of D(D)
then H cannot possibly be asked about behavior that it cannot possibly
see.

It can be asked and be wrong.

What can't be done it create a program that gives the right answer for
all such inputs.

Expecting a correct answer to the wrong question is only foolishness.

The question is just whether D(D) halts.

Where do you disagree with the halting problem proof?

--
joes