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From: joes <noreply@example.com>
Newsgroups: comp.theory
Subject: Re: H(D,D) cannot even be asked about the behavior of D(D)
Date: Sat, 15 Jun 2024 11:34:39 -0000 (UTC)
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Am Fri, 14 Jun 2024 12:39:15 -0500 schrieb olcott:
> On 6/14/2024 10:54 AM, joes wrote:
>> 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:

>>> 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).
What is H1 asked?
>> H is asked whether its input halts, and by definition should give the
>> (right) answer for every input.
> If we used that definition of decider then no human ever decided
> anything because every human has made at least one mistake.
Yes. Humans are not machines.
> I use the term "termination analyzer" as a close fit. The term partial
> halt decider is more accurate yet confuses most people.
I have not seen you use that term before. You have not called it partial.
That was confusing.

>> 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.
> Parroting what you memorized by rote is not very deep understanding.
This was my own phrasing. Can you explain the halting problem proof?
> Understanding that the halting problem counter-example input that does
> the opposite of whatever value the halt decider returns is merely the
> Liar Paradox in disguise is a much deeper understanding.
I know that.

>>> H(D,D) is not even being asked about the behavior of D(D)
>> It can't be asked any other way.
> It can't be asked in any way what-so-ever because it is already being
> asked a different question.
Is that question "Do you answer yes?"?

>>>>> 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.
> No the textbooks have it incorrectly.


>>> 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).
> No H (with a pathological relationship to D) can possibly see the
> behavior of D(D).
That is not a problem with D, but with H not being total.

>>> 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.
> The input DOES NOT SPECIFY THE BEHAVIOR OF D(D).
> The input specifies the behavior WITHIN THE PATHOLOGICAL RELATIONSHIP It
> does not specify the behavior WITHOUT THE PATHOLOGICAL RELATIONSHIP.
There is no difference. If an H exists, it gives one answer. D then does
the opposite. H cannot change its answer. Other analysers can see that
H gives the wrong answer.

>>> 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.
> H cannot simulate D(D) for the same reason that int sum(int x, int y) {
> return x + y; } sum(3,4) cannot return the sum of 5 + 6;

>>>> And note, it only gives definitive 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.
> You don't even have a slight clue about termination analyzers.
Why do you say that? A (partial) termination analyser doesn't disprove
the halting problem.

>>>>> 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 ridiculously stupid to think that the pathological relationship
> between H and D cannot possibly change the behavior of D especially when
> it has been conclusively proven that it DOES CHANGE THE BEHAVIOR OF D
D as a machine is completely specified and a valid Turing machine:
It asks a supposed decider if it halts, and then does the opposite,
making the decider wrong.
Other deciders than the one it calls can simulate or decide it.
D has exactly one fixed behaviour, like all TMs.
The behaviour of H should change because of the recursion, but it has to
make up its mind. D goes "I'm gonna do the opposite of what you said".

>>> 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.
That would be the wrong question.
>> D(D) is a valid input. H should be universal.
> Likewise the Liar Paradox *should* be true or false,
> except for the fact that it isn't.

>>> 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).
> H cannot be asked the right question.
Then H would be faulty.

>>>>> You can not simply 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.
> The fixed question that H is asked is:
> Can your input terminate normally?
Does the input terminate, rather.
> The answer to that question is: NO.
If that were so, this would be given to D, since it asks H about itself.
In this case, it would actually terminate. If H said Yes, it would go
into an infinite loop.

>>>>> 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.
> How crazy is it to expect a correct answer to a different question than
> the one you asked?

>>>> 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?
There are undecidable problems. Like halting.

>>>> 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 is 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?
> There are several different issues the key one of these issues [...]
> is that there is something wrong with it along the lines of it being
> isomorphic to the Liar Paradox.
"Something along the lines"? Can you point to the step where you disagree?

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