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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: H(D,D) cannot even be asked about the behavior of D(D)
Date: Fri, 14 Jun 2024 12:39:15 -0500
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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:
> 
>>>> 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.

If we used that definition of decider then no human ever decided
anything because every human has made at least one mistake.

I use the term "termination analyzer" as a close fit. The term
partial halt decider is more accurate yet confuses most people.
A partial halt decider is a halt decider with a limited domain.

> 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.

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.

>> 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.
>
It can't be asked in any way what-so-ever because it is
already being asked a different question.

>>>> 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).

>> 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.

>> 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 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.
>

You don't even have a slight clue about termination analyzers.

>>>>> 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 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

>>> 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.
>

Likewise the Liar Paradox *should* be true or false,
except for the fact that it isn't.


>>> 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).
>

H cannot be asked the right question.

>>>>> 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.
> 

The fixed question that H is asked is:
Can your input terminate normally?
The answer to that question is: NO.

>>>> 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.
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