On 7/4/23 12:35 AM, olcott wrote:
> On 7/3/2023 11:06 PM, Richard Damon wrote:
>> On 7/3/23 11:47 PM, olcott wrote:
>>> On 7/3/2023 10:22 PM, Richard Damon wrote:
>>>> On 7/3/23 9:51 PM, olcott wrote:
>>>>> On 7/3/2023 4:55 PM, Richard Damon wrote:
>>>>>> On 7/3/23 5:40 PM, olcott wrote:
>>>>>>> On 7/3/2023 4:34 PM, Richard Damon wrote:
>>>>>>>> On 7/3/23 5:30 PM, olcott wrote:
>>>>>>>>> On 7/3/2023 4:07 PM, Richard Damon wrote:
>>>>>>>>>> On 7/3/23 4:08 PM, olcott wrote:
>>>>>>>>>>> On 7/3/2023 2:58 PM, Richard Damon wrote:
>>>>>>>>>>>> On 7/3/23 2:56 PM, olcott wrote:
>>>>>>>>>>>>> On 7/3/2023 1:25 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 7/3/23 2:03 PM, olcott wrote:
>>>>>>>>>>>>>>> On 7/3/2023 11:26 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 7/3/23 12:05 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 7/3/2023 10:58 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 7/3/23 11:44 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 7/3/2023 10:35 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 7/3/23 10:42 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 7/3/2023 8:13 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 7/2/23 11:10 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Only when I show you are wrong. Actually try to
>>>>>>>>>>>>>>>>>>>>>> answer my objections
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> What about a three valued decider?
>>>>>>>>>>>>>>>>>>>>> 0=undecidable
>>>>>>>>>>>>>>>>>>>>> 1=halting
>>>>>>>>>>>>>>>>>>>>> 2=not halting
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Doesn't meet the definition of a Halt Decider.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Because these are semantic properties based on the
>>>>>>>>>>>>>>>>>>> behavior of
>>>>>>>>>>>>>>>>>>> the input it does refute Rice.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Nope. Rice's theorem doesn't allow for an
>>>>>>>>>>>>>>>>>> 'undecidable' output state either.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Either the input is or is not something that is in the
>>>>>>>>>>>>>>>>>> set defined by the function/language defined.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Undecidable is just admitting that Rice is true.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Undecidable <is> a semantic property.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Source of that Claim?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> And you aren't saying the Undecidable <IS> a semantic
>>>>>>>>>>>>>>>> property, but is an answer for if an input <HAS> some
>>>>>>>>>>>>>>>> specific semantic property.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In computability theory, Rice's theorem states that all
>>>>>>>>>>>>>>> non-trivial
>>>>>>>>>>>>>>> semantic properties of programs are undecidable. A
>>>>>>>>>>>>>>> semantic property is
>>>>>>>>>>>>>>> one about the program's behavior
>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Rice%27s_theorem
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Undecidable <is> a semantic property of the finite string
>>>>>>>>>>>>>>> pair: {H,D}.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> As I mentioned, many simple descriptions get it wrong.
>>>>>>>>>>>>>> Note, later in the same page it says:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It is important to note that Rice's theorem does not
>>>>>>>>>>>>>> concern the properties of machines or programs; it
>>>>>>>>>>>>>> concerns properties of functions and languages.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> H correctly accepts every language specified by the pair:
>>>>>>>>>>>>> {H, *}
>>>>>>>>>>>>> (where the first element is the machine description of H
>>>>>>>>>>>>> and the
>>>>>>>>>>>>> second element is any other machine description) or rejects
>>>>>>>>>>>>> this
>>>>>>>>>>>>> pair as undecidable.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> So, you are admitting you don't understand what you are saying.
>>>>>>>>>>>>
>>>>>>>>>>>> D isn't "undecidable" but always has definite behavior based
>>>>>>>>>>>> on the behavior of the definite machine H that it was based
>>>>>>>>>>>> on (and thus you are being INTENTIONALLY dupicious by now
>>>>>>>>>>>> calling H to be a some sort of other decider).
>>>>>>>>>>>>
>>>>>>>>>>>> Since you claim that Halt-Decider-H "Correctly" returned
>>>>>>>>>>>> false for H(D,D) we know that D(D) Halts, so D the problem
>>>>>>>>>>>> of D has an answer so hard to call "undecidable"
>>>>>>>>>>>>
>>>>>>>>>>>> Again, what is the definition of your "Language", and why do
>>>>>>>>>>>> you call {H,D} as UNDECIDABLE, since H will be a FIXED
>>>>>>>>>>>> DEFINED decider that is just WRONG about its input, that
>>>>>>>>>>>> isn't "undecidable".
>>>>>>>>>>>
>>>>>>>>>>> {H,D} undecidable means that D is undecidable for H, which is an
>>>>>>>>>>> verified fact. The set of {H,*} finite string pairs do define a
>>>>>>>>>>> language.  Decidability <is> a semantic property because it
>>>>>>>>>>> can only be correctly decided on the basis of behavior.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> What do you mean by "Undecidable by H?"
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> H correctly determines that it cannot provide a halt status
>>>>>>>>> consistent with the behavior of the directly executed D(D).
>>>>>>>>
>>>>>>>> So? If it REALLY could detect that, it just needs to give the
>>>>>>>> opposite answer.
>>>>>>>>
>>>>>>>> Or, in other words, you are just admitting that H is wrong.
>>>>>>>
>>>>>>> Try and show how D could do that.
>>>>>>> D can loop if H says it will halt.
>>>>>>> D can halt when H says it will loop.
>>>>>>>
>>>>>>> How does D make itself decidable by H to contradict
>>>>>>> H determining that it is undecidable?
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> It doesn't need to, and the fact you are asking the question jkust
>>>>>> shows you don't understand what you are talking about.
>>>>>>
>>>>>> You clearly don't understnad what "Decidability" means.
>>>>>>
>>>>>
>>>>>
>>>>> *Computable set*
>>>>> In computability theory, a set of natural numbers is called
>>>>> computable,
>>>>> recursive, or decidable if there is an algorithm which takes a
>>>>> number as
>>>>> input, terminates after a finite amount of time (possibly depending on
>>>>> the given number) and correctly decides whether the number belongs to
>>>>> the set or not. https://en.wikipedia.org/wiki/Computable_set
>>>>>
>>>>> Because A finite string can be construed as a very large integer the
>>>>> above must equally apply to finite strings. That you are trying to
>>>>> get away with disavowing this doesn't seem quite right. Since you only
>>>>> have an EE degree we could chalk this up to ignorance.
>>>>>
>>>>> It does seem that you acknowledge that there is no way to make
>>>>> decidability undecidable.
>>>>>
>>>>>
>>>>
>>>> Except that "Decidability" isn't a property of an "input"/Machine,
>>>> but of a PROBLEM, or one of the sets you are talking about. (not
>>>> MEMBERS of the set, which are the machines, but the set as a whole)>
>>>>
>>>> So, you are confusing a property of the SET with a property of the
>>>> members.
>>>>
>>>> Decidability is about the ability for there to exist a machine that
>>>> can decide if its input is a member of the set. If there exist such
>>>> a machine, then the SET is computable/decidable. If not, the SET
>>>> isn't computable/decidable.
>>>>
>>>
>>> Since I just quoted that to you it is reasonable that you accept it.
>>
>> Nope, Decidability is a property of PROBLEMS or SETS, not INPUTS.
>>
>> You can't seem to tell the diffence bcause of your ignorance.
>>
>>>
>>>> Nothing he talks about the possible members themselves being in the
>>>> set or not being a property like "decidable", it just isn't a
>>>> property of the members.
>>>>
>>>
>>> Using Rogers' characterization of acceptable programming systems, Rice's
>>> theorem may essentially be generalized from Turing machines to most
>>> computer programming languages: there exists no automatic method that
>>> decides with generality non-trivial questions on the behavior of
>>> computer programs. https://en.wikipedia.org/wiki/Rice%27s_theorem
>>
>> Yes, it doesn't need to be about Turning Machines, but it is still
>> about the ability to create a "program" to compute a Function /
>> Decider for a Language/Set.
>>
>>>
>>> H correctly determines whether or not it can correctly determine the
>>> halting status for all of the members of the set of conventional halting
>>> problem proof counter-examples and an infinite set of other elements.
>>
>> But that isn't a proper property.
>>
>> You don't have "Decidability" on individual inputs, so it isn't a
>> Property of the input that can be decided on.
>
> H divides inputs into halting decidable and halting undecidable.

Which means?

After all, *ALL* inputs have a definite halting state, so there is a
correct answer to them, so there always exists a decider that will get
the right answer.

It seems by your attempt at a definition, a "Decider" that just decides
all machines are non-ha;ting would have all halting machines defined as
undecidable.

>
>>>
>>> H is deciding the semantic property of its own behavior on a set of
>>> finite strings. The above says this can be done in C.
>>
>> Nope, just shows you don't understand a thing about what you are saying.
>
> Any idiot can say that. Provide both reasoning and sources.

>
>>>
>>>> Your question is like asking if 2 is Purple.
>>>
>>> Mere empty rhetoric utterly bereft of any supporting reasoning.
>>>
>>>
>>
>> Nope, since "Decidability" isn't a property of a given input, trying
>> to ask if a given input is Decidable is a simple category error.
>>
>
>    Decidability is about the ability for there to exist a machine
>    that can decide if its input is a member of the set.
>
> H decides an infinite set of elements that are halting decidable for H
> and another set that are halting undecidable for H.

Again, "Halting Decidable" is an improper term, as ALL machines are
"Decidable" to halt by some machine. So there does exist a machine that
will give the right answer. It is sometimes a different machine for
different inputs.

Read that definition again, and perhaps find a better source, as
decidability is the ability for there to exist a machine that can
decider FOR ANY INPUT, if that input is a member of the set.

There ALWAYS exist a machine that will correctly indicate if a SPECIFIC
input is a member of the set. Trivially, it can be one of two possible
machines, Machine 1 always answers YES, Machine 2 always answers no. One
of those machines is right. The key point is that you need to determine
the answer for ALL inputs, thus it isn't a property of one of the
inputs, but of the SET.

As it is a property of the SET and not an input, there can't be
'decider' to determine if an 'input' has that property, since inputs
don't have that property, the set they are being tested for does.

>
>> Your inability to understand that just highlights how ignorant you are
>> of the whole field.
>
> I suspect that you might not have more than bluster and a penchant for
> rebuttal.
>

Really, I guess that is just you projecting, because you describe
yourself to the tee.