XPost: comp.theory, sci.math
From: polcott333@gmail.com
On 12/20/2025 4:22 AM, Mikko wrote:
> On 19/12/2025 16:52, olcott wrote:
>> On 12/19/2025 4:09 AM, Mikko wrote:
>>> On 18/12/2025 15:07, olcott wrote:
>>>> On 12/18/2025 5:10 AM, Mikko wrote:
>>>>> On 18/12/2025 06:29, olcott wrote:
>>>>>> On 12/17/2025 4:41 AM, Mikko wrote:
>>>>>>> On 15/12/2025 16:31, olcott wrote:
>>>>>>>> On 12/15/2025 3:20 AM, Mikko wrote:
>>>>>>>>> On 15/12/2025 02:15, olcott wrote:
>>>>>>>>>> On 12/14/2025 4:46 AM, Mikko wrote:
>>>>>>>>>>> On 11/12/2025 16:38, olcott wrote:
>>>>>>>>>>>> On 12/11/2025 2:53 AM, Mikko wrote:
>>>>>>>>>>>>> olcott kirjoitti 10.12.2025 klo 18.27:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> DD() executed from main() calls HHH(DD) thus is
>>>>>>>>>>>>>> not one-and-the-same-thing as an argument to HHH.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If the last sentence is true then this is not the counter
>>>>>>>>>>>>> exmaple
>>>>>>>>>>>>> mentioned in certain proofs of noncomputability of halting and
>>>>>>>>>>>>> therefore not relevant in that context. The halting problem
>>>>>>>>>>>>> reuqires
>>>>>>>>>>>>> that HHH can determine whether the counter example halts.
>>>>>>>>>>>>> That is,
>>>>>>>>>>>>> you must be able to replace "???" in
>>>>>>>>>>>>>
>>>>>>>>>>>>> #include // or your replacement
>>>>>>>>>>>>> int main (void)
>>>>>>>>>>>>> {
>>>>>>>>>>>>> int Halt_Status = HHH(???); // put the correct
>>>>>>>>>>>>> argument here
>>>>>>>>>>>>> printf("HHH says: %s\n", Halt_Status ? "halts" : "does
>>>>>>>>>>>>> not halt");
>>>>>>>>>>>>> return Halt_Status;
>>>>>>>>>>>>> }
>>>>>>>>>>>>>
>>>>>>>>>>>>> with whatever specifies the behaviour of DD to HHH. If you
>>>>>>>>>>>>> can't
>>>>>>>>>>>>> do this then HHH is not a halt decider nor a partial halt
>>>>>>>>>>>>> decider.
>>>>>>>>>>>
>>>>>>>>>>>> When the halting problem requires a halt decider
>>>>>>>>>>>> to report on the behavior of a Turing machine this
>>>>>>>>>>>> is always a category error.
>>>>>>>>>>>
>>>>>>>>>>> That you don't know what "category error" means does not
>>>>>>>>>>> justify your
>>>>>>>>>>> claim. Apparently you can't apply definitions.
>>>>>>>>>>
>>>>>>>>>> Turing machines only compute functions from finite
>>>>>>>>>> strings they never compute functions from Turing
>>>>>>>>>> machines.
>>>>>>>>>
>>>>>>>>> True, but irrelevant to questions about category errors.
>>>>>>>>>
>>>>>>>>>> A halt decider can at best compute the behavior of
>>>>>>>>>> a Turing machine through the proxy of a finite
>>>>>>>>>> string machine description it never computes it
>>>>>>>>>> directly from another Turing machine.
>>>>>>>>>>
>>>>>>>>>> Whenever any textbook says that a halt decider
>>>>>>>>>> must compute halting for machine M on input w
>>>>>>>>>> is it wrong.
>>>>>>>>>
>>>>>>>>> Which textbook actually says "must"? It is not wrong to say
>>>>>>>>> "must" in
>>>>>>>>> the sense that any decider that does not compute whether machine M
>>>>>>>>> halts on input w is not a halt decider. But using "must" is not
>>>>>>>>> the
>>>>>>>>> clearest way to say it because the word "must" other meanings.
>>>>>>>>>
>>>>>>>>> > It actually computes halting that this input pair specifies
>>>>>>>>> (⟨M⟩, w).
>>>>>>>>>
>>>>>>>>> There is an unbalanced parenthesis above.
>>>>>>>>
>>>>>>>> No halt decider ever computes the halt status
>>>>>>>> of a machine except through the proxy of finite
>>>>>>>> strings.
>>>>>>>
>>>>>>> No halt decider computes anything because there are not halt
>>>>>>> deciders.
>>>>>>
>>>>>> I am trying to state the gist of this and not get so
>>>>>> bogged down in tedious details that the gist cannot
>>>>>> possibly ever be understood because we have too much
>>>>>> detail for the capacity of the human mind.
>>>>>
>>>>> If you can't state the gist without causing more confusion than
>>>>> clarity you should try something else.
>>>>>
>>>> When people demand too many irrelevant details
>>>> I must so no.
>>>
>>> You should put the whole story to GitHub. Then you can add any detail
>>> aomeone asks. If the same quiestion is asked again you only need to
>>> give a pointer as the answer.
>>>
>>
>> I am making one single point.
>
> WHich one?
>
>> A bunch of irrelevant
>> questions distract away from this one point.
>
> A sufficient answer to an irelevant question is "doesn't matter".
> If a quetion is irrelevant it is sufficient to say "doesn't matter".
>
>> I have gone over these things thousands of times
>> and what seem obvious to me cannot possibly be
>> understood by anyone besides LLM systems.
>>
>> These are the correct first principles of all
>> computation.
>>
>> Computations: Transform finite strings by finite
>> string transformation rules into values or non-termination.
>>
>> Deciders: Transform finite strings by finite string
>> transformation rules into {Accept, Reject}.
>
> The terms "computation" and "decider" are not parallel. The suffix
One is a subset of the other.
> of "decider" means that it is an agent. The word "computation" has
> a diferent suffix bedause it is an action. A decider performs a
> computation but it isn't one. But you can say that a decider is a
> computer although more ofthen the term "automaton" is used.
>
> One should also note that definitions are not principles.
>
A definition of computation does specify the principles
of computation.
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.
This required establishing a new foundation
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
|
