XPost: comp.theory, sci.math
From: mikko.levanto@iki.fi
On 20/12/2025 13:54, olcott wrote:
> 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.
No, they are not. Being a subset means they share common elements. But,
as pointed out below, a decider is an agent and a computation is a non-
agent. Therefore one being a subset of another requires either tant one
of the sets is empty or that there are agents that are non-agents.
>> 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.
Note that no counter argument is presented.
>> One should also note that definitions are not principles.
> A definition of computation does specify the principles
> of computation.
A definition may refer to a principle but a definition is not a
principle.
--
Mikko
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