XPost: comp.theory
From: polcott333@gmail.com
On 12/21/2025 5:11 AM, Mikko wrote:
> 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.
>
Computations: Transform finite string inputs by finite
string transformation rules into values or nontermination.
Deciders: Transform finite string inputs by finite
string transformation rules into {Accept, Reject}.
Deciders are the subset of computations that always halt
both Deciders and Computations Transform finite string
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