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From: Mikko
Newsgroups: comp.theory
Subject: Re: HHH decides a non-trivial semantic property of its input
Date: Thu, 8 Aug 2024 10:17:09 +0300
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On 2024-08-07 13:23:54 +0000, olcott said:
> On 8/7/2024 2:06 AM, Mikko wrote:
>> On 2024-08-05 13:46:11 +0000, olcott said:
>>
>>> On 8/5/2024 8:44 AM, Python wrote:
>>>> Le 05/08/2024 à 13:50, olcott a écrit :
>>>>> On 8/5/2024 3:08 AM, Mikko wrote:
>>>>>> On 2024-08-04 14:46:02 +0000, olcott said:
>>>>>>
>>>>>>> When we define an input that does the opposite of whatever
>>>>>>> value that its halt decider reports there is a way for the
>>>>>>> halt decider to report correctly.
>>>>>>>
>>>>>>> int DD()
>>>>>>> {
>>>>>>> int Halt_Status = HHH(DD);
>>>>>>> if (Halt_Status)
>>>>>>> HERE: goto HERE;
>>>>>>> return Halt_Status;
>>>>>>> }
>>>>>>>
>>>>>>> int main()
>>>>>>> {
>>>>>>> HHH(DD);
>>>>>>> }
>>>>>>>
>>>>>>> HHH returns false indicating that it cannot
>>>>>>> correctly determine that its input halts.
>>>>>>> True would mean that its input halts.
>>>>>>
>>>>>> That is called a "partial halt decider". The set of requirements is
>>>>>> a subset of the requirements for "halt decider" but still require
>>>>>> that the answer is not "halts" if the input does not halt and that
>>>>>> the answer is not "does not halt" if the input halts. The difference
>>>>>> is that a "halt decider" is required to give one of these answers
>>>>>> for every input but a "partial halt decider" is not.
>>>>>>
>>>>>> For every computation there is a partial halt decider that answers it.
>>>>>>
>>>>>
>>>>> I call it a halting decidability decider.
>>>>> 1=input halts
>>>>> 0=input does not halt or has pathological relationship with its decider
>>>>
>>>> So it is NOT an halt decider. Case closed. You've lost your time
>>>> for years, and made a lot of people lose their time too.
>>>>
>>>>
>>>>
>>>
>>> It refutes Rice
>>
>> No, it does not. Nothing is refuted as long as you have not proven anything.
>>
>
> 1 = halts = good input = decidable
> 0 = (not halts or pathological) = bad input = not decidable as halting
> HHH decides a non-trivial semantic property of its input.
Your "not decidable as halting" is not a property of input. Another
partial decider may be able to determine that the input is halting
and therefore decidable as halting.
--
Mikko