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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: I call it a halting decidability decider
Date: Wed, 7 Aug 2024 21:03:00 -0400
Organization: i2pn2 (i2pn.org)
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On 8/7/24 9:16 AM, olcott wrote:
> On 8/7/2024 2:04 AM, Mikko wrote:
>> On 2024-08-05 11:50:53 +0000, olcott said:
>>
>>> 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
>>
>> There is no "its decider". The identity of the decider is not a property
>> of the input.
>>
> 
> 1 = halts = good input = decidable
> 0 = (not halts or pathological) = bad input = not decidable as halting
> 
> 

Which isn't a propert of JUST the input, so not a valid thing to ask a 
decider about, since there is no objective map for it to try to compute.