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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: I call it a halting decidability decider
Date: Wed, 7 Aug 2024 10:04:14 +0300
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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.

-- 
Mikko