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From: olcott <abc@def.com>
Newsgroups: comp.theory
Subject: HHH decides a non-trivial semantic property of its input
Date: Wed, 7 Aug 2024 08:23:54 -0500
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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.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer