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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: HHH decides a trivial non-semantic non-property of its input
Date: Thu, 8 Aug 2024 07:34:34 -0400
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On 8/7/24 9:23 AM, olcott wrote:
> 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.
> 

ONe thing you don't seem to understand is that "Decidability" isn't a 
property of an input, but of the whole problem. Given a problem, each 
input HAS a correct answer, and thus we can make a machine that will 
give that answer.

Being non-decidable is a property of the whole problem.

For the Halting Problem, you confuse the design problem with the 
verification problem.

We dont even HAVE an input H^/P/D until you have chosen and completely 
fixed and defined the decider you want to claim to be correct, and thus 
you can not talk about what it "should" or "could" do, only what it 
DOES, and if that answer it the CORRECT one.

It doesn't matter what a different decider would do with a different 
input (which the pathological template generates for that other decider) 
as it isn't the same as THIS input, since each input contains the FULL 
description that defines ALL the code used, including its copy of the 
decider that it is confounding.

Thus, you claim fails at the level of an initial category error before 
you even get off the ground.