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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: HHH decides a non-trivial semantic property of its input
Date: Thu, 8 Aug 2024 13:38:51 -0500
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On 8/8/2024 2:17 AM, Mikko wrote:
> 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.
> 

https://en.wikipedia.org/wiki/Stipulative_definition
The stipulative definition of the semantic property

has_not_ate_lunch_yet means that the input halts and 
~has_not_ate_lunch_yet means the input cannot be
determined to halt.

This is can be used to detect and reject denial of
service attacks that have targeted the detector.


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