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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Defining a correct halting decidability decider
Date: Sat, 10 Aug 2024 06:03:31 -0500
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On 8/10/2024 3:20 AM, Mikko wrote:
> On 2024-08-09 13:47:34 +0000, olcott said:
> 
>> On 8/9/2024 3:56 AM, Mikko wrote:
>>> On 2024-08-08 13:21:57 +0000, olcott said:
>>>
>>>> On 8/8/2024 2:12 AM, Mikko wrote:
>>>>> On 2024-08-07 13:12:43 +0000, olcott said:
>>>>>
>>>>>> On 8/7/2024 1:59 AM, Mikko wrote:
>>>>>>> On 2024-08-04 19:33:36 +0000, olcott said:
>>>>>>>
>>>>>>>> On 8/4/2024 2:05 PM, Richard Damon wrote:
>>>>>>>>> On 8/4/24 2:49 PM, olcott wrote:
>>>>>>>>>> On 8/4/2024 1:38 PM, Richard Damon wrote:
>>>>>>>>>>> On 8/4/24 10:46 AM, olcott wrote:
>>>>>>>>>>>> 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.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> But false indicates that the input does not halt, but it does.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I made a mistake that I corrected on a forum that allows
>>>>>>>>>> editing: *Defining a correct halting decidability decider*
>>>>>>>>>> 1=input does halt
>>>>>>>>>> 0=input cannot be decided to halt
>>>>>>>>>
>>>>>>>>> And thus, not a halt decider.
>>>>>>>>>
>>>>>>>>> Sorry, you are just showing your ignorance.
>>>>>>>>>
>>>>>>>>> And, the problem is that a given DD *CAN* be decided about 
>>>>>>>>> halting, just not by HHH, so "can not be decided" is not a 
>>>>>>>>> correct answer.
>>>>>>>>
>>>>>>>> A single universal decider can correctly determine whether
>>>>>>>> or not an input could possibly be denial-of-service-attack.
>>>>>>>> 0=yes does not halt or pathological self-reference
>>>>>>>> 1=no  halts
>>>>>>>
>>>>>>> Conventionally the value 0 is used for "no" (for example, no errors)
>>>>>>> and value 1 for "yes". If there are different "yes" results other
>>>>>>
>>>>>> A Conventional halt decider is 1 for halts and 0 for does not halt.
>>>>>
>>>>> That is because conventionally the question is "Does thing computation
>>>>> halt?" so "yes" means the same as "halts".
>>>>>
>>>>>> 0 also means input has pathological relationship to decider.
>>>>>
>>>>> It cannot mean both "does not halt" and "has pathological relationship
>>>>> to decider". Those two don't mean the same.
>>>>>
>>>>>> In other words 1 means good input and 0 means bad input.
>>>>>
>>>>> That is not the same in other words.
>>>>>
>>>>> An input is good in one sense if it specifies a computation and bad if
>>>>> it does not. In the latter case the decider is free to do anything as
>>>>> the input is not in its scope.
>>>>>
>>>>> In another sense an input is good if it is as the user wants it to be.
>>>>> If the user wants a non-halting computation then a halting one is bad.
>>>>>
>>>>
>>>> *Semantic property of well-behaved is decided for input*
>>>> It the program well behaved thus halts?
>>>> else The program is not well behaved.
>>>
>>> You don't need any meaning for "well-behaved". A program is good if
>>> it satisfies its purpose.
>>
>> https://en.wikipedia.org/wiki/Stipulative_definition
>> has_eaten_lunch is a Stipulative_definition defined below:
>>
>> A program is said to have the non trivial semantic
>> property of has_eaten_lunch when it halts and
>> ~has_eaten_lunch when it cannot be correctly determined
>> to halt. This defeat Rice's Theorem.
> 
> that is not a useful stipulation. And there is no way to correctly
> determine that it is not possible to determine whether a computation
> halts.
> 

1=halts
0=does not halt or pathological relationship to decider


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