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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Defining a correct halting decidability decider
Date: Thu, 8 Aug 2024 22:52:17 -0400
Organization: i2pn2 (i2pn.org)
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On 8/8/24 9:21 AM, olcott wrote:
> 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.
> 
> 

And since DDD halts for all the DDD built on a actual decider HHH, all 
those DDD are well-behaved, so any HHH that returns 0 is just wrong.

Remember, "Halting" is about the behavior of the actual exectution of 
the program the input represents, which since it must be a 
representation of a program, it must include ALL the code used by DDD, 
including the code of the HHH that it calls, which makes it a different 
input than the DDD that calls the non-aborting HHH, which is non-halting 
and thus not good, but that HHH doesn't report that fact.