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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Defining a correct halting decidability decider
Date: Sat, 10 Aug 2024 07:20:01 -0400
Organization: i2pn2 (i2pn.org)
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On 8/10/24 7:03 AM, olcott wrote:
> 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
> 
> 

Subjective Requirmeent, thus not a property of JUST the input.

To be a valid rquirement, we must have a mapping of JUST The input to 
the answer, and since HHH1 CAN decide DDD that calls HHH, we see that 
you criteria is subjective, and thus invalid.

Note, this is one reason Halting is defined on PROGRAMS and not 
"Templates", because a Template doesn't have uniform behavior, it 
matters what it was paired with, so behavior of a template isn't a valid 
criteria.

This also means that the input must contain ALL the code of the input 
program, including the copy of the input that pathological input was 
making wrong.