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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is correctly rejected as
 non-halting. --- You are not paying attention
Date: Fri, 19 Jul 2024 08:48:49 -0500
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On 7/19/2024 2:30 AM, Mikko wrote:
> On 2024-07-18 13:36:53 +0000, olcott said:
> 
>> On 7/18/2024 2:55 AM, Mikko wrote:
>>> On 2024-07-17 13:14:43 +0000, olcott said:
>>>
>>>> On 7/17/2024 2:08 AM, Mikko wrote:
>>>>> On 2024-07-16 14:46:40 +0000, olcott said:
>>>>>
>>>>>> On 7/16/2024 2:18 AM, Mikko wrote:
>>>>>>> On 2024-07-15 13:32:27 +0000, olcott said:
>>>>>>>
>>>>>>>> On 7/15/2024 2:57 AM, Mikko wrote:
>>>>>>>>> On 2024-07-14 14:48:05 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 7/14/2024 3:49 AM, Mikko wrote:
>>>>>>>>>>> On 2024-07-13 12:18:27 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>> When the source of your disagreement is your own ignorance
>>>>>>>>>> then your disagreement has no actual basis.
>>>>>>>>>>
>>>>>>>>>> *You can comprehend this is a truism or fail to*
>>>>>>>>>> *comprehend it disagreement is necessarily incorrect*
>>>>>>>>>> Any input that must be aborted to prevent the non
>>>>>>>>>> termination of HHH necessarily specifies non-halting
>>>>>>>>>> behavior or it would never need to be aborted.
>>>>>>>>>>
>>>>>>>>>> Disagreeing with the above is analogous to disagreeing
>>>>>>>>>> with arithmetic.
>>>>>>>>>
>>>>>>>>> A lame analogy. A better one is: 2 + 3 = 5 is a proven theorem 
>>>>>>>>> just
>>>>>>>>> like the uncomputability of halting is.
>>>>>>>>
>>>>>>>> The uncomputability of halting is only proven when the problem
>>>>>>>> is framed this way: HHH is required to report on the behavior
>>>>>>>> of an input that was defined to do exactly the opposite of
>>>>>>>> whatever DDD reports.
>>>>>>>
>>>>>>> No, it is proven about the halting problem as that problem is.
>>>>>>
>>>>>> Which is simply a logical impossibility
>>>>>
>>>>> Yes, a halting decider is a logical impossibility, as can be and has
>>>>> been proven.
>>>>
>>>> If it is a logical impossibility then it places no
>>>> actual limit on computation otherwise we would have
>>>> "the CAD problem" of the logical impossibility of making
>>>> a CAD system that correctly draws a square circle.
>>>
>>> A logical impossibility does place a limit on computation.
>>> Otherwise it would be possible to build a CAD system that
>>> can correctly draw a square circle.
>>
>> Of the set of possible things TM's can do them all.
> 
> Depends on the meanings of "possible" and "thing". Of things other than
> computation no TM can do any. A Turing machine can determine whether
> a sentence of Presburger arithmetic is provable but no Turing machine
> can determine whether a sentence of Peano arithmetic is provable.
> 

Some undecidable expressions are only undecidable because
they are self contradictory. In other words they are undecidable
because there is something wrong with them.

The Liar Paradox: "This sentence is not true"
(is neither true nor false) and the HP proof are that way,
yet, only when we expect a decider to return the halt status
of an input that does that opposite of whatever value the
decider returns.

typedef void (*ptr)();
int HHH(ptr P);

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

int main()
{
   DD();
}

*When we understand that*
(a) The halt decider is not allowed to report on the computation
that it is contained within. Then the behavior of the directly
executed DD() is moot.

(b) The self-contradictory part of the input is unreachable from
the emulated DD then a simulating partial halt decider does
correctly compute the mapping from the input finite string to
the non-halting behavior of this finite string.

int main { DD(); } calls HHH(DD) that must abort the emulation
of its input or HHH, emulated DD and executed DD never stop
running.



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