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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: Tue, 16 Jul 2024 09:46:40 -0500
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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 thus no actual
limit to computation more that this logical impossibility:
What time is it (yes or no)?

*This is isomorphic the HP decider/input pair*
Can Carol correctly answer “no” to this (yes/no) question? (Hehner:2018:2)

Giving credit where credit is due Richard corrected
a loophole in the original question.

> The program that predicts what HHH would say and does the opposite
> is just one eample of a program.
> 

It is just like a Liar Paradox input to a True(L, x) predicate.
The correct answer is INVALID INPUT.

>> When HHH is defined such that an input that was defined to
>> do the opposite of whatever HHH reports can never reach this
>> point in its execution trace then the prior halting problem
>> proof has been defeated.
> 

     From a programmer's point of view, if we apply an
     interpreter to a program text that includes a call
     to that same interpreter with that same text as
     argument, then we have an infinite loop. A halting
     program has some of the same character as an interpreter:
     it applies to texts through abstract interpretation.
     Unsurprisingly, if we apply a halting program to a
     program text that includes a call to that same halting
     program with that same text as argument, then we have
     an infinite loop. (Hehner:2011:15)

[5] E C R Hehner. Problems with the Halting Problem, COMPUTING2011 
Symposium on 75 years of Turing Machine and Lambda-Calculus, Karlsruhe 
Germany, invited, 2011 October 20-21; Advances in Computer Science and 
Engineering v.10 n.1 p.31-60, 2013
https://www.cs.toronto.edu/~hehner/PHP.pdf

> No, not anymore that 2 + 3 = 5 is defeated by a 2 that is defined to
> shrink to 1 if 3 is added to it.
> 

*Simulating Termination Analyzer H is Not Fooled by Pathological Input D*
https://www.researchgate.net/publication/369971402_Simulating_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D 


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