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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Can D simulated by H terminate normally?
Date: Tue, 30 Apr 2024 18:46:23 -0400
Organization: i2pn2 (i2pn.org)
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On 4/30/24 12:15 PM, olcott wrote:
> On 4/30/2024 10:44 AM, Alan Mackenzie wrote:
>> olcott <polcott333@gmail.com> wrote:
>>> On 4/30/2024 3:46 AM, Fred. Zwarts wrote:
>>>> Op 29.apr.2024 om 21:04 schreef olcott:
>>
>> [ .... ]
>>
>>>>> The ONLY way that we can determine if any computation is correct is
>>>>> when it meets its specification. When a TM is specified to calculate
>>>>> the sum of a pair of decimal integers and it derives any decimal
>>>>> integer other than 5 from inputs 2,3 then it is incorrect.
>>
>>>> Changing the subject. The question is not whether it is correct, but
>>>> whether it halts. Incorrect programs exist and even those program may
>>>> halt.
>>
>>> I had to address this:
>>
>>> On 4/29/2024 11:17 AM, Alan Mackenzie wrote:
>>>> There is no notion of "correct" in a turing machine.  It is either
>>>> running, or has reached a final state.  In the TM equivalent of "core
>>>> dump", a final state has most definitely been reached.
>>
>> I would indeed be charmed if you would address it, but you have evaded
>> it, as you have evaded most of the points I made yesterday.
>>
>> Note that I said there is no correctness _IN_ a turing machine.  This is
>> independent of whether or not that turing machine is useful for some
>> external purpose.
>>
>> Note also that you wilfully distorted my meaning by trimming.  The full
>> context was:
>>
>>>>> Core dump abnormal termination does not count as the program
>>>>> correctly finished its processing.
>>
>>>> There is no notion of "correct" in a turing machine.  It is either
>>>> running, or has reached a final state.  In the TM equivalent of "core
>>>> dump", a final state has most definitely been reached.
>>
>> Your use of the word "correctly" in "correctly finished its processing"
>> is wrong.  A turing machine is either running or it's finished its
>> processing.  From the point of view of the tm, there is no "correct" or
>> "incorrect" associated with the latter condition; it's simply reached a
>> final state.
>>
>> You are thus mistaken in believing "abnormal" termination isn't a final
>> state.
>>
> 
> When we add the brand new idea of {simulating termination analyzer} to
> the existing idea of TM's then we must be careful how we define halting
> otherwise every infinite loop will be construed as halting.
> 

Why?

That doesn't mean the machine reached a final state.

Only if you try to define something that is NOT related to Halting, do 
you get into that issue.

Your problem is you want to try to define "Halting" as something that 
can ALWAYS be measured finitely. Yes, that makes it decidable, but makes 
it also not the same as the actual halting.

It also gets very hard (if not impossible) to define it in terms that 
can ACTUALLY be measured finitely, and also not have a trivial decay path.


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