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From: Alan Mackenzie <acm@muc.de>
Newsgroups: comp.theory,sci.logic
Subject: Re: Simulating termination analyzers by dummies --- What does halting mean?
Followup-To: comp.theory
Date: Tue, 18 Jun 2024 21:36:53 -0000 (UTC)
Organization: muc.de e.V.
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[ Followup-To: set ]

In comp.theory olcott <polcott333@gmail.com> wrote:
> On 6/18/2024 12:57 PM, joes wrote:
>> Am Tue, 18 Jun 2024 12:25:44 -0500 schrieb olcott:
>>> On 6/18/2024 12:06 PM, joes wrote:
>>> void DDD()
>>> {
>>>     H0(DDD);
>>> }
>>> DDD correctly simulated by any H0 cannot possibly halt.
>>>> DDD halts iff H0 halts.

>> So H0 returns "doesn't halt" to DDD, which then stops running,
>> so H0 should have returned "halts".

> This was three messages ago.
> I had to make sure that you understood that halting
> does not mean stopping for any reason and only includes
> the equivalent of terminating normally.

No.  You're wrong, here.  A turing machine is either running or it's
halted.  There's no third alternative.  If your C programs are not in one
of these two states, they're not equivalent to turing machines.

> DDD correctly emulated by H0 DOES NOT TERMINATE NORMALLY.

There is no concept of "normal" termination in a turing machine.  The
thing is either running or it's halted.

>>> Some TM's loop and thus never stop running, this is classical
>>> non-halting behavior. UTM's simulate Turing machine descriptions.
>>> This is the same thing as an interpreter interpreting the source-code of
>>> a program.
>> Some TMs do not loop and do not halt.

>>> A UTM can be adapted so that it only simulates a fixed number of
>>> iterations of an input that loops.

As has often been said, it is then no longer a universal turing machine.

>>> When this UTM stops simulating this Turing machine description we
>>> cannot correctly say that this looping input halted.

Yes, we can.  It has been designed to count to 42 then halt.  It is then
in the halted state.

>> Yes. We also cannot say that that input was simulated correctly.

Indeed, not.

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

-- 
Alan Mackenzie (Nuremberg, Germany).