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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Simulating termination analyzers by dummies --- What does halting
 mean?
Date: Tue, 18 Jun 2024 16:54:31 -0500
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On 6/18/2024 4:36 PM, Alan Mackenzie wrote:
> [ 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.
> 

Although I agree with this there seems to be nuances of
disagreement across the experts.

>> 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.
> 

I develop one within the conventional notions below.

>>>> 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.
> 

None-the-less it does derive the notion of abnormal termination
as applied to Turing Machines.

>>>> 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.
> 

Two different machines.
(a) The TM description of a looping machine.
(b) A UTM that has been adapted to count to five repeating
states before it aborts its simulation of the looping machine.

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

It is a mistake for a simulating termination analyzer
to simulate infinite repeating states.

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

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