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From: Alan Mackenzie <acm@muc.de>
Newsgroups: comp.theory
Subject: Re: This function proves that only the outermost HHH examines the execution trace
Date: Sun, 28 Jul 2024 11:31:24 -0000 (UTC)
Organization: muc.de e.V.
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Mike Terry <news.dead.person.stones@darjeeling.plus.com> wrote:
> On 27/07/2024 19:14, Alan Mackenzie wrote:
>> olcott <polcott333@gmail.com> wrote:

>>> Stopping running is not the same as halting.
>>> DDD emulated by HHH stops running when its emulation has been aborted.
>>> This is not the same as reaching its ret instruction and terminating
>>> normally (AKA halting).

>> I think you're wrong, here.  All your C programs are a stand in for
>> turing machines.  A turing machine is either running or halted.  There is
>> no third state "aborted".  An aborted C program certainly doesn't
>> correspond with a running turing machine - so it must be a halted turing
>> machine.

>> So aborted programs are halted programs.  If you disagree, perhaps you
>> could point out where in my arguments above I'm wrong.


> Aborting is an action performed by a simulator, not the TM being simulated.

OK, so if a simulator aborts the program it's simulating, that program is
still in state running, even though it's a suspended animation which will
never get any further.  The simulator, having aborted the program, then
has no more work to do, so the simulator will be in state halted.  Is
that right?

> If we want to count "aborted" as some kind of final status, it will
> have to be the status of a specific /PARTIAL SIMULATOR's/ simulation of
> a given computation.  That's not a property of the computation itself,
> as different partial simulators can simulate the same computation and
> terminate for different reasons.  Like HHH(DDD) aborts, while UTM(DDD)
> simulates to completion and so the final simulation status is halts.
> [Neither of those outcomes contradict the fact that the computation
> DDD() halts.]

> If some partial simulator halts when simulating a computation [as with
> UTM(DDD)] that implies the computation DDD() halts.  But if the
> simulator aborts, it doesn't say that much (in and of itself) about
> whether the /computation/ halts.  The halting problem statement is not
> concerned with simulations or how the simulations end.

Indeed not!

> Every time anyone in these PO threads says "halts" it ought to be 100%
> clear to everyone whether the computation itself is being discussed, or
> whether some simulation final status is intended.  (But that's far from
> being the case!)  Since the halting problem is concerned with
> computations halting and not how partial simulations are ended, I
> suggest that PO explicitly make clear that he is referring to
> simulations, whenever that is the case.  It seems reasonable that
> readers seeing "halts" with no further clarification can interpret that
> as actual computation behaviour, as that is how the term is always used
> in the literature.  Same with other terms like "reach"...

> So when PO says "DDD simulated by HHH cannot reach its final ret
> instruction" is he talking about the computation DDD() [as defined
> mathematically], or its simulation by HHH?  He means the latter, but
> its far from clear, I'd say!  [I think most readers now have come
> around to reading it as a statement about simulations rather than the
> actual computation, which totally changes things...]

OK.  Thanks for the explanations!

> Mike.

-- 
Alan Mackenzie (Nuremberg, Germany).