Re: Simulating termination analyzers by dummies --- What does halting mean?

Am Wed, 19 Jun 2024 09:05:29 -0500 schrieb olcott:

On 6/19/2024 4:29 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 6/18/2024 4:36 PM, Alan Mackenzie wrote:

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:

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.

I doubt that very much.  The whole point of turing machines is to
remove ambiguity and unneeded features from the theory of computation.
A third alternative state is unneeded.

Some people say that a TM can halt in a non-final state.

None here do. End of thread.

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.

You don't need it.  You just confuse yourself (and possibly others)
with it.  What you call the "aborted state" is just one more final
state for the TM to halt in.

When the adapted UTM halts after simulating ten state transitions of a
Turing Machine Description that only loops we cannot correctly say that
the looping input has halted.

Yes!

When the adapted UTM halts after recognizing the repeating state of a
Turing Machine Description that only loops and transitions to its reject
state then this adapted UTM is a halt decider for inputs that only loop.

But not a simulator.

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.

So what?

You wanted to simulate the input.

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

As I said, that is not a useful notion.  It just confuses.

It is a perfectly useful notion as I have defined above because the
adapted UTM becomes a halt decider for inputs that only loop.

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

(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.

(b) is not a universal turing machine.  It is a TM, one of whose
halting states is having counted five repeating states.

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

How can that be a "mistake" if it's what the thing is programmed to do?

Termination analyzers are required to halt so it fails to meet its spec.

What use is an analyser that can't deal with possible loops?

--
joes