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

On 6/19/2024 3:18 AM, Fred. Zwarts wrote:

Op 18.jun.2024 om 19:25 schreef 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.

>
Halting is a technical term-of-the-art that corresponds
to terminates normally. Because Turing machines are
abstract mathematical objects there has been no notion
of abnormal termination for a Turing machine.
>
We can derive a notion of abnormal termination for Turing
machines from the standard terms-of-the-art.
>
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.
>
A UTM can be adapted so that it only simulates a fixed number
of iterations of an input that loops. When this UTM stops
simulating this Turing machine description we cannot correctly
say that this looping input halted.
>

 If the code specifies 5 iterations and the simulator simulates only 3 iterations, it is incorrect to conclude that the repetition show non-halting behaviour.

It is correct do say that the simulated input did not terminate
normally, thus defining the notion of abnormal termination
within Turing machines.

Similarly, when your H, H0, or other H simulates itself, its simulation aborts one cycle too early and therefore the non-halting conclusion is incorrect.

I was confused bout this for three days four years ago and then I
got over it. No simulating termination analyzer can wait for an
inner instance of itself to abort the simulation or it waits forever.
Whenever the outer directly executed simulating termination analyzer
waits for any fixed number of repeating states it remains permanently
ahead of the next inner instance by exactly one repeating state. If
this is going to be permanently over your head then we need to stop
talking.
I only have three months of good health left before I will be on
a medicine that has a side effect of low blood counts for a year.
Chemotherapy was supposed to permanently ruin my T4 counts yet
I lucked out on that one.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer