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

Am Tue, 18 Jun 2024 21:30:43 -0500 schrieb olcott:

On 6/18/2024 9:16 PM, Richard Damon wrote:

On 6/18/24 1:25 PM, olcott wrote:

On 6/18/2024 12:06 PM, joes wrote:

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.

And then are no longer UTMs, and YES, if a machine based on such am
modifed UTM (so it is no long a UTM) when the UTM stops simulating, we
can not say the input halted, nor can we say it didn't halt.

When such a UTM has been adapted to only simulate the first ten states
of its input TMD, then every simulated TMD with more than ten states did
not terminate normally.

You are confusing the machines with their simulators. No longer simulating
has nothing to do with the simulatee. It does not "know" it is being
simulated. That is entirely in the power of the simulator. Only it can
freely choose to simulate more steps. The simulated machine then proceeds.

The not-a-UTM just came to a no-answer state.

I have to go one-step-at-a-time with everyone or they get overwhelmed
and leap to the conclusion that I am wrong.

The answer will be provided by useing an ACTUAL UTM that keeps on
going, or the direct execution of the machine,

You are stuck on the idea that repeating states cannot be recognized in
a finite number of steps.

Oh, they can. It's just that repeating states don't halt in a finite
number of steps.

--
joes