Some very important points for Language Identification
[Infinite multiplication can’t be done by Finite Automata (FA), because FA has finite memory]
In fact, Push Down Automata (PDA) is not able to do infinite multiplication.
Infinite Multiplication only can be done by Context-Sensitive Language (CSL).
And it can be done by Finite Automata (FA).
Why it is finite or FA because it has a finite set of strings.
So, all finite languages are regular.
So, only CSL has the capacity to do multiplication and division for the infinite set.
So, multiplication and division can only do by tape (CSL) for the infinite set.
It is CSL because how we detect prime by division and multiplication and we know multiple and division infinite time can be only done by Tape (CSL).
# But for the finite numbers all are regular.