I got recently introduced to automata and couldn't find an answer to the following question: Let $A$ and $B$ two finite state automata (with a starting state) acting on the same formal language $\Omega$.
Can we describe the map $A \circ B: \omega \mapsto A(B(\omega))$ also as a finite state automaton?
If not, does it work for $A=B$, i.e. are iterations of the same finite state automaton again finite state automatons?