$2$ Finite Automata $2$

Consider the finite automaton A from Figure $2.$

Figure $2$: Finite automaton $A.$

$2\mathrm{.}1$ Determine the marked language $L_m(A).$

$2\mathrm{.}2$ Consider the specification $K\frac{?}{b}=ar(\{ab{a}^{**}b,ba\})$ and the set of uncontrollable events $E_{uc}=\{a\}.$

Is $K$ controllable? If not, determine $K^C$ and $K^{\text{d}\text{a}\text{r}\text{r}}..$