For the deterministic finite automaton $M$ with state set $\{0,1,2\}$, alphabet of input symbols $\{a, b\}$, initial state $0 ,$ accepting states 1 and 2 , and next-state function
$$(0, a) \mapsto 2, \quad(1, a) \mapsto 1, \quad(2, a) \mapsto 0,\\
(0, b) \mapsto 1, \quad(1, b) \mapsto 0, \quad(2, b) \mapsto 2$$.
Which of the following is correct regular expression $r$ such that $\mathrm{L}(\mathrm{M})=\mathrm{L}(\mathrm{r})$ :
- $b a^{\ast }+a b^{\ast }$
- $\left(b a^{\ast } b+a b^{\ast } a\right)^{\ast }(b+a)$
- $\left(b a^{\ast } b+a b^{\ast } a\right)^{\ast }\left(b a^{\ast }+a b^{\ast }\right)$
- None of the above
