Find the regular expression for the following DFA.

$(3$ marks$)$

Given the set of alphabet, $=\{a,b\}.$ Draw the DFA for the following languages:

a$)$ The set of all strings that start with $b$ and end with $a.$

$(6$ marks$)$

b$)$ The set of all strings that start with the prefix $\text{'}ab\text{'}.$

$(6$ marks$)$

Given the language is

$L(G)=\{ab(bbaa{)}^n$bba$(ba{)}^n$:$n0\}$

Construct $($a$)$ Left$-$Linear Grammar; $($b$)$ Right$-$Linear Grammar for the language

$L(G)=\{a^n{b}^m$:$n2,m3\}$

$(8$ marks$)$