DFA for the language L $=($w starts with an a and contains the substring abb$)[7$ marks$]$ Consider the following language:

$L=\{\begin{array}{cc}\text{w}\text{i}\text{n}& {}^{**}|\end{array}$ each pair of consecutive $b\text{'}$s in $w$ is separated by a substring of $a\text{'}$s of length $\{$:$2i,i0\}$

$($a$)$ Give the state diagram and the formal $5-$tuple definition of an NFA $N=(Q,,,q_0,F)$ which

recognizes $L,$ with a transition table describing $.$

$($b$)$ Give a regular expression $R$ where $L(R)=L.$