a$.$ Consider the following NFA helaxx$-$

i$.$ Convert the automaton to a DFA.

$[12$ marks$]$

ii$.$ Using the resulting DFA, create a regular expression by eliminating states. Clearly show every step of the algorithm.

$[4$ marks$]$

b$.$ Consider the language $L_1=\{a{a}^{**}b\}$ over the alphabet $\{a,b\}$

i$.$ Construct a PDA to accept the language.

$[4$ marks$]$

ii$.$ Write a Context Free Grammar to accept the same language.

$[2$ marks$]$

c$.$ Use pumping lemma to determine if the language