$($a$)$ Find a context$-$free grammar $($CFG$)$ for the language L of all words

with length multiples of $4$ and where every fourth letter is an a$.$

Assume that the alphabet is $\backslash$Sigma $=\{$ a$,$ b $\}.($You need not prove that the

language generated by your grammar is the same as L$).$ Hint: You may

find it helpful to draw an FA$.$

$($b$)$ Convert the following CFG to Chomsky Normal Form $($CNF$)$:

S $$ XaX $|$ YY $|$ XY

X $/\backslash |$ b

Y $$ Xa