$($Context Free Languages$)$

Question $1$: Design $($DRAW$)$ WITH EXPLIAN PDA for the given language descriptions $($preferred with minimum states$).[1$ marks$]$

$L=a^n{b}^{3n}$;$n>0.$

$L=a^{n+1}{b}^{n+3}$;$n0$

Question $2$: Write CFGs for the following language descriptions in normalized form. $[1$ marks$]$

$L=a^n{b}^{3n}$;$n>0.$

$L=a^{n+1}{b}^{n+3}$;$n0$

Question $3$: Using the Pumping lemma to prove that the given language is not context free.

mark$]$

$\{a^m{b}^n{c}^{mn}$:$m0,n0\}.$

$\{a^{n}b{a}^{2n}b{a}^{3n}$:$n0\}.$

$\{a^n{b}^n{a}^n{b}^n$:$n0\}.$