Question $1.(20$ points$)$

Let $=\{a,b\}.$ For each of the following languages, find a grammar that generates it$.$

$($a$).L=\{a^n{b}^{2n}$:$n0\}$

$($b$).L=\{a^m{b}^n$:$mn0\}$

Question $2.(30$ points$)$

Consider the set of strings on $\{0,1\}$ defined by the requirements below. For each, construct an accepti

dfa:

$($b$).$ All strings containing $00$ but not $000.$

$($c$).$ The leftmost symbol differs from the rightmost one.

Question $3.(15$ points$)$

Convert the following nfa into an equivalent dfa