Question

3. [10 pts] Let $L = \{a^nb^n | n \ge 0\}$. The complement of this language is the language $\overline{L}$. For example, abb \in \overline{L} $\epsilon \notin L$ aab \in \overline{L} ab \notin L baab \in \overline{L} aabb \notin L abab \in L aaabbb \notin L Give a context-free grammar generating $\overline{L}$. Hint: There are four separate cases you need to consider. You might want to design the grammar to consider each of these four cases independently of one another.

          3. [10 pts] Let $L = \{a^nb^n | n \ge 0\}$. The complement of this language is the language $\overline{L}$.
For example,
abb \in \overline{L}
$\epsilon \notin L$
aab \in \overline{L}
ab \notin L
baab \in \overline{L}
aabb \notin L
abab \in L
aaabbb \notin L
Give a context-free grammar generating $\overline{L}$.
Hint: There are four separate cases you need to consider. You might want to design
the grammar to consider each of these four cases independently of one another.

$3. [10 pts] Let L = {a^nb^n | n ≥ 0}. The complement of this language is the language L. For example, abb ∈L ϵ∉ L aab ∈L ab ∉L baab ∈L aabb ∉L abab ∈L aaabbb ∉L Give a context-free grammar generating L. Hint: There are four separate cases you need to consider. You might want to design the grammar to consider each of these four cases independently of one another.$

Added by Roberta S.

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