1. Construct a grammar G such that L(G) = L(M) where M is the PDA in the previous question. Then show that the word aaaabb is generated by G.
2. Prove, using the Pumping Lemma for Context-Free Languages, that the language L = {a^{k} | k is a perfect square} is not context-free.
2. Consider the language L = {a^{k} b^{k} | k > 0}. Explain whether this language is context-free, context-sensitive, recursive, recursively, enumerable, and/or regular. While formal proofs are not required, justify your assertions.