Properties of Context-Free Languages

State the Pumping Lemma for Context-Free Languages (CFLs) and explain its structure.

Apply the Pumping Lemma to prove that a given language is not context-free (e.g., {aⁿbⁿcⁿ}).

Prove that CFLs are closed under union, concatenation, and Kleene star using grammar-based constructions.

Prove that CFLs are not closed under intersection and complement using counterexamples.

Solve the membership problem for CFLs using the CYK algorithm with a grammar in CNF.

Formulate and solve the decision problems of emptiness and finiteness for CFLs by analyzing their grammars.