This question appeared on my Theory of Computer Science final:
True | False: $A^*$ is context-free $\implies$ $A$ is context-free.
My professor says the answer is false, and I believe him, but am having trouble constructing a counterexample or even just convincing myself why. It seems to me that if a grammar can describe repeated concatenation, there must be some nonterminal that is concatenated.
Does anyone have a counterexample?