Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 1 / 4G / c

Take a context-free grammar for $L$ with start symbol $S$, rename nonterminals if necessary, and add a fresh start symbol $S_0$ withEvery derivation concatenates finitely many words of $L$, and every finite concatenation can be derived. The resulting grammar generates $L^{\ast }$, proving closure of context-free languages under Kleene star.