Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 12I / c

This language is context-free. One grammar iswhich independently chooses at least one outer $a,c$ pair and at least one $b$.

It is not context-free. Intersecting it with the regular language $a^{\ast }{b}^{\ast }{c}^{\ast }$ would give $\{a^n{b}^n{c}^n:n\ge 0\}$, which violates the pumping lemma for context-free languages. Context-free languages are closed under intersection with regular languages.