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

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- Solution d

Solution

No production introduces

A

, so the two rules containing

A

are unreachable. The effective derivations are

S \Rightarrow a^{n} b C (BC)^{n - 1} \Rightarrow a^{n} b^{n} C^{n} \Rightarrow a^{n} b^{n} c^{n} .

Thus the language is ${a^{n} b^{n} c^{n} : n \geq 1}$ , which is not context-free language, although the displayed grammar itself also visibly has non-type-2 left sides.

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