 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/4f/d/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Take

G = ({a, b, c}, {S, A, B}, {S \to A B, A \to a, B \to b}, S)

and

G^{'} = ({a, b, c}, {T}, {T \to c}, T) .

These are variable based and have disjoint variable sets. They satisfy

L (G) L (G^{'}) = {ab c} .

H^{reg}

, however, both terminal productions of

G

are replaced:

A \to a T, B \to b T .

Consequently its only terminal derivation is

S \Rightarrow A B \Rightarrow a TB \Rightarrow a T b T \Rightarrow a c b c,

L (H^{reg}) = {a c b c} \neq = {ab c} .

T

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