 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/12f/ii/solution

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

The language

{a^{i} b^{j} : i \geq j \geq 0}

is context free. For example the grammar

S \to a S b ∣ A, A \to a A ∣ ϵ

generates

a^{j + k} b^{j}

with

j, k \geq 0

, and every required word has this form.

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