 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/4j/b/solution

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

Induction on word length gives

f (δ^{*} (q_{0}, w)) = δ^{' *} (q_{0}^{'}, w) .

The final-state condition then says that the state reached by

D

is accepting exactly when the state reached by

D^{'}

is accepting. Therefore

w \in L (D)

exactly when

w \in L (D^{'})

, and the languages are equal.

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