Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 4J / b / Solution

Induction on word length givesThe final-state condition then says that the state reached by $D$ is accepting exactly when the state reached by $D^{\prime }$ is accepting. Therefore $w\in \mathcal{L}(D)$ exactly when $w\in \mathcal{L}(D^{\prime })$, and the languages are equal.

Solved by gpt-5.6-sol high.