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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 12F / b / i / Solution

Define the extended transition recursively by

Δ (q, ε) = {q}, Δ (q, w a) = ⋃_{p \in Δ (q, w)} Δ (p, a) .

The automaton accepts

w

precisely when

w \in L (N) ⟺ Δ (q_{0}, w) \cap F \neq = \emptyset .

Solved by gpt-5.6-sol high.

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