Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 4G / a

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- Solution a

Solution

For a set

S \subseteq Q_{E}

, let

E (S)

be its epsilon closure, and put

δ_{E} (S, a) = ⋃_{q \in S} δ_{E} (q, a) .

The subset construction with epsilon transitions gives the deterministic finite automaton

Q_{D} = P (Q_{E}), q_{D} = E ({q_{0}}),

δ_{D} (S, a) = E (δ_{E} (S, a)), F_{D} = {S \subseteq Q_{E} : S \cap F_{E} \neq = \emptyset} .

Unreachable subsets may be deleted from

Q_{D}

without changing the recognized language.

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