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Illustration DFA - word contains at least one a

<span>DFA - word contains at least one a</span>
DFA - word contains at least one a
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Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):$$ L ~=~ \{ w \in \{ a,b \}^* ~:~ w \text{ contains at least one } a \} $$

This is an infinite language with, for example, the following words:$$ L ~=~ \{ a, ab, ba, aba, bba, ~.... \} $$