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Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):$$ L ~=~ \{ w \in \{ a,b \}^* ~:~ \text{ 2nd symbol of } w \text{ from RHS is } a \} $$
This is an infinite language with, for example, the following words:$$ L ~=~ \{ aa, baa, aab, babaa, ~.... \} $$