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Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):`$$ L ~=~ \{ w \in \{0,1\}^* ~:~ |w|_0 ~\text{mod}~ 3 = 0 \} $$`

This is an infinite language with, for example, the following words \(w\):`$$ L ~=~ \{ \varepsilon, 1, 000, 111, 000000,~... \} $$`

This automaton accepts all words \(w\) for which the length \( |w|_0 \) is divisible by three.