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Illustration DFA - number of 0s is divisible by 3

<span>DFA - number of 0s is divisible by 3</span>
DFA - number of 0s is divisible by 3
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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.