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Illustration DFA - even number of 0s and 1s

<span>DFA - even number of 0s and 1s</span>
DFA - even number of 0's and 1's

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Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):$$ L ~=~ \{ w \in \{0,1\}^* ~:~ |w|_0 ~\text{mod}~ 2 = 0 ~\text{UND}~ |w|_1 ~\text{mod}~ 2 = 0 \} $$

This is an infinite language with, for example, the following words \(w\):$$ L ~=~ \{\varepsilon, 00, 11, 001100,~... \} $$

This automaton accepts all words \(w\) where the number \( |w|_0\) of zeros and the number \( |w|_1\) of ones is divisible by two.