# Illustration Minimal DFA - even number of 0s and 1s

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

This is an infinite language where $$|w|_0$$ (number of 0s in the word $$w$$) and $$|w|_1$$ (number of 1s in the word $$w$$) are both either even or odd:$$L ~=~ \{ \varepsilon, 00, 11, 01, 10, 1111, ~... \}$$