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Illustration DFA - number of a's and b's have the same remainder when divided by 3

DFA - number of a's and b's have the same remainder when divided by 3
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Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):$$ L ~=~ \{ w \in \{a,b\}^* ~:~ |w|_a \equiv |w|_b \text{ mod } 3 \} $$

This is an infinite language where \(|w|_a\) (number of a's in the word \(w\)) and \(|w|_b\) (number of b's in the word \(w\)) both give the same remainder when \(|w|_a\) and \(|w|_b\) are divided by two:$$ L ~=~ \{ \varepsilon, aaa, bbb, aabb, aabbba, ~.... \} $$