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Minimum DFA for $\{ w \in \{a,b\}^* \mid \forall x,y: (w=xay \Rightarrow |x|_b\in\dot{2}) \}$

Describe the minimum DFA that recognizes the words over $\{a,b\}$ such that to
the left of each occurrence of $a$ there is an even number of $b$’s.

Authors: Guillem Godoy
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