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Minimum DFA for $\{ w \in \{a,b,c\}^* \mid \forall x,y,z: (w=xbybz \Rightarrow |y|_a\geq 2) \}$

Describe the minimum DFA that recognizes the words over $\{a,b,c\}$ such that
between every two occurrences of $b$ there are at least two occurrences of $a$.

Authors: Guillem Godoy
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