The First-Order Theory of Binary Overlap-Free Words is Decidable

We show that the first-order logical theory of the binary overlap-free words (and, more generally, the $α$-free words for rational $α$, $2 < α \leq 7/3$), is decidable. As a consequence, many results previously obtained about this class through tedious case- based proofs can now be proved "automatically", using a decision procedure.

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