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