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The first-order theory of binary overlap-free words is decidable
Part of
Luke Schaeffer, Jeffrey Shallit
Journal:

Canadian Journal of Mathematics / Volume 76 / Issue 4 / August 2024

Published online by Cambridge University Press:

26 May 2023, pp. 1144-1162

Print publication:

August 2024
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We show that the first-order logical theory of the binary overlap-free words (and, more generally, the $\alpha $-free words for rational $\alpha $, $2 < \alpha \leq 7/3$), 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, and new claims can be proved or disproved simply by restating them as logical formulas.