Proof of Dejean's conjecture for alphabets with 5, 6, 7, 8, 9, 10 and 11 letters
Theoretical Computer Science
Decision problems for patterns
Journal of Computer and System Sciences
Some combinatorial properties of Sturmian words
Theoretical Computer Science
Handbook of formal languages, vol. 1
The Expressibility of Languages and Relations by Word Equations
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Quantifier Hierarchies over Word Relations
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
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We consider several open problems of Karhumäki, Mignosi, and Plandowski, cf. [KMP], concerning the expressibility of languages and relations as solutions of word equations. We show first that the (scattered) subword relation is not expressible. Then, we consider the set of k-power-free finite words and solve it negativelly for all nontrivial integer values of k. Finally, we consider the Fibonacci finite words. We do not solve the problem of the expressibility of the set of these words but prove that a negative answer (as believed) cannot be given using the tools in [KMP].