On the number of C∞-words of each length
Journal of Combinatorial Theory Series A
On repeated factors in C∞ -words
Information Processing Letters
Information Processing Letters
A note on differentiable palindromes
Theoretical Computer Science
Computing forbidden words of regular languages
Fundamenta Informaticae - Special issue on computing patterns in strings
Combinatorial properties of smooth infinite words
Theoretical Computer Science
On a word avoiding near repeats
Information Processing Letters
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We exhibit the construction of a deterministic automaton that, given k0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this construction to the case of C^~-words, i.e., words differentiable arbitrarily many times. We thus obtain an infinite automaton for representing the set of C^~-words. We derive a classification of C^~-words induced by the structure of the automaton. Then, we introduce a new framework for dealing with C^~-words, based on a three letter alphabet. This allows us to define a compacted version of the automaton, that we use to prove that every C^~-word admits a repetition whose length is polynomially bounded.