arXiv 1102.09132011-02cs.DMcs.FL

Automata and Differentiable Words

Jean-Marc Fédou, Gabriele Fici

备注：: Accepted for publication
发表信息：: Theoretical Computer Science 443:46-62 (2012)
DOI：: 10.1016/j.tcs.2012.03.033

英文摘要：

We exhibit the construction of a deterministic automaton that, given k > 0, 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\infinity-words, i.e., words differentiable arbitrary many times. We thus obtain an infinite automaton for representing the set of C\infinity-words. We derive a classification of C\infinity-words induced by the structure of the automaton. Then, we introduce a new framework for dealing with \infinity-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\infinity-word admits a repetition in C\infinity whose length is polynomially bounded.

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