Transfinite Lyndon Words
In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are locally decreasing, a relaxation of the condition used in the case of finite words.
In a second part, we prove that the factorization of a rational word has a special form and that it can be computed in polynomial time from a rational expression describing the word.
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