Affiliations: Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland. amsaar@utu.fi
Correspondence:
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Address for correspondence: Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland
Abstract: For a given language L, we study the languages X such that for all distinct words u, v ∈ L, there exists a word x ∈ X that appears a different number of times as a factor in u and in v. In particular, we are interested in the following question: For which languages L does there exist a finite language X satisfying the above condition? We answer this question for all regular languages and for all sets of factors of infinite words.
Keywords: combinatorics on words, k-abelian equivalence, regular language, infinite word
