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Separating the Words of a Language by Counting Factors

Saarela Aleksi

Fundamenta Informaticae

2021

Vol. 180, nr 4

375--393

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.