Separating Many Words by Counting Occurrences of Factors

摘要

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 appearing 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.