Computing maximal Kleene closures that are embeddable in a given subword-closed language

Motivated by certain coding techniques for reliable DNA computing, we consider the problem of characterizing nontrivial languages D that are maximal with the property that D* is contained in the subword closure of a given set S of words of some fixed length k. This closure is simply the set of all words whose subwords of length k must be in S. We provide a deep structural characterization of these languages D, which leads to polynomial time algorithms for computing such languages.

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