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

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Abstract

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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Notes

  1. In this case, ℓ should be such that D 1(ℓ) is of cardinality at least 1024 + 28 = 1280, which is the sum of the number of rows and the number of possible 8-bit colours.

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Acknowledgments

This study was supported by NSERC.

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Correspondence to Stavros Konstantinidis.

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Konstantinidis, S., Santean, N. Computing maximal Kleene closures that are embeddable in a given subword-closed language. Nat Comput 12, 211–222 (2013). https://doi.org/10.1007/s11047-013-9364-y

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