Computing maximal Kleene closures that are embeddable in a given constrained DNA language

Authors:
Stavros Konstantinidis;Nicolae Santean
Affiliations:
Department of Mathematics and Computing Science, Saint Mary's University, Halifax, Nova Scotia, Canada;Department of Mathematics and Computing Science, Saint Mary's University, Halifax, Nova Scotia, Canada
Venue:
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
Year:
2011

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Abstract

We consider the problem of characterizing nontrivial languages D that are maximal with the property that D*, the Kleene closure of D, is contained in the subword closure of a given set S of words of some fixed length k. The subword closure of S is simply the set of words for which all subwords of length k are in S. We provide a deep structural characterization of these languages D, which leads to polynomial time algorithms for computing such languages. This work is motivated by the problem of encoding arbitrary data into a set of DNA molecules such that all blocks of length k in these molecules satisfy the constraint S - eg, they can form no stable bonds between them, or they have a desired g-c ratio.