State Complexity of the Subword Closure Operation with Applications to DNA Coding

We are interested in the state complexity of languages that are defined via the subword closure operation. The subword closure of a set S of fixed-length words is the set of all words w for which any subword of w of the fixed length is in S. This type of constraint appears to be useful in various situations related to data encodings and in particular to DNA encodings. We present a few results related to this concept. In particular we give a general upper bound on the state complexity of a subword closed language and show that this bound is tight infinitely often. We also discuss the state complexity of DNA computing related cases of the subword closure operation.