Further Properties of Self-assembly by Hairpin Formation

Abstract

We continue the investigation of three operations on words and languages with motivations coming from DNA biochemistry, namely unbounded and bounded hairpin completion and hairpin lengthening. We first show that each of these operations can be used for replacing the third step, the most laborious one, of the solution to the CNF-SAT reported in [28]. As not all the bounded/unbounded hairpin completion or lengthening of semilinear languages remain semilinear, we study sufficient conditions for semilinear languages to preserve their semilinearity property after applying once either the bounded or unbounded hairpin completion, or lengthening. A similar approach is then started for the iterated variants of the three operations. A few open problems are finally discussed.