Towards the Sequence Design Preventing Pseudoknot Formation

This paper addresses a pseudoknot-freeness problem of DNA and RNA sequences, motivated by biomolecular computing. WatsonCrick (WK) complementarity forces DNA strands to fold into themselves and form so-called secondary structures, which are usually undesirable for biomolecular computational purposes. This paper studies pseudoknot-bordered words, a mathematical formalization of a common secondary structure, the pseudoknot. We obtain several properties of WK-pseudoknot-bordered and -unbordered words. One of the main results of the paper is that a sufficient condition for a WK-pseudoknotunbordered word u to result in all words in u being WK-pseudoknotunbordered is for u not to be a primitive word.