On pseudoknot words and their properties ?

We study a generalization of the classical notions of bordered and unbordered words, motivated by biomolecular computing. DNA strands can be viewed as finite strings over the alphabet {A, G, C, T}, and are used in biomolecular computing to encode information. Due to the fact that A is Watson-Crick (WK) complementary to T and G to C, DNA single strands that are WK complementary can bind to each other or to themselves forming so-called secondary structures. Secondary structures are usually undesirable for biomolecular computational purposes since the strands involved in such structures cannot further interact with other strands. This paper studies pseudoknot-bordered words, a mathematical formalization of a common secondary structure, the pseudoknot. We obtain several properties of WK-pseudoknotbordered and -unbordered words. One of the main results of the paper is that a sufficient condition for a WK-pseudoknot-unbordered word u to result in all words in u+ being WK-pseudoknot-unbordered is for u not to be primitive word. All our results hold for arbitrary antimorphic involutions, of which the WK complementarity function is a particular case.