Pseudoknot-generating operation

A pseudoknot is a crucial intra-molecular structure formed primarily in RNA strands and closely related to important biological processes. This motivates us to define an operation that generates all pseudoknots from a given sequence and consider algorithmic and language theoretic properties of the operation. We design an efficient algorithm that decides whether or not a given string is a pseudoknot of a regular language L. Our algorithm runs in linear time if L is given by a deterministic finite automaton. We study closure and decision properties of the pseudoknot-generating operation. For DNA encoding applications, pseudoknot structures are undesirable. We give polynomial-time algorithms that check whether or not a regular language L contains a pseudoknot or a pseudoknot generated by some string of L. Furthermore, we show that the corresponding questions for context-free languages are undecidable.