Pseudoknot-Generating Operation

A pseudoknot is an intra-molecular structure formed primarily in RNA strands and much research has been done to predict efficiently pseudoknot structures in RNA. We define an operation that generates all pseudoknots from a given sequence and consider algorithmic and language theoretic properties of the operation. We give an efficient algorithm to decide whether a given string is a pseudoknot of a regular language L—the runtime is linear if L is given by a deterministic finite automaton. We consider closure and decision properties of the pseudoknot-generating operation. For DNA encoding applications, pseudoknot structures are undesirable. We give polynomial-time algorithms to decide whether 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.