\recent Methods for Rna Modeling Using Stochastic Context-free Grammars," Proc. Combinatorial Pattern

Ribonucleic acid (RNA) strings are strings over the four-letter alphabet fA;C;G;Ug with a secondary structure of base-pairing between A U and C G pairs in the string 1 . Edges are drawn between two bases that are paired in the secondary structure and these edges have traditionally been assumed to be noncrossing. The noncrossing base-pairing naturally leads to a tree-like representation of the secondary structure of RNA strings. In this paper, we address several notions of similarity between two RNA strings that take into account both the primary sequence and secondary base-pairing structure of the strings. We present e cient algorithms for exact matching and approximate matching between two RNA strings. We de ne a notion of alignment between two RNA strings and devise algorithms based on dynamic programming. We then present a method for optimally aligning a given RNA string with unknown secondary structure to one with known sequence and structure, thus attacking the structure prediction problem in the case when the structure of a closely related sequence is known. The techniques employed to prove our results include reductions to well-known string matching problems allowing wild cards and ranges, and speeding up dynamic programming by using the tree structures implicit in the secondary structure of RNA strings.