On the Generative Power of Grammars for RNA Secondary Structure

Several grammars have been proposed for representing RNA secondary structure including pseudoknots such as simple linear tree adjoining grammar (sl-tag), extended sl-tag (esl-tag) and RNA pseudoknot grammar (rpg). The main purpose of this paper is to compare the generative power of these grammars by identifying them as subclasses of multiple context-free grammars (mcfg). Specifically, it is shown that the class of languages generated by esl-tag (ESL-TAL) properly includes the class of languages generated by sl-tag (SL-TAL) and the class of languages generated by cfg. Also, we show that the class of languages generated by rpg coincides with the class of languages generated by mcfg with dimension one or two and rank one or two. Furthermore, it is shown that SL-TAL is a full trio and ESL-TAL is a substitution closed full AFL. key words: RNA secondary structure, pseudoknot, multiple context-free grammar, tree adjoining grammar