A model based on intersections of stochastic context free grammars is presented to allow for the modeling of RNA pseudoknot structures. The model runs relatively fast, having the same order running time as stochastic context free grammar parsers. The model is shown to be able to perform database searches and find RNA sequences which resemble RNA pseudoknots which bind biotin. The problem domain of RNA biotin binders has significance in the support of the RNA world model of early life on earth.