Brute force search. The distribution of sensitivity and corresponding PPV of grammars with at most 2 nonterminal variables. Approximately one quarter of grammars have sensitivity 0, as many cannot produce long strings. It is only the larger grammars that start to predict long strings which might correspond to structure. However, the prediction quality is still poor by both measures.
WJ Anderson et al. BMC Bioinformatics 2012 13:78 doi:10.1186/1471-2105-13-78