Despite their considerable expressive power, all PEGs can be parsed in linear time using a tabular or memoizing parser (8). These properties strongly suggest that CFGs and PEGs define incomparable language classes, although a formal proof that there are context-free languages not expressible via PEGs appears surprisingly elusive.  Bryan Ford, Parsing Expression Grammars: A Recognition-Based Syntactic Foundation, 2002.Is there a context-free language that is not expressible as a PEG?As pointed out by Emil, my proposed language $a^n a^* b^n$ does not work. It can be expressed as the PEG $S \to a S b / a S / \varepsilon$.
Does PEG contain CFG?
fl.formal languages;open problem;grammars;context free;parsing