October 14 2016 4:15 AM, "Peter Cashin" <cashin.pe...@gmail.com> wrote: > Hi > > Yes, I seem to remember that Bryan Ford pointed out the “middle finder” > grammar. > > It is CF but not PEG: > > s = x s x / x > i.e an odd number of x’s. There is a similar one for an even number. > > I was interested to discover that this can be done with an extended PEG > grammar. > > Cheers, > Peter.
That is also a PEL (parsing expression language, i.e. recognizable by a PEG), you just have to rewrite it: <S> = xx <S> / x There is, as far as I know, no known examples of a CFL which cannot be described by a PEG. The argument for "CF not-less-than PEG" instead relies on a complexity result due to Lee[1] which says that a linear-time CFG parser would imply the existence of an efficient O(m^2.333333...) algorithm for boolean matrix multiplication. To the best of my knowledge, there is no proof that such an algorithm cannot exist, but none has been found despite a mountain of work on the subject. So, the question "CF < PEG?" is currently open: neither a formal proof nor a counter-example has been found. [1] https://arxiv.org/abs/cs/0112018 Regards, Ulrik Rasmussen _______________________________________________ PEG mailing list PEG@lists.csail.mit.edu https://lists.csail.mit.edu/mailman/listinfo/peg
