text: There may be some interesting ideas here,  but I think in many places the mathematical\ndescription is very confusing and/or flawed. To give some examples:\n\n* Just before section 2.1.1, P(T) = \\prod_{p \\in Path(T)} ... : it's not clear \nat all clear that this defines a valid distribution over trees. There is an\nimplicit order over the paths in Path(T) that is simply not defined (otherwise\nhow for x^p could we decide which symbols x^1 ... x^{p-1} to condition\nupon?)\n\n \"We can write S -> O | v | \\epsilon...\"  with S, O and v defined as sets.\n This is certainly non-standard notation, more explanation is needed.\n\n \"The observation is generated by the sequence of left most \nproduction rules\". This appears to be related to the idea of left-most\nderivations in context-free grammars.  But no discussion is given,  and\nthe writing is again vague/imprecise.\n\n \"Although the above grammar is not, in general, context free\" - I'm not\nsure what is being referred to here.  Are the authors referring to the underlying grammar,\nor the lack of independence assumptions in the model?  The grammar\nis clearly context-free;  the lack of independence assumptions is a separate\nissue.\n\n \"In a probabilistic context-free grammar (PCFG), all production rules are\nindependent\":  this is not an accurate statement,  it's not clear what is meant\nby production rules being independent.  More accurate would be to say that\nthe choice of rule is conditionally independent of all other information \nearlier in the derivation, once the non-terminal being expanded is\nconditioned upon.