  Treebanks, such as the Penn Treebank (PTB), offer a simple approach to
obtaining a broad coverage grammar: one can simply read the grammar off the
parse trees in the treebank. While such a grammar is easy to obtain, a
square-root rate of growth of the rule set with corpus size suggests that the
derived grammar is far from complete and that much more treebanked text would
be required to obtain a complete grammar, if one exists at some limit. However,
we offer an alternative explanation in terms of the underspecification of
structures within the treebank. This hypothesis is explored by applying an
algorithm to compact the derived grammar by eliminating redundant rules --
rules whose right hand sides can be parsed by other rules. The size of the
resulting compacted grammar, which is significantly less than that of the full
treebank grammar, is shown to approach a limit. However, such a compacted
grammar does not yield very good performance figures. A version of the
compaction algorithm taking rule probabilities into account is proposed, which
is argued to be more linguistically motivated. Combined with simple
thresholding, this method can be used to give a 58% reduction in grammar size
without significant change in parsing performance, and can produce a 69%
reduction with some gain in recall, but a loss in precision.
