Evaluating two methods for Treebank grammar compaction

Treebanks, such as the Penn Treebank, provide a basis for the automatic creation of broad coverage grammars. In the simplest case, rules can simply be ‘read off’ the parse-annotations of the corpus, producing either a simple or probabilistic context-free grammar. Such grammars, however, can be very large, presenting problems for the subsequent computational costs of parsing under the grammar. In this paper, we explore ways by which a treebank grammar can be reduced in size or ‘compacted’, which involve the use of two kinds of technique: (i) thresholding of rules by their number of occurrences; and (ii) a method of rule-parsing, which has both probabilistic and non-probabilistic variants. Our results show that by a combined use of these two techniques, a probabilistic context-free grammar can be reduced in size by 62% without any loss in parsing performance, and by 71% to give a gain in recall, but some loss in precision

On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic