The generative power of probabilistic and weighted context-free grammars

Authors:
Timothy A. D. Fowler
Affiliations:
Department of Computer Science, University of Toronto, Toronto, ON, Canada
Venue:
MOL'11 Proceedings of the 12th biennial conference on The mathematics of language
Year:
2011

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Abstract

Over the last decade, probabilistic parsing has become the standard in the parsing literature where one of the purposes of those probabilities is to discard unlikely parses. We investigate the effect that discarding low probability parses has on both the weak and strong generative power of context-free grammars. We prove that probabilistic context-free grammars are more powerful than their non-probabilistic counterparts but in a way that is orthogonal to the Chomsky hierarchy. In particular, we show that the increase in power cannot be used to model any dependencies that discrete context-free grammars cannot.