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Summary: Relating Probabilistic Grammars and Automata
Steven Abney David McAllester Fernando Pereira
AT&T Labs-Research
180 Park Ave
Florham Park NJ 07932
{abney, dmac, pereira}@research.att.com
Abstract
Both probabilistic context-free grammars
(PCFGs) and shift-reduce probabilistic push-
down automata (PPDAs) have been used for
language modeling and maximum likelihood
parsing. We investigate the precise relationship
between these two formalisms, showing that,
while they define the same classes of probabilis-
tic languages, they appear to impose different
inductive biases.
1 Introduction
Current work in stochastic language models
and maximum likelihood parsers falls into two
main approaches. The first approach (Collins,
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