Consistency of Probabilistic Context-Free Grammars

Abstract

We present an algorithm for deciding whether an arbitrary proper probabilistic context-free grammar is consistent, i.e., whether the probability that a derivation terminates is one. Our procedure has time complexity $\\\\mathcal O(n^3)$ in the unit-cost model of computation. Moreover, we develop a novel characterization of consistent probabilistic context-free grammars. A simple corollary of our result is that training methods for probabilistic context-free grammars that are based on maximum-likelihood estimation always yield consistent grammars