On a property of probabilistic context-free grammars

Abstract

It is proved that for a probabilistic context-free language L(G), the population density of a character (terminal symbol) is equal to its relative density in the words of a sample S from L(G) whenever the production probabilities of the grammar G are estimated by the relative frequencies of the corresponding productions in the sample.

Keywords

• probabilistic grammars
• stochastic expectation matrix
• consistency and character density.