International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 2, Pages 403-406
doi:10.1155/S0161171283000356
On the property of probabilistic context-free grammars
R. Chaudhuri1
and A.N.V. Rao2
1Computer Science Group, Department of Mathematics, East Carolina University, Greenville 27834, North Carolina, USA
2Centre of Applied Mathematics, Department of Mathematics, University of South Florida, Tampa 33620, Florida, USA
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.