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International Journal of Mathematics and Mathematical Sciences
Volume 6, Issue 2, Pages 403-407
http://dx.doi.org/10.1155/S0161171283000356

On a property of probabilistic context-free grammars

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

Received 14 February 1983

Copyright © 1983 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.