By Topic

Entropies and combinatorics of random branching processes and context-free languages

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
M. I. Miller ; Dept. of Electr. Eng., Washington Univ., St. Louis, MO, USA ; J. A. O'Sullivan

The entropies and combinatorics of trees that branch according to fixed but finite numbers of rules are studied. Context-free grammars are used to categorize the ways in which nodes branch to yield daughter nodes, thus providing an organized setting to examine the entropies for random branching processes whose realizations are trees and whose probabilities are determined by probabilities associated with the substitution rules of the grammar. Normalized entropy rates H are derived for the critical branching rate and supercritical branching rate processes. An equipartition theorem is proved for the supercritical processes. A strong departure from classical theorems for Markov sources occurs for supercritical branching processes as the typical sets have supergeometric growth rates. The combinatorics of the set of all trees that can be generated from the context-free substitution rules is also studied

Published in:

IEEE Transactions on Information Theory  (Volume:38 ,  Issue: 4 )