Entropies and combinatorics of random branching processes andcontext-free languages
Miller, M.I.; Oapos;Sullivan, J.A.
Information Theory, IEEE Transactions on
Volume 38, Issue 4, Jul 1992 Page(s):1292 - 1310
Digital Object Identifier   10.1109/18.144710
Summary: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

» View citation and abstract

Log in by entering your IEEE Web Account Username and Password.

IEEE Communications Society members: If you subscribe to the IEEE Electronic Periodicals Package or IEEE Electronic Periodicals Package Plus, you must access your subscription at www.comsoc.org.

Check with your librarian, information professional, or system manager to determine if you need to log in. Please complete the online Technical Support Form if you need assistance.

Select the Purchase History link to access the document. You will have 5 Days after purchase to access the Full Text PDF. Please complete the online Technical Support Form if you need assistance.

• Search and access Abstract records free of charge
• Register for table of contents alerts
• Purchase Full Text PDF documents

» Learn more about subscription options or how to become an IEEE Member.