On vocabulary size of grammar-based codes
arXiv:cs/0701047 · doi:10.1109/ISIT.2007.4557209
Abstract
We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog of algorithmic mutual information. The aim is to strengthen inequalities which were discussed in a weaker form in linguistics but shed some light on redundancy of efficiently computable codes. The main contribution of the paper is a construction of universal grammar-based codes for which the excess lengths can be bounded easily.
5 pages, accepted to ISIT 2007 and corrected