On vocabulary size of grammar-based codes

Details On vocabulary size of grammar-based codes On vocabulary size of grammar-based codes

2007-01-08

arxiv.org/abs/cs/0701047v2

Computer Science

Information Theory

5 pages, accepted to ISIT 2007 and corrected

Scientific paper

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.

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