English

On vocabulary size of grammar-based codes

Information Theory 2020-03-11 v2 Computation and Language math.IT

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.

Keywords

Cite

@article{arxiv.cs/0701047,
  title  = {On vocabulary size of grammar-based codes},
  author = {Lukasz Debowski},
  journal= {arXiv preprint arXiv:cs/0701047},
  year   = {2020}
}

Comments

5 pages, accepted to ISIT 2007 and corrected

R2 v1 2026-07-22T12:27:40.146Z