On vocabulary size of grammar-based codes
<|reference_start|>On vocabulary size of grammar-based codes: 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.<|reference_end|>
@article{debowski2007on,
    title={On vocabulary size of grammar-based codes},
    author={Lukasz Debowski},
    journal={2007 IEEE International Symposium on Information Theory, 91-95},
    year={2007},
    doi={10.1109/ISIT.2007.4557209},
    archivePrefix={arXiv},
    eprint={cs/0701047},
    primaryClass={cs.IT cs.CL math.IT}
}