On vocabulary size of grammar-based codes

Lukasz Debowski

doi:10.1109/isit.2007.4557209

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On vocabulary size of grammar-based codes

Lukasz Debowski

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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.

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Lukasz Debowski. 2007-01-08. On vocabulary size of grammar-based codes. https://doi.org/10.1109/isit.2007.4557209

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