On the Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts

{\L}ukasz D\k{e}bowski
Arxiv ID: 810.3125Last updated: 3/11/2020
The article presents a new interpretation for Zipf-Mandelbrot's law in natural language which rests on two areas of information theory. Firstly, we construct a new class of grammar-based codes and, secondly, we investigate properties of strongly nonergodic stationary processes. The motivation for the joint discussion is to prove a proposition with a simple informal statement: If a text of length $n$ describes $n^\beta$ independent facts in a repetitive way then the text contains at least $n^\beta/\log n$ different words, under suitable conditions on $n$. In the formal statement, two modeling postulates are adopted. Firstly, the words are understood as nonterminal symbols of the shortest grammar-based encoding of the text. Secondly, the text is assumed to be emitted by a finite-energy strongly nonergodic source whereas the facts are binary IID variables predictable in a shift-invariant way.

PaperStudio AI Chat

I'm your research assistant! Ask me anything about this paper.

Related papers

Commercial Disclosure
© 2023 Paper Studio™. All Rights Reserved.