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{{Randomness, Structure and Causality}}
{{Randomness, Structure and Causality}}


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== Abstracts ==
 
<br>
 
The Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts<br>
 
Debowski, Lukasz (ldebowsk@ipipan.waw.pl<br>
Polish Academy of Sciences<br>
<br>
<p>
We will present a new explanation for the distribution of words in
natural language which is grounded in information theory and inspired
by recent research in excess entropy. Namely, we will demonstrate a
theorem with the following 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.  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. Besides the theorem, we will exhibit a few stochastic processes
to which this and similar statements can be related.
 
<p>
 
[[http://arxiv.org/abs/0810.3125]] and [[http://arxiv.org/abs/0911.5318]]

Revision as of 18:39, 16 December 2010

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Abstracts


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

Debowski, Lukasz (ldebowsk@ipipan.waw.pl
Polish Academy of Sciences

We will present a new explanation for the distribution of words in natural language which is grounded in information theory and inspired by recent research in excess entropy. Namely, we will demonstrate a theorem with the following 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.  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. Besides the theorem, we will exhibit a few stochastic processes to which this and similar statements can be related.

[[1]] and [[2]]