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[[Media:Agenda.pdf|Agenda PDF]]
== 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 <math>n</math>
 
describes <math>n^\beta</math> independent facts in a repetitive way then the
 
text contains at least <math>n^\beta/\log n</math> 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.
 
<br>
 
<br>
 
 
 
Links: [[http://arxiv.org/abs/0810.3125]] and [[http://arxiv.org/abs/0911.5318]]
 

Latest revision as of 01:17, 3 January 2011