# Randomness, Structure and Causality - Agenda

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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 ${\displaystyle n}$ describes ${\displaystyle n^{\beta }}$ independent facts in a repetitive way then the text contains at least ${\displaystyle n^{\beta }/\log n}$ 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.

Links: [[1]] and [[2]]

Automatic Identification of Information-Processing Structures in Cellular Automata

Mitchell, Melanie (mm@cs.pdx.edu)
SFI & Portland State University
Cellular automata have been widely used as idealized models of natural spatially-extended dynamical systems.  An open question is how to best understand such systems in terms of their information-processing capabilities.   In this talk we address this question by describing several approaches to automatically identifying the structures underlying information processing in cellular automata. In particular, we review the computational mechanics methods of Crutchfield et al.,  the local sensitivity and local statistical complexity filters proposed by Shalizi et al., and the information theoretic filters proposed by Lizier et al.   We illustrate these methods by applying them to several one- and two-dimensional cellular automata that have been designed to perform the so-called density (or majority) classification task.