Information Theory

Recently our group and others conjectured that, in general, systems with continuously evolving spatio-temporal structures are open to symbolic encoding. In this respect we showed that parallel cellular automata with microscopic stochastic update rules are amenable to the modeling of macroscopic processes and the explicit simulation on parallel and distributed systems.

A possible approach comes from recent work on epsilon-machines revealing the group and semi-group symmetries possessed by the spatial patterns and indicating the minimum amount of memory required to reproduce the configuration ensemble, a quantity known as the statistical complexity. It was shown that the notion of excess entropy, a form of mutual information, can be used as an information theoretic measure of apparent spatial memory required to describe the complex systems. However, there is no unique indicator of complexity in the same way as e.g. entropy characterizes disorder, nor are there any successful mean field approaches or renormalization theories known to capture the hierarchy of information processing observed.
Evolution of space-time processes in parallel cellular automata is studied through (epsilon-tau)-entropy models.

To summarize, within the context of cellular automata as universal parallel computing machines and as generic models of dynamic complex systems, we aim to study fundamental questions related to the (distributed) computational structure of natural processes.