Formally testing liveness by means of compression rates

Abstract

We present a formal method to determine whether there exist living creatures in a given computational environment. Our proposal is based on studying the evolution of the entropy of the studied system. In particular, we check whether there exist entities decreasing the entropy in some parts, while increasing it in the rest of the world, which fits into the well-known maximum entropy production principle. The entropy of a computational environment is measured in terms of its compression rate with respect to some compression strategy. Some life-related notions such as biodiversity are quantified as well. These ideas are presented by means of formal definitions. A toy example where a simple living structure is identified in a video stream is presented, and some results are reported. © 2008 Springer-Verlag Berlin Heidelberg.