Evolutionary Information Theory

Evolutionary information theory is a constructive approach that studies information in the context of evolutionary processes, which are ubiquitous in nature and society. In this paper, we develop foundations of evolutionary information theory, building several measures of evolutionary information and obtaining their properties. These measures are based on mathematical models of evolutionary computations, machines and automata. To measure evolutionary information in an invariant form, we construct and study universal evolutionary machines and automata, which form the base for evolutionary information theory. The first class of measures introduced and studied in this paper is evolutionary information size of symbolic objects relative to classes of automata or machines. In particular, it is proved that there is an invariant and optimal evolutionary information size relative to different classes of evolutionary machines. As a rule, different classes of algorithms or automata determine different information size for the same object. The more powerful classes of algorithms or automata decrease the information size of an object in comparison with the information size of an object relative to weaker4 classes of algorithms or machines. The second class of measures for evolutionary information in symbolic objects is studied by introduction of the quantity of evolutionary information about symbolic objects relative to a class of automata or machines. To give an example of applications, we briefly describe a possibility of modeling physical evolution with evolutionary machines to demonstrate applicability of evolutionary information theory to all material processes. At the end of the paper, directions for future research are suggested.