Evolutionary Information Theory

Mark Burgin

doi:10.3390/info4020124

Abstract

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.

Highlights

Evolutionary information theory studies information in the context of evolutionary processes
Developing the main ideas of algorithmic information theory in the direction of evolutionary processes, here we introduce and study two kinds of evolutionary information: evolutionary information necessary to develop a constructive object by a given system of evolutionary algorithms and evolutionary information in an object, e.g., in a text that allows making simpler development of another object by a given system of evolutionary algorithms
We introduce and study evolutionary information necessary to develop a constructive object by a given system of evolutionary algorithms

Summary

Introduction

Evolutionary information theory studies information in the context of evolutionary processes. After biologists found basic regularities of biological evolution, computer scientists began simulating evolutionary processes and utilizing operations found in nature for solving problems with computers. The evolutionary information size of an object x with respect to a class H shows how much information it is necessary for building (computing or constructing) this object by algorithms/automata from the class H. The quantity of evolutionary information in an object y about an object x with respect to an automaton/machine A shows to what extent utilization of information in y reduces information necessary for building (computing or constructing) the object x by A without any additional information. The author is grateful to unknown reviewers for their useful comments

Evolutionary Machines and Computations

Universal Evolutionary Automata

Evolutionary Information Size

Evolutionary Information in an Object

Modeling Physical Evolution with Evolutionary Machines

Conclusions