Evolutionary Turing in the Context of Evolutionary Machines

TL;DR

This paper develops a mathematical framework for evolutionary machines inspired by Turing's unorganized machines, analyzing their properties, computational power, and relation to classical automata.

Contribution

It introduces a general approach to modeling evolutionary processes in computational systems, connecting Turing's ideas with modern evolutionary computation theory.

Findings

Defined operations for evolutionary machines and studied their closure properties.

Analyzed linguistic and functional equivalence of evolutionary machines.

Compared the computational power of evolutionary machines to classical automata.

Abstract

One of the roots of evolutionary computation was the idea of Turing about unorganized machines. The goal of this work is the development of foundations for evolutionary computations, connecting Turing's ideas and the contemporary state of art in evolutionary computations. To achieve this goal, we develop a general approach to evolutionary processes in the computational context, building mathematical models of computational systems, functioning of which is based on evolutionary processes, and studying properties of such systems. Operations with evolutionary machines are described and it is explored when definite classes of evolutionary machines are closed with respect to basic operations with these machines. We also study such properties as linguistic and functional equivalence of evolutionary machines and their classes, as well as computational power of evolutionary machines and their classes, comparing of evolutionary machines to conventional automata, such as finite automata or Turing machines.