Recursively Generated Evolutionary Turing Machines and Evolutionary Automata

Abstract

One of the roots of evolutionary computation was the idea of Turing about unorganized machines. The goal of this paper is the development of foundations for evolutionary computations, connecting Turing’s ideas and the contemporary state of art in evolutionary computations. The theory of computation is based on mathematical models of computing automata, such as Turing machines or finite automata. In a similar way, the theory of evolutionary computation is based on mathematical models of evolutionary computing automata, such as evolutionary Turing machines or evolutionary finite automata. The goal of the chapter is to study computability in the context of the theory of evolutionary computation and genetic algorithms. We use basic models of evolutionary computation, such as different types of evolutionary machines, evolutionary automata and evolutionary algorithms, for exploration of the computing and accepting power of various kinds of evolutionary automata. However, we consider not only how evolutionary automata compute but also how they are generated because a rigorous study of construction techniques for computational systems is an urgent demand of information processing technology. Generation schemas for evolutionary automata are studied and applied to computability problems.