Evolutionary Automata: Expressiveness and Convergence of Evolutionary Computation

Abstract

Expressiveness and convergence of evolutionary computation (EC) is studied using the evolutionary automata model. It turns out that all standard classes of evolutionary automata are equally expressive when they operate in the terminal mode, i.e. in the terminal mode, evolutionary finite automata (EFA) are as expressive as evolutionary pushdown automata, evolutionary linearly bounded automata, evolutionary Turing machines or evolutionary inductive Turing machines. For example, the simplest class of evolutionary automata, EFA, can accept all recursively enumerable languages (i.e. EFA have power of Turing machines) and even more—they can accept languages that are not recursively enumerable. Due to utilization of evolutionary automata, we obtain also very simple sufficient conditions for convergence of EC.