Universality for Turing Machines, Inductive Turing Machines and Evolutionary Algorithms

Authors:
Mark Burgin;Eugene Eberbach
Affiliations:
(Correspd.) Dept. of Mathematics, University of California, Los Angeles, CA 90095, USA. mburgin@math.ucla.edu;Dept. of Engineering and Science, Rensselaer Polytechnic Institute, Hartford, CT 06120, USA. eberbe@rpi.edu
Venue:
Fundamenta Informaticae - Machines, Computations and Universality, Part I
Year:
2009

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Abstract

The aim of this paper is the development of foundations for evolutionary computations. To achieve this goal, a mathematical model of evolutionary automata is introduced and studied. The main classes of evolutionary automata considered in this paper are evolutionary Turing machines and evolutionary inductive Turing machines. Various subclasses and modes of evolutionary computation are defined. Problems of existence of universal objects in these classes are explored. Relations between Turing machines, inductive Turing machines, evolutionary Turing machines, and evolutionary inductive Turing machines are investigated.