Self-reproducing Automata Research Articles

R70-32 Tessellation Automata

In the last fifteen years many researchers working in such diverse areas as pattern recognition, parallel computation, self-reproducing automata, pattern recognition, evolution theory, information retrieval, and integrated circuit technology have found it convenient to use an array of identical intercommunicating finite-state machines as their underlying model. This naturally suggests that it would be worthwhile to develop a comprehensive theory of such arrays which would then provide a common framework for all these areas. Yamada and Amoroso have taken up this suggestion, and this paper is the first in a proposed series of papers reporting their results. However, as they readily admit, they have not attempted to produce a truly comprehensive model (an ill-defined, if not impossible, task), but rather they have been concerned with a "fairly general" model based largely on the earlier work of Moore.

Tessellation Automata

Certain mathematical studies of pattern recognition, evolution theories, and self-reproducing automata motivated the definition of the tessellation automaton which is a mathematical model of an infinite array of uniformly interconnected identical finite-state machines. Each machine is capable of changing state at discrete time steps as a function of the states of other machines in the array and inputs that act as environmental changes to the array. This model can embed all the models used in the studies mentioned above, and may serve as a unifying framework. In this first paper certain basic properties of tessellation automata are developed that are intended to serve as an introduction to the more specific studies to be reported in the sequel.

Automata theory and development: Part I

In his recent book “Cybernetics and Development”, Michael Apter has persuasively shown that many problems of embryological development are ripe for cybernetic treatment. Recent results, based on von Neumann's theory of self-reproducing automata, yield models more “biological” than those presented by Apter. We extend these results to emphasize their relevance to a theory of development.

A resolution of Rosen's paradox for self-reproducing automata.

Rosen (Bull. Math Biophysics. 1959) has argued that a self-reproducing automaton of the type originally described by von Neumann is impossible because of a logical paradox inherent in its definition. The paradox is resolved by explicitly allowing errors (mutations) in the system and thus introducing evolution. There is no paradox in an automaton, originating from a slightly different ancestor through mutation. The von Neumann model thus becomes realistic and useful for a discussion of biological phenomena.

On a logical paradox implicit in the notion of a self-reproducing automation

The notion of automaton as used by J. von Neumann is formalized according to methods previously described (Rosen, 1958,Bull. Math. Biophysics 20, 245–60; 317–41). It is observed that a logical paradox arises when one attempts to describe the notion of self-reproducing automaton in this formalism. This paradox is discussed, together with some of the recent attempts to construct automata which exhibit self-reproduction. The relation of these results to biological problems is then investigated.

Automata of high complexity and methods of increasing their reliability by redundancy

A natural question regarding the limits of automation is: What are the limits of automata, or how closely can an automaton imitate the human being—what kind of specific processes can an automaton do better, more quickly, and more reliably than the human being? Aspects of these questions may be treated from the standpoint of automata theory. We will give brief summaries of two far-reaching theories in this field: the Turing theory of the possibilities of computing machines, and the von Neumann theory of self-reproducing automata. The question of reliability becomes rather serious when the complexity of the automaton becomes large. An attempt towards a theory of how redundancy should be applied on different levels for reducing the influence of temporary component errors in a universal computing machine is given.