ON A SIMPLE COMBINATORIAL STRUCTURE SUFFICIENT FOR SYBLYING NONTRIVIAL SELF-REPRODUCTION

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Abstract
An abstract research on self-reproduction from the viewpoint of systems theory is made, investigating the problem of how simple the combinatorial laws of formal systems can be chosen and to still ensure nontrivial self-reproduction. We take as a base the heuristic of the theory of cellular automata in the sense of von Neumann. We operate in a formal, microscopic, submolecular world as our patterns of cells shall represent some kind of artificial molecules. Computation- and construction-universal, self-reproducing systems are regarded as artificial living beings according to the common heuristic. A simple combinatorial system M of only four very simple dynamic laws is introduced and it can be shown that even in a world governed by this system M nontrivial self-reproduction can be established, thus illuminating what simple combinatorial structures allow for the handling of such logical somewhat difficult phenomenas as self-organization, self-reproduction, etc. To receive a model slightly more adapted to nature than the concepts of cellular automata our system M obeys the law of microscopic reversibility, allows concurrent activities, and needs no regulation by a synchronizing device.

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