Outline for a Logical Theory of Adaptive Systems

The purpose of this paper is to outline a theory of automata appropriate to the properties, requirements and questions of adaptation. The conditions that such a theory should satisfy come from not one but several fields: It should be possible to formulate, at least in an abstract version, some of the key hypotheses and problems from relevant parts of biology, particularly the areas concerned with molecular control and neurophysiology. The work in theoretical genetics initiated by R. A. Fisher [5] and Sewall Wright [24] should find a natural place in the theory. At the same time the rigorous methods of automata theory should be brought to bear (particularly those parts concerned with growing automata [1, 2, 3, 7, 8, 12, 15, 18, 23]). Finally the theory should include among its models abstract counterparts of artificial adaptive systems currently being studied, systems such as Newell-Shaw-Simon's "General Problem Solver" [13], Selfridge's "Pandemonium" [17], von Neumann's self-reproducing automata [22] and Turing's morphogenetic systems [19, 20]. The theory outlined here (which is intended as a theory and not the theory) is presented in four main parts. Section 2 discusses the study of adaptation via generation procedures and generated populations. Section 3 defines a continuum of generation procedures realizable in a reasonably direct fashion. Section 4 discusses the realization of generation procedures as populations of interacting programs in an iterative circuit computer. Section 5 discusses the process of adaptation in the context of the earlier sections. The paper concludes with a discussion of the nature of the theorems of this theory. Before entering upon the detailed discussion, one general feature of the theory should be noted. The interpretations or models of the theory divide into two broad categories: "complete" models and "incomplete" models. The "complete" models comprise the artificial systems--systems with properties and specifications completely delimited at the outset (cf. the rules of a game). One set of "complete" models for the theory consists of various programmed parallel computers. The "incomplete" models encompass natural systems. Any natural system involves an unlimited number of factors and, inevitably, the theory can handle only a selected few of these. Because there will always be variables which do not have explicit counterparts in the theory, the derived statements must be approximate relative to natural systems. For this reason it helps greatly that