Finite Automata, Pattern Recognition and Perceptrons

A large class of finite au tomata can be classified as devices which exhibit some type of selective responses to parts of their "environment ." In addition, many au tomata tha t are of current interest are intended to have definite similarities with, or to be in some sense analogous to human nervous systems (insofar as the lat ter are understood). The all too frequent overemphasis on these aspects of automata , with the subsequent morass of psychological and physiological terminology introduced, conceals the nature of the basic (mathematical) problem tha t must be considered. The first par t of this paper (Section 2) presents a formulat ion of the general problem posed by many automata, namely, to find a specific set function or class of set functions. The formulation presented can be extended easily to include a more general class of au tomata (or discrimination problems) than tha t explicitly considered; one such extension is discussed in Section 7. The problem of "recognizing" geometric pat terns by automata is considered in Section 3. A specific device tha t solves such problems with some generality is described. This example serves to yield insight into the formalities introduced and discussed throughout the other sections of the paper. The principles of this au tomaton are so t ransparent tha t an anthropomorphic description of it, in such terms as "concept formation", "cognitive system", etc. is clearly not called for. However, if the device were described only by its function, and the simple trick of its operation were concealed, it would certainly qualify as an automaton with similarities to certain types of human stimulus-response reactions. Sections 4 and 5 are concerned with a more or less specifically defined device called a "perceptron." An a t tempt is made to define a perception-like automaton as a nerve-net (in the sense of Kleene [2] and yon Neumann [3]). Although there are some difficulties in this formulation, due to vagueness and contradictions in the descriptions of pereeptrons in [4], it seems clear tha t the proposed model has or can have all of the features of a perceptron which are claimed to be novel. I t is then shown tha t such a device can be represented a t any ins tant of time as a very special type of set function. Some questions regarding the possibility of solving the basic discrimination problem with these special set functions are then considered.