## Cellular Automaton Model

The Hungarian-born American mathematician John von Neumann (1903-1957) described the cellular automaton model, a mathematical model of self-replication and destruction that is represented, typically, by a checkerboard of either fixed or infinite dimensions - each cell of which has a finite number of states (including, usually, a "quiescent/empty" state), and a finite set of neighboring cells that may influence its state. In the model, the pattern of changes are determined by transition rules that apply simultaneously to all cells in each discrete time unit. The cellular automata also incorporate certain universal features, such as "Turing machines" - named after the English mathematician Alan Mathison Turing (1912-1954) - which are hypothetical computing machines consisting of a movable head that reads, writes, or erases discrete symbols drawn from a finite set (usually, just "1" or "0"); a "Turing machine" deals with the symbols, one at a time, in separate frames marked on a limitless length of tape, and that always assumes one of a finite number of states; in principle, a "universal Turing machine" can compute anything that is computable, given sufficient time. Other related terms are Turing's test - a hypothetical test, also called the "imitation game," that attempts to determine whether or not computers can "think" (involving an actual person and an actual interrogator in different rooms who engage in a dialogue over an electronic link; at some point the first person is replaced by an "intelligent software" program that simulates human responses; Turing argued that if the remaining interrogator is free to ask probing questions, but is unable to determine whether the replies are generated by a human being or by a computer, then the computer passes the test and it is declared that the computer can "think"); and artificial intelligence (AI)

- first described by the American computer engineer John McCarthy (1927- ) - refers to the design of hypothetical, or actual, computer programs or machines to accomplish things normally done by human minds, such as writing poetry, playing chess, thinking logically, or composing music; the most demanding situations for AI (also called "machine intelligence") are problems simulating functions of intelligence that are mainly unconscious (e.g., vision and language functions); strong AI refers to the viewpoint that all thinking is computation where conscious thought may be explained according to computational principles, and where feelings of "conscious awareness" are elicited merely by particular computations performed by the brain or by a computer; and weak AI refers to the viewpoint that "conscious awareness" is a property of certain brain processes, and advances the notion that -whereas any physical behavior may be simulated by a computer using purely computational processes - computational simulation does not, in itself, elicit "conscious awareness" (cf. adaptive production system

- in AI, a production system that is able to learn by building new productions which it then adds to its memory). One of the first major events in the history of AI was the appearance of the "General Problem

Solver" - a computer program designed to simulate human problem solving, developed in 1958, and improved in 1972, by the American cognitive scientist Allen Newell (1927-1992) and the American economists/decision theorists John Clark Shaw (1933- ) and Herbert Alexander Simon (1916-2001). See also FUZZY SET THEORY; GODEL'S THEOREM. REFERENCES

Turing, A. M. (1936-37). On computable numbers. Proceedings of the London Mathematical Society, 42, pt. 3-4 (Nov.-Dec.). Turing, A. M. (1950). Computing machinery and intelligence. Mind, 59, 433-453.

(1958). Elements on a theory of human problem solving. Psychological Review, 65, 151-166. von Neumann, J. (1958). Computer and the brain. New Haven: Yale University Press.

von Neumann, J. (1966). Theory of self-reproducing automata. Edited and completed by Arthur W. Burks. Urbana: University of Illinois Press.

Minsky, M. L., & Papert, S. (1969). Per-ceptrons. Oxford, UK: M. I. T. Press.

McCarthy, J., & Lifschitz, V. (1991). Artificial intelligence and mathematical theory of computation. Boston: Academic Press.

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