Mechanisms and Robots

Abstract

A mechanism is a device with N states Pl ..... PN which change automatically and this change p. - p. is given by a function Ri -- j. The z j behavior of a mechanism is specified by an iterative structure which is independent of the enumeration of the states. The number of such structures can be obtained using methods of G. Polya, Acta Mathematica, v. 68 (1937) p. 145-254. The relation with Boolean algebra is readily obtained. If the change of state is dependent on the environment, the mechanism is termed a robot. Robots which have specified probability responses to changes in the environment are described. The asymptotic behavior of a robot is investigated. A general method for constructing mechanisms and robots and their relation to computers are described. Mathematical notions are used rather than the methods of formal logic and, consequently, much irrevelant discussion is avoided.