Mechanisms and Robots

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. I n t r o d u c t i o n A mechanism is a discrete s tate device whose states change automatically. If this change is dependent upon the environment, the mechanism is called a robot. Our treatment is based on mathematical notions and we consider the device as a whole. While such a device can be described by Boolean algebra, this would normally be done in the present treatment only if the device is a combination of binary components. The use of mathematical notions rather than those from formal logic avoids the introduction of much irrelevant discussion. We obtain a mathematical description of a mechanism in section 1 and also an analysis of the possibili t ies for different behaviors. The number of such possibil i t ies is discussed in section 2 and evaluated by means * R e c e i v e d . J u n e . 1954. r e v i s e d Sep tember , t954 C o p y r i g h t , 1 955, A s s o c i a t i o n for C o m p u t i n g Machinery