The role of randomness in cybernetic systems

This paper demonstrates that random phenomena, although most often treated in the context of system malfunction, can play major constructive roles in the philosophy, theory and application of cybernetic systems. A control-theoretic example is given to show that a simple stochastic automaton can solve a regulator problem otherwise requiring a recursive automaton, and insoluble for finite-state automata. An identification-theoretic example is given to show that the assumption of causality in modelling a simple acausal system can lead to models which grow in size, on average, precisely at the rate of acquisition of observations. The significance and applications of these results are discussed and illustrated. Finally, it is suggested that the interpretation of stochastic automata theory in terms of system malfunction is far too restrictive in its stimulation of theoretical developments. A wider view of the role of random phenomena might aid the development of results and techniques which actually deliver what automata theory has always seemed to promise.