Computational Mechanics: Pattern and Prediction, Structure and Simplicity

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation—an -machine—is the minimal one consistent with accurate prediction. We establish several results on -machine optimality and uniqueness and on how -machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from -machines to those from ergodic and information theories.