Journal of Statistical Physics, Vol. 104, Nos. 3/4, 2001. p. 817-879.
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 e-machine—is the minimal one consistent with accurate prediction. We establish several results on e-machine optimality and uniqueness and on how e-machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from e-machines to those from ergodic and information theories.