Computational mechanics, an approach to structural complexity, defines a pr
ocess's causal states and gives a procedure for finding them. We show that
the causal-state representation -an epsilon -machine-is the minimal one con
sistent with accurate prediction. We establish several results on epsilon -
machine optimality and uniqueness and on how epsilon -machines compare to a
lternative representations. Further results relate measures of randomness a
nd structural complexity obtained from epsilon -machines to those from ergo
dic and information theories.