Computational Mechanics: Pattern and Prediction, Structure and Simplicity

IV Computational Mechanics 9 A Causal States . . . . . . . . . . . . . . 9 Causal States of a Process Defined . . . 9 1 Morphs . . . . . . . . . . . . . . . . 10 Independence of Past and Future Conditional on a Causal State . . . 10 2 Homogeneity . . . . . . . . . . . . . 11 Strict Homogeneity . . . . . . . . . 11 Weak Homogeneity . . . . . . . . . 11 Strict Homogeneity of Causal States 11 B Causal State-to-State Transitions . . . 11 Causal Transitions . . . . . . . . . . . . 11 Transition Probabilities . . . . . . . . . 11 C -Machines . . . . . . . . . . . . . . . . 12 An -Machine Defined . . . . . . . . . . 12 -Machines Are Monoids . . . . . . . . 12 -Machines Are Deterministic . . . . . 12 -Machines Are Markovian . . . . . . . 12 -Machine Reconstruction . . . . . . . . 13