Computational Mechanics: Pattern and Prediction, Structure and Simplicity

Details Computational Mechanics: Pattern and Prediction, Structure and Simplicity Computational Mechanics: Pattern and Prediction, Structure and Simplicity

1999-07-13

arxiv.org/abs/cond-mat/9907176v2

Journal of Statistical Physics 104 (2001): 816--879

Physics

Condensed Matter

Statistical Mechanics

29 pages, 4 EPS figures, http://www.santafe.edu/projects/CompMech/papers/cmppss.html Revision: Typos fixed, minor tweaks to

Scientific paper

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 $\epsilon$-machine--is the minimal one consistent with accurate prediction. We establish several results on $\epsilon$-machine optimality and uniqueness and on how $\epsilon$-machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from $\epsilon$-machines to those from ergodic and information theories.

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