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Computational Mechanics: Pattern and Prediction, Structure and Simplicity

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Abstract

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.

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  1. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico, 87501

    Cosma Rohilla Shalizi & James P. Crutchfield

  2. Physics Department, University of Wisconsin-Madison, Madison, Wisconsin, 53706

    Cosma Rohilla Shalizi

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Shalizi, C.R., Crutchfield, J.P. Computational Mechanics: Pattern and Prediction, Structure and Simplicity. Journal of Statistical Physics 104, 817–879 (2001). https://doi.org/10.1023/A:1010388907793

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