Journal of Statistical Physics

, Volume 104, Issue 3–4, pp 817–879 | Cite as

Computational Mechanics: Pattern and Prediction, Structure and Simplicity

  • Cosma Rohilla Shalizi
  • James P. Crutchfield
Article

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.

complexity computation entropy information pattern statistical mechanics causal state ∈-machine 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Cosma Rohilla Shalizi
    • 1
    • 2
  • James P. Crutchfield
    • 1
  1. 1.Santa Fe InstituteSanta Fe
  2. 2.Physics DepartmentUniversity of Wisconsin-MadisonMadison

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