Computational Mechanics: Pattern and Prediction, Structure and Simplicity
Cosma Rohilla Shalizi, James P. Crutchfield
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 ε-machine--is the minimal one consistent with accurate prediction. We establish several results on ε-machine optimality and uniqueness and on how ε-machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from ε-machines to those from ergodic and information theories.
Create a lesson
Related papers
Global Minima of the Thomson Problem in a Disk: A Molecular Dynamics Approach with Fixed Border Charges
Georgiy K. Lavrov, Eduard G. Nikonov
Martingale theory for heat and phase-space contraction in heterogeneous diffusions
Jing Qin, Nariya Uchida, Édgar Roldán
Formal Fluctuation-Response Relations for Non-Stationary Systems: The Dynamic Conjugate Variable
Igor M. Sokolov
Khinchin's ergodicity and typicality in statistical mechanics
Dario Lucente, Marco Baldovin, Giacomo Gradenigo et al.
Universal 1/f Noise in the Power Spectra of Energy Time-series in Solvated DNA Dynamics
Harsh Sahu, Deepika Sardana, Pramod Kumar et al.
Landau diamagnetism and the de Haas-van Alphen effect from a single geometric construction
Sung-Hoon Lee