119 citations · 606 across the 12 of their papers we have counts for
7 papers · 1 filter
Exact Complexity: The Spectral Decomposition of Intrinsic Computation
James P. Crutchfield, Christopher J. Ellison, Paul M. Riechers
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions…
Information Symmetries in Irreversible Processes
Christopher J. Ellison, John R. Mahoney, Ryan G. James +2
We study dynamical reversibility in stationary stochastic processes from an information theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focu…
Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation
James P. Crutchfield, Christopher J. Ellison, Ryan G. James +1
We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchroniza…
Information Accessibility and Cryptic Processes: Linear Combinations of Causal States
John R. Mahoney, Christopher J. Ellison, James P. Crutchfield
We show in detail how to determine the time-reversed representation of a stationary hidden stochastic process from linear combinations of its forward-time -machine causal states…
Information Accessibility and Cryptic Processes
John R. Mahoney, Christopher J. Ellison, James P. Crutchfield
We give a systematic expansion of the crypticity--a recently introduced measure of the inaccessibility of a stationary process's internal state information. This leads to a hierarc…
Prediction, Retrodiction, and The Amount of Information Stored in the Present
Christopher J. Ellison, John R. Mahoney, James P. Crutchfield
We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmet…
Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information
James P. Crutchfield, Christopher J. Ellison, John R. Mahoney
We show why the amount of information communicated between the past and future--the excess entropy--is not in general the amount of information stored in the present--the statistic…