Thermodynamic depth is an appealing but flawed complexity measure. It depends on a set of macroscopic states for a system, but neither its original introduction by Lloyd and Pagels nor any follow-up work has considered how to select these states. Depth, therefore, is at root subjective....

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can...

Discovering relevant, but possibly hidden, variables is a key step in constructing useful and predictive theories about the natural world. This brief note explains the connections between three approaches to this problem: the recently introduced information-bottleneck method, the computational...

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 e-machine--is the minimal one consistent with accurate prediction. We establish several results on e-machine...

We critique the measure of complexity introduced by Shiner, Davison, and Landsberg in Ref. [1]. In particular, we point out that it is over-universal, in the sense that it has the same dependence on disorder for structurally distinct systems. We also point out a misinterpretation of a result...

Discovering relevant, but possibly hidden, variables is a key step in constructing useful and predictive theories about the natural world. This brief note explains the connections between three approaches to this problem: the recently introduced information-bottleneck method, the computational...

Evolving one-dimensional cellular automata (CAs) with genetic algorithms has provided insight into how improved performance on a task requiring global coordination emerges when only local interactions are possible. Two approaches that can affect the search efficiency of the genetic algorithm are...

We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second, statistical complexity, measures the amount of memory...

We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space-time behavior of elementary one-dimensional cellular automaton rule 54. The CA's dominant regular domain filter is constructed to locate and classify defects in the domain....

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to stochastic and deterministic processes by using a...