Cellular Automata and Groups

Topological Dimension and Dynamical Systems

“…A detailed exposition of the theory of amenable groups may be found for example in [41,85,88], and [22,Chap. 4].…”

“…Actually, the question of the existence of a non-sofic group is still open. For an introduction to the theory of sofic groups, the reader is referred to the survey paper [87] and to [22,Chap. 7].…”

A new network approach to Bayesian inference in partial differential equations

“…We can hence approximate the global transition distribution by a product of the same local transition distribution at every node. Such a locality concept is at the core of cellular automata theory [53,54]. The local transition probabilities from the variables at a node's parents to the variable at node i itself can be specified as a conditional probability distribution.…”

“…First, a finite difference scheme transfers the PDE into a time-discrete and space-discrete dynamical system. Then the state space is discretized with tools of set-oriented numerics [50][51][52], and afterwards, the neighborhood concept [53,54] of cellular automata theory [55][56][57] is used to exploit the locality of the interaction. The result is a completely discrete system that consists of graph-based time slices with local transition probabilities between them.…”

A Garden of Eden theorem for linear subshifts

“…In this section we collect some preliminaries and background material that will be needed in the following (for more details the reader is referred to [6] …”