Ininvertible cellular automata: a review
Physica D
Garden of Eden configurations for cellular automata on Cayley graphs of groups
SIAM Journal on Discrete Mathematics
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Simulations between cellular automata on Cayley graphs
Theoretical Computer Science
Cellular automata and strongly irreducible shifts of finite type
Theoretical Computer Science
Tessellations with local transformations
Journal of Computer and System Sciences
On Pattern Density and Sliding Block Code Behavior for the Besicovitch and Weyl Pseudo-distances
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Generalized Besicovitch and Weyl spaces: Topology, patterns, and sliding block codes
Theoretical Computer Science
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Consider the space of configurations from a finitely generated group to a finite alphabet. We look at the translation-invariant closed subsets of this space, and at their continuous transformations that commute with translations. It is well-known that such objects can be described ''locally'' via finite patterns and finitary functions; we are interested in re-using these descriptions with larger groups, a process that usually does not lead to objects isomorphic to the original ones. We first characterize, in terms of group actions, those dynamics that can be presented via structures like those above. We then prove that some properties of the ''induced'' entities can be deduced from those of the original ones, and vice versa. We finally show how to simulate the smaller structure into the larger one. Special attention is given to the class of sofic shifts.