An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Cellular automata and strongly irreducible shifts of finite type
Theoretical Computer Science
When–and how–can a cellular automaton be rewritten as a lattice gas?
Theoretical Computer Science
Information and Computation
Generalized Besicovitch and Weyl spaces: Topology, patterns, and sliding block codes
Theoretical Computer Science
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Initially proposed by Formenti et al. for bi-infinite sequences, the Besicovitch and Weyl pseudo-distances express the viewpoint of an observer moving infinitely far from the grid, rather than staying close as in the product topology. We extend their definition to a more general setting, which includes the usual infinite hypercubic grids, and highlight some noteworthy properties. We use them to measure the "frequency" of occurrences of patterns in configurations, and consider the behavior of sliding block codes when configurations at pseudo-distance zero are identified. One of our aims is to get an alternative characterization of surjectivity for sliding block codes.Mathematics Subject Classification 2000: 37B15, 68Q80.