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Cellular Automata and Groups
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Cellular automata were introduced by John von Neumann who used them as models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups.§The volume is entirely self-contained, includes more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. Based on the interplay between amenability, geometric and combinatorial group theory, and symbolic dynamics it considers linear cellular automata: this gives applications to the theory of group rings (Kaplansky conjectures on the structure theory of group rings) that have no counterpart in other books on the same topics.
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