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arXiv · 1711.04563

Computing Aggregate Properties of Preimages for 2D Cellular Automata

Randall D. Beer
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Abstract

Computing properties of the set of precursors of a given configuration is a common problem underlying many important questions about cellular automata. Unfortunately, such computations quickly become intractable in dimension greater than one. This paper presents an algorithm --- incremental aggregation --- that can compute aggregate properties of the set of precursors exponentially faster than na{ï}ve approaches. The incremental aggregation algorithm is demonstrated on two problems from the two-dimensional binary Game of Life cellular automaton: precursor count distributions and higher-order mean field theory coefficients. In both cases, incremental aggregation allows us to obtain new results that were previously beyond reach.

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Randall D. Beer. 2017-11-13. Computing Aggregate Properties of Preimages for 2D Cellular Automata. https://doi.org/10.1063/1.5006143

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