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Representation of reversible cellular automata with block permutations

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Abstract

We demonstrate the structural invertibility of all reversible one- and two-dimensional cellular automata. More precisely, we prove that every reversible two-dimensional cellular automaton can be expressed as a combination of four block permutations, and some shift-like mappings. Block permutations are very simple functions that uniformly divide configurations into rectangular regions of equal size and apply a fixed permutation on all regions.

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  1. Mathematics Department, University of Turku, 20500, Turku, Finland

    J. Kari

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  1. J. Kari
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Kari, J. Representation of reversible cellular automata with block permutations. Math. Systems Theory 29, 47–61 (1996). https://doi.org/10.1007/BF01201813

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  • DOI: https://doi.org/10.1007/BF01201813

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