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Communication Dans Un Congrès Année : 2010

The Block Neighborhood

Pablo Arrighi
Vincent Nesme
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Résumé

We define the block neighborhood of a reversible CA, which is related both to its decomposition into a product of block permutations and to quantum computing. We give a purely combinatorial characterization of the block neighborhood, which helps in two ways. First, it makes the computation of the block neighborhood of a given CA relatively easy. Second, it allows us to derive upper bounds on the block neighborhood: for a single CA as function of the classical and inverse neighborhoods, and for the composition of several CAs. One consequence of that is a characterization of a class of "elementary" CAs that cannot be written as the composition of two simpler parts whose neighborhoods and inverse neighborhoods would be reduced by one half.
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Dates et versions

hal-00542488 , version 1 (02-12-2010)

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Pablo Arrighi, Vincent Nesme. The Block Neighborhood. Journées Automates Cellulaires 2010, Dec 2010, Turku, Finland. pp.43-53. ⟨hal-00542488⟩
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