A constructive approach to the algebraic (monoidal) representation of cubic structures is developed. An expansion of a cubant set by the introduction of cross-cubants is proposed. The cubant metric (Hausdorff-Hamming metric) and topological properties are studied. Some peculiarities of the implementation of concurrent computer operations on monoids are considered as a tool of supercomputing. This work was supported by the Russian Foundation for Basic Research (project N 09-07-12135).

Keywords: n-cube, cubants and cross-cubants, monoid, Hausdorff-Hamming metric, concurrent digitwise operations, supercomputing, 3D-sphere

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