Вычислительные методы и приложения

On the metric-topological computing in the constructive world of cubic structures

G. G. Ryabov, V. A. Serov

Lomonosov Moscow State University, Research Computing Center

Abstract: 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 09-07-12135).

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

UDC: 004.38; 515.14; 519.766.2