A General Approach for Density in the n-Dimensional Boolean Space

Antônio de Pádua BragaMarcelo Azevedo Costa

Kanerva presented a model to estimate the intersection of two circles, or hyperspheres, in the n-dimensional Boolean space. The results were applied to show the properties of the Sparse Distributed Memory model. In a recent work, Braga and Aleksander presented a more general model that is able to estimate any density in the Boolean space and is not restricted to the intersection problem. In both previous work, the densities are calculated in relation to two fixed points in the space. It is shown in this work that the previous work of Braga and Aleksander can be extended to estimate densities in relation to more than two fixed points. With these results, intersections of three or more hyperspheres can be estimated. The results can be applied to provide a more accurate study of the properties of Boolean associative memories.

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