A general approach for density estimation in the n-dimensional Boolean space

Kanerva (1988) 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. Braga and Aleksander (1994) 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 works, the densities are calculated in relation to two fixed points in the space. It is shown 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.