Spectrally Preconditioned Threshold Logic

Abstract

In a more visual sense, consider f _d to be a pattern consisting of a pasting of black and white stickers on some or all of the vertices of a d-dimensional boolean hypercube. It is at this early juncture that two important questions arise. First, how can we efficiently code or store a random pattern, or how, when presented with a d-bit address of a vertex on the hypercube, can we decide, either with total certainty or within a given error tolerance, the color at the vertex without using a look up technique? Second, some patterns appear more random or complex than ethers. Can this random quality be defined and is there a metric or even a fuzzy measure for it?