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We present a new method for accelerating matrix multiplication asymptotically. This work builds on recent ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product. We make novel use of the Salem-Spencer Theorem, which gives a fairly dense set of integers with no three-term arithmetic progression. Our resulting matrix exponent(More)
Construction of algorithms is a time honored mathematical activity. Euclid's algorithm for finding the greatest common divisor of two integers, as well as the many constructions by a ruler and compass are some of the fruits of the search for algorithms by the Greek mathematicians. In our days, we have the whole field of Numerical Analysis devoted to finding(More)
A problem related to the decentralized control of a multiple access channel is considered: Suppose <italic>k</italic> stations from an ensemble of <italic>n</italic> simultaneously transmit to a multiple access channel that provides the feedback 0, 1, or 2+, denoting <italic>k</italic> = 0, <italic>k</italic> = 1, or <italic>k</italic> &#8805; 2,(More)