Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin algorithm can be viewed as an algorithmic analogue of such a decomposition as it ... more >>>

We show that there are families of polynomials having small depth-two arithmetic circuits that cannot be expressed by algebraic branching programs of width two. This clarifies the complexity of the problem of computing the product of a sequence of two-by-two matrices, which arises in several
settings.

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Assume that Alice is running a program $P$ on a RAM, and an adversary
Bob would like to get some information about the input or output of the
program. At each time, during the execution of $P$, Bob is able to see
the addresses of the memory cells involved in ... more >>>