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On representations by low-degree polynomials

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1 Author(s)
R. Smolensky ; Dept. of Comput. Sci., Hebrew Univ., Jerusalem, Israel

In the first part of the paper we show that a subset S of a boolean cube Bn embedded in the projective space Pn can be approximated by a subset of Bn defined by nonzeroes of a low-degree polynomial only if the values of the Hilbert function of S are sufficiently small relative to the size of S. The use of this property provides a simple and direct technique for proving lower bounds on the size of ACC[pr] circuits. In the second part we look at the problem of computing many-output function by ACC[pr] circuit and give an example when such a circuit can be correct only at exponentially small fraction of assignments

Published in:

Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

Date of Conference:

3-5 Nov 1993