On the complexity of powering in finite fields
Proceedings of the forty-third annual ACM symposium on Theory of computing
On beating the hybrid argument
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
| Hi-index | 0.01 |
In the first part of the paper we show that a subset S of a boolean cube B/sub n/ embedded in the projective space P/sup n/ can be approximated by a subset of B/sub n/ 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[p/sup r/] circuits. In the second part we look at the problem of computing many-output function by ACC[p/sup r/] circuit and give an example when such a circuit can be correct only at exponentially small fraction of assignments.