Introduction to finite fields and their applications
Introduction to finite fields and their applications
Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
n&OHgr;(logn) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom
Information Processing Letters
On the computational power of depth 2 circuits with threshold and modulo gates
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A weight-size trade-off for circuits with MOD m gates
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A note on the power of majority gates and modular gates
Information Processing Letters
Lower Bounds for (MODp - MODm) Circuits
SIAM Journal on Computing
Lower Bounds for Approximations by Low Degree Polynomials Over Z_m
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
The Correlation Between Parity and Quadratic Polynomials Mod 3
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Separating the polynomial-time hierarchy by oracles
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Threshold circuits of bounded depth
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
A note on the power of threshold circuits
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Guest Column: correlation bounds for polynomials over {0 1}
ACM SIGACT News
On the Power of Small-Depth Computation
Foundations and Trends® in Theoretical Computer Science
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We consider the problem of bounding the correlation between parity and modular polynomials over ℤq, for arbitrary odd integer q ≥3. We prove exponentially small upper bounds for classes of polynomials with certain linear algebraic properties. As a corollary, we obtain exponential lower bounds on the size necessary to compute parity by depth-3 circuits of certain form. Our technique is based on a new representation of the correlation using exponential sums. Our results include Goldmann's result [Go] on the correlation between parity and degree one polynomials as a special case. Our general expression for representing correlation can be used to derive the bounds of Cai, Green, and Thierauf [CGT] for symmetric polynomials, using ideas of the [CGT] proof. The classes of polynomials for which we obtain exponentially small upper bounds include polynomials of large degree and with a large number of terms, that previous techniques did not apply to.