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
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
Communication complexity and quasi randomness
SIAM Journal on Discrete Mathematics
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
n&OHgr;(logn) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom
Information Processing Letters
Threshold circuits of bounded depth
Journal of Computer and System Sciences
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Separating the communication complexities of MOD m and MOD p circuits
Journal of Computer and System Sciences
Boosting a weak learning algorithm by majority
Information and Computation
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Communication complexity
The BNS-chung criterion for multi-party communication complexity
Computational Complexity
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of 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
Journal of Computer and System Sciences - Special issue on computational complexity 2002
Symmetric polynomials over Zm and simultaneous communication protocols
Journal of Computer and System Sciences - Special issue on FOCS 2003
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
The complexity of hardness amplification and derandomization
The complexity of hardness amplification and derandomization
Low-degree tests at large distances
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Pseudorandom Bits for Constant-Depth Circuits with Few Arbitrary Symmetric Gates
SIAM Journal on Computing
Pseudorandom Bits for Polynomials
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Inverse conjecture for the gowers norm is false
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Unconditional pseudorandom generators for low degree polynomials
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Algebrization: a new barrier in complexity theory
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The Sum of d Small-Bias Generators Fools Polynomials of Degree d
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Randomness-Efficient Sampling within NC1
Computational Complexity
Constant-Depth circuits for arithmetic in finite fields of characteristic two
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
On the correlation between parity and modular polynomials
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Random Low Degree Polynomials are Hard to Approximate
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
| Hi-index | 0.00 |
This article is a unified treatment of the state-of-the-art on the fundamental challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over {0 1 }. It discusses long-standing results and recent developments, related proof techniques, and connections with pseudorandom generators. It also suggests several research directions.