Log depth circuits for division and related problems
SIAM Journal on Computing
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
With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
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
When do extra majority gates help?: polylog(N) majority gates are equivalent to one
Computational Complexity - Special issue on circuit complexity
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
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
An Explicit Lower Bound of 5n - o(n) for Boolean Circuits
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exponential lower bounds for restricted monotone circuits
STOC '83 Proceedings of the fifteenth 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
On Constructing Parallel Pseudorandom Generators from One-Way Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
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
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
On the constant-depth complexity of k-clique
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
Separating the polynomial-time hierarchy by oracles
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Randomness-Efficient Sampling within NC1
Computational Complexity
Arithmetic Circuits: A Chasm at Depth Four
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
Poly-logarithmic Independence Fools AC^0 Circuits
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on 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
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
Guest column: a casual tour around a circuit complexity bound
ACM SIGACT News
On beating the hybrid argument
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Arithmetic circuits: The chasm at depth four gets wider
Theoretical Computer Science
ACM Transactions on Computation Theory (TOCT)
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In this monograph we discuss selected topics on small-depth computation, presenting a few unpublished proofs along the way. The four sections contain: A unified treatment of the challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over {0,1}. An unpublished proof that small bounded-depth circuits (AC0) have exponentially small correlation with the parity function. The proof is due to Klivans and Vadhan; it builds upon and simplifies previous ones. Valiant's simulation of log-depth linear-size circuits of fan-in 2 by sub-exponential size circuits of depth 3 and unbounded fan-in. To our knowledge, a proof of this result has never appeared in full. Applebaum, Ishai, and Kushilevitz's cryptography in bounded depth.