Bounded-depth, polynomial-size circuits for symmetric functions
Theoretical Computer Science
Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
PP is closed under intersection
Selected papers of the 23rd annual ACM symposium on Theory of computing
When do extra majority gates help?: polylog(N) majority gates are equivalent to one
Computational Complexity - Special issue on circuit complexity
Complex polynomials and circuit lower bounds for modular counting
Computational Complexity - Special issue on circuit complexity
A complex-number fourier technique for lower bounds on the mod-m degree
Computational Complexity
An exact characterization of symmetric functions in qAC0[2]
Theoretical Computer Science
Computing Symmetric Functions with AND/OR Circuits and a Single MAJORITY Gate
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Pseudorandom Bits for Constant Depth Circuits with Few Arbitrary Symmetric Gates
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Perceptrons: An Introduction to Computational Geometry
Perceptrons: An Introduction to Computational Geometry
Separating the polynomial-time hierarchy by oracles
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Lower bounds for circuits with few modular and symmetric gates
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Weights of exact threshold functions
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Learning and lower bounds for AC0 with threshold gates
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Exponential lower bound for bounded depth circuits with few threshold gates
Information Processing Letters
Hi-index | 0.00 |
We consider constant depth circuits augmented with few exact threshold gates with arbitrary weights. We prove strong (up to exponential) size lower bounds for such circuits computing symmetric Boolean functions. Our lower bound is expressed in terms of a natural parameter, the balance, of symmetric functions. Furthermore, in the quasi-polynomial size setting our results provides an exact characterization of the class of symmetric functions in terms of their balance.