Perceptrons: expanded edition
Threshold circuits of bounded depth
Journal of Computer and System Sciences
Explicit Constructions of Depth-2 Majority Circuits for Comparison and Addition
SIAM Journal on Discrete Mathematics
Circuit complexity and neural networks
Circuit complexity and neural networks
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
Simulating Threshold Circuits by Majority Circuits
SIAM Journal on Computing
On the power of a threshold gate at the top
Information Processing Letters
Computing Boolean functions by polynomials and threshold circuits
Computational Complexity
A linear lower bound on the unbounded error probabilistic communication complexity
Journal of Computer and System Sciences - Complexity 2001
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
A Note on the Simulation of Exponential Threshold Weights
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Relations Between Communication Complexity, Linear Arrangements, and Computational Complexity
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
New degree bounds for polynomial threshold functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Polynomials That Sign Represent Parity and Descartes Rule of Signs
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Polynomials that Sign Represent Parity and Descartes' Rule of Signs
Computational Complexity
Energy complexity and depth of threshold circuits
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Lower bounds for linear decision trees via an energy complexity argument
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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The paper investigates the complexity of depth-two circuits with threshold gates and consisting of two parts. First, we develop a method for deriving a lower bound on the size of depth two circuits with a threshold gate at the top and a certain type of gates at the bottom. We apply the method for circuits with symmetric gates at the bottom that compute the “inner product mod 2”, and obtain a lower bound of 1.3638n. Although our lower bound is slightly weaker than the best known lower bound of Ω(2n/2/n), which was recently proved by Forster et al. [5,6], our method has unique features: A lower bound is obtained by solving a certain linear program, and solving larger linear programs yield higher lower bounds. We also discuss the generalization of the proposed method. Second, we develop a simplified simulation of a depth-one threshold circuit with unbounded weights by a depth-two threshold circuit with small weights. Precisely, we give an explicit construction of depth-two circuits with small weights consist of Õn5 gates that compute an arbitrary threshold function. We also give the construction of such circuits with O(n3/log n) gates computing the COMPARISON and CARRY functions, and that with O(n4/log n) gates computing the ADDITION function. These improve the previously known constructions on its size and simplicity.