Signed Digit Addition and Related Operations with Threshold Logic
IEEE Transactions on Computers
Structural Complexity and Neural Networks
WIRN VIETRI 2002 Proceedings of the 13th Italian Workshop on Neural Nets-Revised Papers
Monotone circuits for monotone weighted threshold functions
Information Processing Letters
Powering requires threshold depth 3
Information Processing Letters
Separating AC0 from depth-2 majority circuits
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Every Linear Threshold Function has a Low-Weight Approximator
Computational Complexity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Cryptographic hardness for learning intersections of halfspaces
Journal of Computer and System Sciences
Monotone circuits for monotone weighted threshold functions
Information Processing Letters
Bounded Independence Fools Halfspaces
SIAM Journal on Computing
SIAM Journal on Computing
On the complexity of depth-2 circuits with threshold gates
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Decomposition of threshold functions into bounded fan-in threshold functions
Information and Computation
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We prove that a single threshold gate with arbitrary weights can be simulated by an explicit polynomial-size, depth-2 majority circuit. In general we show that a polynomial-size, depth-d threshold circuit can be simulated uniformly by a polynomial-size majority circuit of depth d + 1. Goldmann, Håstad, and Razborov showed in [Comput. Complexity, 2 (1992), pp. 277--300] that a nonuniform simulation exists. Our construction answers two open questions posed by them: we give an explicit construction, whereas they use a randomized existence argument, and we show that such a simulation is possible even if the depth d grows with the number of variables n (their simulation gives polynomial-size circuits only when d is constant).