Abstract

We prove upper bounds on the randomized communication complexity of evaluating a threshold gate (with arbitrary weights). For linear threshold gates this is done in the usual 2 party communication model, and for degree-d threshold gates this is done in the multiparty model. We then use these upper bounds together with known lower bounds for communication complexity in order to give very easy proofs for lower bounds in various models of computation involving threshold gates. This generalizes several known bounds and answers several open problems.

Citations

536	Communication complexity - Kushilevitz, Nisan - 1997
342	Some complexity questions related to distributive computing - Yao - 1979
159	Unbiased bits from sources of weak randomness and probabilistic communication complexity - Chor, Goldreich - 1985
130	The probabilistic communication complexity of set intersection - Kalyanasundaram, Schnitger - 1992
97	Multi-Party protocols - CHANDRA, FURST, et al.
95	Complexity classes in communication complexity theory (preliminary version - Babai, Frankl, et al. - 1986
90	On the distributional complexity of disjointness - Razborov - 1992
88	On the power of small-depth threshold circuits Computational Complexity - Hastad, Goldmann - 1991
88	Lower bounds by probabilistic arguments - YAO - 1983
80	Majority gates vs. general weighted threshold gates - Goldmann, H˚astad, et al. - 1992
78	Harmonic analysis of polynomial threshold functions - Bruck - 1990
73	Private vs. common random bits in communication complexity - Newman - 1991
56	Rounds in communication complexity revisited - Nisan, Wigderson - 1993
48	Multi-party protocols and logspace-hard pseudorandom sequences - Babai, Nisan, et al. - 1989
48	Strong communication complexity or generating quasirandom sequences form two communicating semi-random sources - Vazirani - 1987
46	On the power of threshold circuits with small weights - Siu, Bruck - 1991
37	Las Vegas is better than determinism in VLSI and distributive computing - Mehlhorn, Schmidt - 1982
36	Depth efficient neural networks for division and related problems - Siu, Bruck, et al. - 1993
32	Polynomial Threshold Functions, AC Functions and Spectral Norms - Bruck, Smolensky - 1992
32	Lower bounds on communication complexity - Duris, Galil, et al. - 1987
31	Computing with unreliable information - Feige, Peleg, et al. - 1990
28	On notions of information transfer in VLSI circuits - Aho, Ullman, et al. - 1983
25	The Perceptron strikes back - Beigel, Reingold, et al. - 1991
22	On the size of weights required for linear-input switching functions - Myhill, Kautz - 1961
22	Lower bounds on the size of depth 3 threshold circuits with AND gates at the bottom - Razborov, Wigderson
21	Wigderson: Probabilistic Communication Complexity of Boolean Relations - Raz, A - 1989
19	Different Modes of Communication - Halstenberg, Reischuk - 1993
16	Some notes on threshold circuits and multiplication - Hofmeister, Hohberg, et al.
11	On interpolation by analytic functions with special properties and some weak lower bounds on the size of circuits with symmetric gates, 31st FOCS - Smolensky - 1990
5	Lower bounds on threshold and related circuits via communication complexity - Roychowdhury, Orlitsky, et al. - 1994
4	A note on the power of threshold circuts - Allender - 1989
2	Some lower and upper bounds for algebraic decision trees and the separation problem - Vatan - 1992
1	the polynomial time heirarchy - Perceptrons - 1992
1	On linear decison trees computing boolean functions - Groger, Turan - 1991