Energy-efficient threshold circuits computing mod functions

Authors:
Akira Suzuki;Kei Uchizawa;Xiao Zhou
Affiliations:
Tohoku University, Aramaki-aza Aoba, Aoba-ku, Sendai, Japan;Tohoku University, Aramaki-aza Aoba, Aoba-ku, Sendai, Japan;Tohoku University, Aramaki-aza Aoba, Aoba-ku, Sendai, Japan
Venue:
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Year:
2011

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Abstract

We prove that the modulus function MODm of n variables can be computed by a threshold circuit C of energy e and size s = O(e(n/m)1/(e−1)) for any integer e ≥ 2, where the energy e is defined to be the maximum number of gates outputting "1" over all inputs to C, and the size s to be the number of gates in C. Our upper bound on the size s almost matches the known lower bound s = Ω(e(n/m)1/e).