Energy and fan-in of threshold circuits computing mod functions

Authors:
Akira Suzuki;Kei Uchizawa;Xiao Zhou
Affiliations:
Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, Japan
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

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Abstract

In this paper, we consider a threshold circuit C computing the modulus function MODm, and investigate a relationship between two complexity measures, fan-in l and energy e of C, where the fan-in l is defined to be the maximum number of inputs of every gate in C, and the energy e to be the maximum number of gates outputting "1" over all inputs to C. We first prove that MODm of n variables can be computed by a threshold circuit of fan-in l and energy e = O(n/l), and then provide an almost tight lower bound e = Ω((n - m)/l). Our results imply that there exists a tradeoff between the fan-in and energy of threshold circuits computing the modulus function.