TY - GEN

T1 - Energy and fan-in of threshold circuits computing mod functions

AU - Suzuki, Akira

AU - Uchizawa, Kei

AU - Zhou, Xiao

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Boolean function

KW - MOD function

KW - energy complexity

KW - fan-in

KW - threshold circuit

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U2 - 10.1007/978-3-642-20877-5_16

DO - 10.1007/978-3-642-20877-5_16

M3 - Conference contribution

AN - SCOPUS:79955750863

SN - 9783642208768

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 154

EP - 163

BT - Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings

T2 - 8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011

Y2 - 23 May 2011 through 25 May 2011

ER -