Abstract
In this paper, we consider a threshold circuit C computing the modulus function MOD m , 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 MOD m 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.
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Suzuki, A., Uchizawa, K., Zhou, X. (2011). Energy and Fan-In of Threshold Circuits Computing Mod Functions. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_16
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DOI: https://doi.org/10.1007/978-3-642-20877-5_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20876-8
Online ISBN: 978-3-642-20877-5
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