TY - GEN

T1 - An exponential lower bound on the size of constant-depth threshold circuits with small energy complexity

AU - Uchizawa, Kei

AU - Takimoto, Eiji

N1 - Funding Information:
We are grateful to Professor Takao Nishizeki of Tohoku University, the supervisor of the first author, for thorough rewriting and reorganization of the paper numerous times over half a year. We also thank Professor Kazuyuki Amano of Gunma University for fruitful discussions, and the referees for helpful comments. This work is supported by MEXT Grant-in-Aid for Scientific Research on Priority Area ‘‘New Horizon in Computing’’.

PY - 2007

Y1 - 2007

N2 - A complexity measure for threshold circuits, called the energy complexity, has been proposed to measure an amount of energy consumed during computation in the brain. Biological neurons need more energy to transmit a "spike" than not to transmit one, and hence the energy complexity of a threshold circuit is defined as the number of gates in the circuit that output "1" during computation. Since the firing activity of neurons in the brain is quite sparse, the following question arises: what Boolean functions can or cannot be computed by threshold circuits with small energy complexity. In the paper, we partially answer the question, that is, we show that there exists a tradeoff among three complexity measures of threshold circuits: the energy complexity, size, and depth. The tradeoff implies an exponential lower bound on the size of constant-depth threshold circuits with small energy complexity for a large class of Boolean functions.

AB - A complexity measure for threshold circuits, called the energy complexity, has been proposed to measure an amount of energy consumed during computation in the brain. Biological neurons need more energy to transmit a "spike" than not to transmit one, and hence the energy complexity of a threshold circuit is defined as the number of gates in the circuit that output "1" during computation. Since the firing activity of neurons in the brain is quite sparse, the following question arises: what Boolean functions can or cannot be computed by threshold circuits with small energy complexity. In the paper, we partially answer the question, that is, we show that there exists a tradeoff among three complexity measures of threshold circuits: the energy complexity, size, and depth. The tradeoff implies an exponential lower bound on the size of constant-depth threshold circuits with small energy complexity for a large class of Boolean functions.

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U2 - 10.1109/CCC.2007.4

DO - 10.1109/CCC.2007.4

M3 - Conference contribution

AN - SCOPUS:34748903048

SN - 0769527809

SN - 9780769527802

T3 - Proceedings of the Annual IEEE Conference on Computational Complexity

SP - 169

EP - 178

BT - Proceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007

T2 - 22nd Annual IEEE Conference on Computational Complexity, CCC 2007

Y2 - 13 June 2007 through 16 June 2007

ER -