TY - JOUR
T1 - Exponential lower bounds 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 - 2008/11/6
Y1 - 2008/11/6
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 trade-off among three complexity measures of threshold circuits: the energy complexity, size, and depth. The trade-off 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 trade-off among three complexity measures of threshold circuits: the energy complexity, size, and depth. The trade-off 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 - 10.1016/j.tcs.2008.07.028
DO - 10.1016/j.tcs.2008.07.028
M3 - Article
AN - SCOPUS:53349177823
VL - 407
SP - 474
EP - 487
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
IS - 1-3
ER -