Upper and lower bounds on switching energy in VLSI
Journal of the ACM (JACM)
Neurocomputing: foundations of research
n&OHgr;(logn) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom
Information Processing Letters
Threshold circuits of bounded depth
Journal of Computer and System Sciences
Circuit complexity and neural networks
Circuit complexity and neural networks
Discrete neural computation: a theoretical foundation
Discrete neural computation: a theoretical foundation
Communication complexity
A linear lower bound on the unbounded error probabilistic communication complexity
Journal of Computer and System Sciences - Complexity 2001
How Close Are We to Understanding V1?
Neural Computation
On the computational power of threshold circuits with sparse activity
Neural Computation
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Energy complexity and depth of threshold circuits
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Energy and depth of threshold circuits
Theoretical Computer Science
Size-energy tradeoffs for unate circuits computing symmetric Boolean functions
Theoretical Computer Science
Energy and fan-in of threshold circuits computing mod functions
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Lower bounds for linear decision trees via an energy complexity argument
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Energy-efficient threshold circuits computing mod functions
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Energy-efficient threshold circuits computing mod functions
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Energy and fan-in of logic circuits computing symmetric Boolean functions
Theoretical Computer Science
Hi-index | 5.23 |
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.