The complexity of Boolean functions
The complexity of Boolean functions
Energy consumption in VLSI circuits
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Upper and lower bounds on switching energy in VLSI
Journal of the ACM (JACM)
The complexity of the parity function in unbounded fan-in, unbounded depth circuits
Theoretical Computer Science
Circuit complexity and neural networks
Circuit complexity and neural networks
Discrete neural computation: a theoretical foundation
Discrete neural computation: a theoretical foundation
Size--Depth Tradeoffs for Threshold Circuits
SIAM Journal on Computing
Lower Bounds for (MODp - MODm) Circuits
SIAM Journal on Computing
Lower bounds for circuits with MOD_m gates
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
On the computational power of threshold circuits with sparse activity
Neural Computation
Theoretical Computer Science
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Size and Energy of Threshold Circuits Computing Mod Functions
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Energy and depth of threshold circuits
Theoretical Computer Science
Rational approximation techniques for analysis of neural networks
IEEE Transactions on Information Theory
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 threshold circuits computing mod functions
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Complexity of counting output patterns of logic circuits
CATS '13 Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141
Energy and fan-in of logic circuits computing symmetric Boolean functions
Theoretical Computer Science
Hi-index | 5.23 |
A unate gate is a logical gate computing a unate Boolean function, which is monotone in each variable. Examples of unate gates are AND gates, OR gates, NOT gates, threshold gates, etc. A unate circuit C is a combinatorial logic circuit consisting of unate gates. Let f be a symmetric Boolean function of n variables, such as the Parity function, MOD function, and Majority function. Let m"0 and m"1 be the maximum numbers of consecutive 0's and consecutive 1's in the value vector of f, respectively, and let l=min{m"0,m"1} and m=max{m"0,m"1}. Let C be a unate circuit computing f. Let s be the size of the circuit C, that is, C consists of s unate gates. Let e be the energy of C, that is, e is the maximum number of gates outputting ''1'' over all inputs to C. In this paper, we show that there is a tradeoff between the size s and the energy e of C. More precisely, we show that (n+1-l)/m@?s^e. We also present lower bounds on the size s of C represented in terms of n, l and m. Our tradeoff immediately implies that logn@?elogs for every unate circuit C computing the Parity function of n variables.