Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Top-down lower bounds for depth-three circuits
Computational Complexity
Relations Among Complexity Measures
Journal of the ACM (JACM)
Exponential lower bounds for depth three boolean circuits
Computational Complexity
Explicit lower bound of 4.5n - o(n) for boolena circuits
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
An Explicit Lower Bound of 5n - o(n) for Boolean Circuits
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
An Improved Exponential-Time Algorithm for k-SAT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On monotone formulae with restricted depth
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
An improved exponential-time algorithm for k-SAT
Journal of the ACM (JACM)
Hi-index | 0.89 |
We give tight lower bounds for the size of depth-3 circuits with limited bottom fanin computing symmetric Boolean functions. We show that any depth-3 circuit with bottom fanin k which computes the Boolean function Exactn/(k+1)n, has at least (1 + 1/k)n/(n + 1) gates. We show that for k = o(√n) this lower bound is essentially tight, by generalizing a known upper bound on the size of depth-3 circuits with bottom fanin 2, computing symmetric Boolean functions.