Linear decision trees: volume estimates and topological bounds
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
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
Communication complexity
An exponential lower bound on the size of algebraic decision trees for max
Computational Complexity
Decision trees: old and new results
Information and Computation
Lower bounds for linear satisfiability problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
A linear lower bound on the unbounded error probabilistic communication complexity
Journal of Computer and System Sciences - Complexity 2001
On Linear Decision Trees Computing Boolean Functions
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Relations Between Communication Complexity, Linear Arrangements, and Computational Complexity
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
On the computational power of threshold circuits with sparse activity
Neural Computation
Theoretical Computer Science
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
On the complexity of depth-2 circuits with threshold gates
MFCS'05 Proceedings of the 30th 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
Hi-index | 0.00 |
A linear decision tree is a binary decision tree in which a classification rule at each internal node is defined by a linear threshold function. In this paper, we consider a linear decision tree T where the weights w1, w2, ...,wn of each linear threshold function satisfy Σi |wi| ≤ w for an integer w, and prove that if T computes an n-variable Boolean function of large unbounded-error communication complexity (such as the Inner-Product function modulo two), then T must have 2Ω(√n)/w leaves. To obtain the lower bound, we utilize a close relationship between the size of linear decision trees and the energy complexity of threshold circuits; the energy of a threshold circuit C is defined to be the maximum number of gates outputting "1," where the maximum is taken over all inputs to C. In addition, we consider threshold circuits of depth ω(1) and bounded energy, and provide two exponential lower bounds on the size (i.e., the number of gates) of such circuits.