A Dual Version of Reimer's Inequality and a Proof of Rudich's Conjecture
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Proof of the Van den Berg–Kesten Conjecture
Combinatorics, Probability and Computing
The dual bkr inequality and rudich's conjecture
Combinatorics, Probability and Computing
ACM Transactions on Computation Theory (TOCT)
| Hi-index | 0.00 |
(MATH) Let f: {0,1}n → {0,1} be a boolean function. For &egr;&roe; 0 De(f) be the minimum depth of a decision tree for f that makes an error for &xie;&egr; fraction of the inputs &khar; &Egr; {0,1}n. We also make an appropriate definition of the approximate certificate complexity of f, C&egr;(f). In particular, D0(f) and C0(f) are the ordinary decision and certificate complexities of f. It is known that $D_0(f) \leq (C_0(f))^2$. Answering a question of Tardos from 1989, we show that for all $\Ge 0$ there exists a $\Gd' 0$ such that for all $0 \leq \Gd 0$ is a constant independent of f. The algorithm used in the proof is modeled after those developed by R. Impagliazzo and S. Rudich for use in other problems.