Reimer's inequality and tardos' conjecture

Let f : {0, 1}n {0, 1} be a boolean function. For 0 let D (f) be the minimum depth of a decision tree for f that makes an error for fraction of the inputs x {0, 1}n . We also make an appropriate definition of the approximate certificate complexity of f, C (f). In particular, D0(f) and C0(f) are the ordinary decision and certificate complexities of f. It is known that D0(f) (C0(f))2 . Answering a question of Tardos from 1989, we show that for all > 0 there exists a > 0 such that for all 0 < , we have D (f) K(C(f))2 where K = K( , ) > 0 is a constant independent of f.

• Type: Conference
• Year: 2002
• Where: STOC
• Authors: Clifford D. Smyth
• Keywords: Algorithms, Approximate Certificate Complexity, Certificate Complexities, Ordinary Decision, STOC 2002