We consider the deterministic and the randomized decision tree complexities for Boolean functions, denoted DC(f) and RC(f), respectively. A major open problem is how small RC(f) ca...
Abstract. We prove lower bounds on the randomized two-party communication complexity of functions that arise from read-once boolean formulae. A read-once boolean formula is a formu...
We discuss several complexity measures for Boolean functions: certi cate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial. ...
A Direct Sum Theorem holds in a model of computation, when for every problem solving some k input instances together is k times as expensive as solving one. We show that Direct Su...
We give an algorithm that learns any monotone Boolean function f : {-1, 1}n {-1, 1} to any constant accuracy, under the uniform distribution, in time polynomial in n and in the de...