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For any proper binary boolean function o, the complexity of [L.
Definition 7 Nonlinearity: Let, f be a Boolean function of variables, [x.
A Boolean function f is called Sensitive if any two distinct falsifying assignments [Alpha], [Beta] [element of] [f.
In practice, we need more than a simple YES/NO judgment about older stored quests, so we have developed an ad hoc method for assigning weights to documents based on how strongly they match individual terms in the Boolean function.
We say that a Boolean function [Psi] is down-closed if [[Psi]] is closed under intersection.
In stark contrast, no explicit family of boolean functions has been shown to have w(log n) communication complexity for k = w(log n) players.
k](f) when k tends to infinity (in this approach f is treated as a boolean function of countably many variables, even though it depends only on the finite number of them).
If v[member of]V has in-degree k, 0 < k < 2, then [beta](v) is a k-ary boolean function from B.
Thus, a set of terms can be represented by a Boolean function that is true for a valuation iff the corresponding term is in the set.
15) gives a Boolean function, invariant under the cyclic shift of the variables, which still shows the quadratic gap between sensitivity and block sensitivity.