boolean operation

m](n([summation])) such that each proper binary boolean function ([L.

If there are n variables, then the Boolean function is a logical mapping from a set of {[v.

c) The procedures of translations of a Boolean function f([k.

Definition 6 Balanced Boolean Function: If the Hamming weight of a Boolean function of n variables is 2n-1, it is called a balanced Boolean function.

Graph-based algorithms for Boolean function manipulation.

Control inputs are used to specify the functionality of the circuit and remaining four inputs are used to implement Boolean function of four variables.

A]) for f a Boolean function, let Vars(f) denote the set of variables appearing in f.

A Boolean function involves any number of variables whose values and arguments are binary (for example, taking values 0 or 1).

However, we prefer not to complicate the notation, instead relying on an understanding that, at any time, there is a set of variables of interest, say, VI = (x, y, z) so that a formula [Psi] denotes the Boolean function [Lambda]xyz : [Psi].

A simple counting argument shows that, for a randomly chosen boolean function of kn variables, the k-party communication complexity is [OMEGA](n) with high probability, regardless of the dependence of k on n.

k] (f) denote the density of and/or trees defining a boolean function f within the set of and/or trees with fixed number of variables k.

2]} or [beta](v) is a 0-ary boolean function from B.

The idea of BDDs is similar to decision trees: A Boolean function is represented as a rooted acyclic-directed graph.

But for an arbitrary Boolean function the best known upper bound on block sensitivity in terms of sensitivity is exponential.

is given by a non trivial Boolean function f : [{0,1}.