Universal algorithms for evaluating boolean functions

Quantum algorithms for testing Boolean functions

We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same...

Algorithms counting monotone Boolean functions

We give a new algorithm counting monotone Boolean functions of n variables (or equivalently the elements of free distributive lattices of n generators). We computed the number of monotone functions of 8 variables which is 56 130 437 228 687 557 907 788.  2001 Elsevier Science B.V. All rights reserved.

Monotone Boolean Functions Are Universal Approximators

The employment of proper codings, such as the base-2 coding, has allowed to establish the universal approximation property of Boolean functions: if a sufficient number b of inputs (bits) is taken, they are able to approximate arbitrarily well any real Borel measurable mapping. However, if the reduced set of monotone Boolean functions, whose expression involves only and and or operators, is cons...

Boolean Functions - Theory, Algorithms, and Applications

Learning Complex Boolean Functions: Algorithms and Applications

The most commonly used neural network models are not well suited to direct digital implementations because each node needs to perform a large number of operations between floating point values. Fortunately, the ability to learn from examples and to generalize is not restricted to networks ofthis type. Indeed, networks where each node implements a simple Boolean function (Boolean networks) can b...