Problems in minimalization theory of Boolean expressions

Random Boolean expressions

We examine how we can define several probability distributions on the set of Boolean functions on a fixed number of variables, starting from a representation of Boolean expressions by trees. Analytic tools give us a systematic way to prove the existence of probability distributions, the main challenge being the actual computation of the distributions. We finally consider the relations between t...

Handling Complexity in Boolean Expressions

Indexing Boolean Expressions

We consider the problem of efficiently indexing Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF) Boolean expressions over a high-dimensional multi-valued attribute space. The goal is to rapidly find the set of Boolean expressions that evaluate to true for a given assignment of values to attributes. A solution to this problem has applications in online advertising (where a Boolean...

Compactness of Boolean Index Expressions

Computing Boolean Expressions with OBDDs

We present a method to compute the bdd for an arbitrary Boolean expression, where the operands are themselves bdds. Such expressions are usually computed by the successive application of binary operators. However, cases exist where this method performs wasteful intermediate computations and creates bdd nodes not used in the nal result. In contrast, our method never creates a bdd node unless it ...