Random Boolean expressions

Abstract

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 the probability of a Boolean function and its complexity.

Keywords

• boolean function
• complexity
• probability distribution for boolean functions
• probability of tautologies
• [info.info-lo] computer science [cs]/logic in computer science [cs.lo]
• [info.info-sc] computer science [cs]/symbolic computation [cs.sc]
• [info.info-hc] computer science [cs]/human-computer interaction [cs.hc]