A sprouting tree model for random boolean functions

ABSTRACT We define a new probability distribution for Boolean functions of k variables. Consider the random Binary Search Tree of size n, and label its internal nodes by connectives and its leaves by variables or their negations. This random process defines a random Boolean expression which represents a random Boolean function. Finally, let n tend to infinity: the asymptotic distribution on Boolean functions exists; we call it the sprouting tree distribution. We study this model and compare it with two previously‐known distributions induced by two other random trees: the Catalan tree and the Galton‐Watson tree. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 635–662, 2015