Section: New Results

Random Graphs

Participant : Nicolas Broutin.

And/Or trees for random Boolean functions

For some time, a number of teams have tried to devise natural probability distributions on Boolean functions. Indeed, the most natural one, the uniform one, is not quite satisfactory: almost all Boolean functions have maximal complexity, while it is extremely difficult to construct some with high complexity. One approach consists in generating functions by seeing them as "expressions" encoded as a tree of computation. We generalize and unify the previous approaches that are restricted to very specific cases by looking at the distributions induced on the Boolean function by large computation trees that are arbitrary, except for the fact they the neighborhoods of the root (where the computation concentrates) stabilizes in distribution as the sizes of the tree increases [12] .