Danièle Gardy

Generating functions for generating trees

Generating trees describe conveniently certain families of combinatorial objects: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumeration sequences (sometimes, to explicit formulae as well) while providing efficient random generation algorithms. In this paper, we investigate the relationship between structural properties of the rules defining such trees and the rationality, algebraicity, or transcendence of the corresponding generating functions.

And/Or Trees Revisited

We consider Boolean functions over

Classical and intuitionistic logic are asymptotically identical

n

Asymptotics and random sampling for BCI and BCK lambda terms

variables. Any such function can be represented (and computed) by a complete binary tree with and or or in the internal nodes and a literal in the external nodes, and many different trees can represent the same function, so that a fundamental question is related to the so-called complexity of a Boolean function:

A unified presentation of some urn models

L(f):=

The permutation-path coloring problem on trees

minimal size of a tree computing

An urn model from learning theory

f

Boys-and-girls Birthdays and Hadamard Products

.The existence of a limiting probability distribution

Tautologies over implication with negative literals

P(\cdot)

Dynamic analysis of some relational databases parameters

on the set of and/or trees was shown by Lefmann and Savický [8]. We give here an alternative proof, which leads to effective computation in simple cases. We also consider the relationship between the probability