Equivalence Classes of Random Boolean Trees and Application to the Catalan Satisfiability Problem

Antoine Genitrini (1) , Cécile Mailler (2)

1 APR - Algorithmes, Programmes et Résolution
2 LMV - Laboratoire de Mathématiques de Versailles

An and/or tree is a binary plane tree, with internal nodes labelled by connectives, and with leaves labelled by literals chosen in a fixed set of $k$ variables and their negations. We introduce the first model of such Catalan trees, whose number of variables $k_n$ is a function of $n$, its number of leaves. We describe the whole range of the probability distributions depending on the functions $k_n$, as soon as it tends jointly with $n$ to infinity. As a by-product we obtain a study of the satisfiability problem in the context of Catalan trees. Our study is mainly based on analytic combinatorics and extends the Kozik’s pattern theory, first developed for the fixed-$k$ Catalan tree model.

Domaines: Informatique [cs]

Antoine Genitrini, Cécile Mailler. Equivalence Classes of Random Boolean Trees and Application to the Catalan Satisfiability Problem. International Symposium on Latin American Theoretical Informatics, LATIN 2014, Mar 2014, Montevideo, Uruguay. pp.466-477, ⟨10.1007/978-3-642-54423-1_41⟩. ⟨hal-01217466⟩