What is the satisfiability threshold of random balanced Boolean expressions?. Issue 3 (18th December 2021) - Lindenstrauss, Naomi; Talagrand, Michel
Abstract: We consider the model of random Boolean expressions based on balanced binary trees with 2 N 2^N leaves, to which are randomly attributed one of k N k_N Boolean variables or their negations. We prove that if for every c > 0 c>0 it holds that k N exp ( − c N ) → 0 k_N(-cN)→ 0 then asymptotically with high probability the Boolean expression is either a tautology or an antitautology. Our methods are based on the study of a certain binary operation on the set of probability measures on 0, 1 I {0, 1}^I for a finite set I .