Proof of the Satisfiability Conjecture for Large k

Abstract

We establish the satisfiability threshold for random k-SAT for all k ≥ k0. That is, there exists a limiting density αs(k) such that a random k-SAT formula of clause density α is with high probability satisfiable for α < αs, and unsatisfiable for α > αs. The satisfiability threshold αs is given explicitly by the one-step replica symmetry breaking (1SRB) prediction from statistical physics. We believe that our methods may apply to a range of random constraint satisfaction problems in the 1RSB class.