The number of satisfying assignments of random 2‐SAT formulas
Dimitris Achlioptas, Amin Coja‐Oghlan, Max Hahn‐Klimroth, Joon Lee, Noëla Müller, Manuel Penschuck, Guangyan Zhou · Random Structures and Algorithms · 2021
Abstract We show that throughout the satisfiable phase the normalized number of satisfying assignments of a random 2‐SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to “true” under a uniformly random satisfying assignment.