The random 2-SAT partition function

Dimitris Achlioptas, Amin Coja-Oghlan, Max Hahn-Klimroth, Joon Lee, Noela Müller, Manuel Penschuck, Guangyan Zhou

Published 2020-02-10Version 1

We show that throughout the satisfiable phase the normalised 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.