Complete convergence of message passing algorithms for some satisfiability problems

TL;DR

This paper proves that Warning Propagation, a message passing algorithm, reliably finds satisfying assignments for certain random 3CNF formulas with high clause-variable ratios, demonstrating its complete convergence in these cases.

Contribution

It provides a rigorous analysis of Warning Propagation's performance on planted 3CNF formulas, establishing conditions for guaranteed convergence and satisfiability.

Findings

Warning Propagation converges to a satisfying assignment for large clause-variable ratios.

The algorithm successfully finds solutions in planted 3CNF formulas under specified conditions.

Convergence and correctness are proven for a class of random satisfiable formulas.

Abstract

In this paper we analyze the performance of Warning Propagation, a popular message passing algorithm. We show that for 3CNF formulas drawn from a certain distribution over random satisfiable 3CNF formulas, commonly referred to as the planted-assignment distribution, running Warning Propagation in the standard way (run message passing until convergence, simplify the formula according to the resulting assignment, and satisfy the remaining subformula, if necessary, using a simple "off the shelf" heuristic) results in a satisfying assignment when the clause-variable ratio is a sufficiently large constant.