The Satisfiability Threshold of Random 3-SAT Is at Least 3.52

TL;DR

This paper establishes that random 3-SAT problems with a clause-to-variable ratio below 3.52 are highly likely to be satisfiable, using a degree-based variable assignment algorithm.

Contribution

It provides a new lower bound on the satisfiability threshold for random 3-SAT instances through a novel algorithmic approach.

Findings

Proves satisfiability for densities below 3.52 with high probability.

Introduces a degree-dependent variable assignment algorithm.

Improves understanding of the 3-SAT phase transition.

Abstract

We prove that a random 3-SAT instance with clause-to-variable density less than 3.52 is satisfiable with high probability. The proof comes through an algorithm which selects (and sets) a variable depending on its degree and that of its complement.