The decimation process in random k-SAT

TL;DR

This paper investigates the decimation process in random k-SAT problems, identifying phase transitions that influence the success of the Belief Propagation Guided Decimation algorithm inspired by statistical mechanics.

Contribution

It characterizes phase transitions in the decimation process and connects them to the algorithm's performance, providing new insights into random k-SAT solving methods.

Findings

Identified multiple phase transitions in the decimation process

Linked phase transitions to algorithm success and failure

Provided a theoretical framework for understanding message passing algorithms in k-SAT

Abstract

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying assignments of F. This algorithm can be viewed as an attempt at implementing a certain thought experiment that we call the Decimation Process. In this paper we identify a variety of phase transitions in the decimation process and link these phase transitions to the performance of the algorithm.