From Total Assignment Enumeration to Modern SAT Solver

TL;DR

This paper introduces a new framework that explains the core functionalities of modern SAT solvers by linking backtracking, resolution, and inference techniques, providing insights into their inference power and design.

Contribution

It presents a step-by-step derivation of a modern SAT solver from DLL, analyzing key inference mechanisms and offering a foundational understanding for future research and development.

Findings

Analysis of Boolean Constraint Propagation's inference power

Evaluation of Non-Chronological Backtracking effectiveness

Assessment of 1UIP-based Conflict-Directed Backjumping

Abstract

A new framework for presenting and analyzing the functionality of a modern DLL-based SAT solver is proposed. Our approach exploits the inherent relation between backtracking and resolution. We show how to derive the algorithm of a modern SAT solver from DLL step-by-step. We analyze the inference power of Boolean Constraint Propagation, Non-Chronological Backtracking and 1UIP-based Conflict-Directed Backjumping. Our work can serve as an introduction to a modern SAT solver functionality and as a basis for future work on the inference power of a modern SAT solver and on practical SAT solver design.