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On the Structure of the Boolean Satisfiability Problem: A Survey

Published: 30 March 2022 Publication History

Abstract

The Boolean satisfiability problem (SAT) is a fundamental NP-complete decision problem in automated reasoning and mathematical logic. As evidenced by the results of SAT competitions, the performance of SAT solvers varies substantially between different SAT categories (random, crafted, and industrial). A suggested explanation is that SAT solvers may exploit the underlying structure inherent to SAT instances. There have been attempts to define the structure of SAT in terms of structural measures such as phase transition, backbones, backdoors, small-world, scale-free, treewidth, centrality, community, self-similarity, and entropy. Still, the empirical evidence of structural measures for SAT has been provided for only some SAT categories. Furthermore, the evidence has not been theoretically proven. Also, the impact of structural measures on the behavior of SAT solvers has not been extensively examined. This work provides a comprehensive study on structural measures for SAT that have been presented in the literature. We provide an overview of the works on structural measures for SAT and their relatedness to the performance of SAT solvers. Accordingly, a taxonomy of structural measures for SAT is presented. We also review in detail important applications of structural measures for SAT, focusing mainly on enhancing SAT solvers, generating SAT instances, and classifying SAT instances.

Supplementary Material

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Supplemental movie, appendix, image and software files for, On the Structure of the Boolean Satisfiability Problem: A Survey

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  1. On the Structure of the Boolean Satisfiability Problem: A Survey

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      Published In

      cover image ACM Computing Surveys
      ACM Computing Surveys  Volume 55, Issue 3
      March 2023
      772 pages
      ISSN:0360-0300
      EISSN:1557-7341
      DOI:10.1145/3514180
      Issue’s Table of Contents

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      Published: 30 March 2022
      Accepted: 01 October 2021
      Revised: 01 September 2021
      Received: 01 April 2021
      Published in CSUR Volume 55, Issue 3

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      Author Tags

      1. SAT
      2. structural measures
      3. backbone
      4. backdoor
      5. small-world
      6. scale-free
      7. treewidth
      8. centrality
      9. community
      10. self-similarity
      11. entropy

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      • (2025)WANCE: Learnt Clause Evaluation Method for SAT Solver Using Graph StructureLearning and Intelligent Optimization10.1007/978-3-031-75623-8_15(190-204)Online publication date: 3-Jan-2025
      • (2024)A fast algorithm for MaxSAT above half number of clausesProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/214(1935-1943)Online publication date: 3-Aug-2024
      • (2024)A Novel Approach for Traveling Salesman Problem Via Probe Machine2024 IEEE 24th International Conference on Software Quality, Reliability and Security (QRS)10.1109/QRS62785.2024.00076(713-723)Online publication date: 1-Jul-2024
      • (2024)Balancing Individual and Collective Strategies: A New Approach in Metaheuristic Optimization.Mathematics and Computers in Simulation10.1016/j.matcom.2024.08.004Online publication date: Aug-2024
      • (2024)Vulnerability impact analysis in software project dependencies based on Satisfiability Modulo Theories (SMT)Computers and Security10.1016/j.cose.2023.103669139:COnline publication date: 16-May-2024
      • (2024)All-quantum-dot information systemNano Research10.1007/s12274-024-6911-z17:12(10570-10584)Online publication date: 31-Aug-2024
      • (2024)Deep learning-based software engineering: progress, challenges, and opportunitiesScience China Information Sciences10.1007/s11432-023-4127-568:1Online publication date: 24-Dec-2024
      • (2024)A Backtracking Algorithm for Solving the Nearly Equitable Strong Edge-coloring Problem on Transportation NetworkNetworks and Spatial Economics10.1007/s11067-024-09661-zOnline publication date: 18-Dec-2024
      • (2023)Machine Learning Methods in Solving the Boolean Satisfiability ProblemMachine Intelligence Research10.1007/s11633-022-1396-220:5(640-655)Online publication date: 1-Jun-2023
      • (2022)Boosting the Performance of CDCL-Based SAT Solvers by Exploiting Backbones and BackdoorsAlgorithms10.3390/a1509030215:9(302)Online publication date: 26-Aug-2022

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