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A verified SAT solver with watched literals using imperative HOL

Authors:

Mathias Fleury,

Jasmin Christian Blanchette,

Peter LammichAuthors Info & Claims

CPP 2018: Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs

Pages 158 - 171

https://doi.org/10.1145/3167080

Published: 08 January 2018 Publication History

Abstract

Based on our earlier formalization of conflict-driven clause learning (CDCL) in Isabelle/HOL, we refine the CDCL calculus to add a crucial optimization: two watched literals. We formalize the data structure and the invariants. Then we refine the calculus to obtain an executable SAT solver. Through a chain of refinements carried out using the Isabelle Refinement Framework, we target Imperative HOL and extract imperative Standard ML code. Although our solver is not competitive with the state of the art, it offers acceptable performance for some applications, and heuristics can be added to improve it further.

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Cited By

Chappe NHenrio LZakowski YStark KTimany ABlazy STabareau N(2025)Monadic Interpreters for Concurrent Memory ModelsProceedings of the 14th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3703595.3705890(283-298)Online publication date: 10-Jan-2025
https://dl.acm.org/doi/10.1145/3703595.3705890
Lammich P(2024)Refinement of Parallel Algorithms Down to LLVM: Applied to Practically Efficient Parallel SortingJournal of Automated Reasoning10.1007/s10817-024-09701-w68:3Online publication date: 19-Jun-2024
https://doi.org/10.1007/s10817-024-09701-w
Tan YHeule MMyreen M(2023)Verified Propagation Redundancy and Compositional UNSAT Checking in CakeMLInternational Journal on Software Tools for Technology Transfer10.1007/s10009-022-00690-y25:2(167-184)Online publication date: 27-Feb-2023
https://doi.org/10.1007/s10009-022-00690-y
Show More Cited By

Index Terms

A verified SAT solver with watched literals using imperative HOL
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Software and its engineering
  1. Software creation and management
    1. Software verification and validation
      1. Formal software verification
  2. Software organization and properties
    1. Software functional properties
      1. Formal methods
        Software verification

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Published In

cover image ACM Conferences

CPP 2018: Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs

January 2018

306 pages

ISBN:9781450355865

DOI:10.1145/3176245

Program Chairs:
June Andronick
Data61 at CSIRO, Australia / UNSW, Australia
,
Amy Felty
University of Ottawa, Canada

Copyright © 2018 ACM.

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Published: 08 January 2018

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European Research Council

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CPP '18

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SIGPLAN

CPP '18: Certified Proofs and Programs

January 8 - 9, 2018

CA, Los Angeles, USA

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Overall Acceptance Rate 18 of 26 submissions, 69%

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Cited By

Chappe NHenrio LZakowski YStark KTimany ABlazy STabareau N(2025)Monadic Interpreters for Concurrent Memory ModelsProceedings of the 14th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3703595.3705890(283-298)Online publication date: 10-Jan-2025
https://dl.acm.org/doi/10.1145/3703595.3705890
Lammich P(2024)Refinement of Parallel Algorithms Down to LLVM: Applied to Practically Efficient Parallel SortingJournal of Automated Reasoning10.1007/s10817-024-09701-w68:3Online publication date: 19-Jun-2024
https://doi.org/10.1007/s10817-024-09701-w
Tan YHeule MMyreen M(2023)Verified Propagation Redundancy and Compositional UNSAT Checking in CakeMLInternational Journal on Software Tools for Technology Transfer10.1007/s10009-022-00690-y25:2(167-184)Online publication date: 27-Feb-2023
https://doi.org/10.1007/s10009-022-00690-y
Lotz KKulczynski MNowotka DPoulsen DSchlichtkrull A(2023)Verified Verifying: SMT-LIB for Strings in IsabelleImplementation and Application of Automata10.1007/978-3-031-40247-0_15(206-217)Online publication date: 10-Aug-2023
https://doi.org/10.1007/978-3-031-40247-0_15
Baek SCarneiro MHeule M(2021)A Flexible Proof Format for SAT Solver-Elaborator CommunicationTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-72016-2_4(59-75)Online publication date: 20-Mar-2021
https://doi.org/10.1007/978-3-030-72016-2_4
Tan YHeule MMyreen M(2021)cake_lpr: Verified Propagation Redundancy Checking in CakeMLTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-72013-1_12(223-241)Online publication date: 23-Mar-2021
https://doi.org/10.1007/978-3-030-72013-1_12
Schlichtkrull ABlanchette JTraytel DWaldmann U(2020)Formalizing Bachmair and Ganzinger’s Ordered Resolution ProverJournal of Automated Reasoning10.1007/s10817-020-09561-0Online publication date: 17-Jun-2020
https://doi.org/10.1007/s10817-020-09561-0
Lammich P(2020)Efficient Verified Implementation of Introsort and PdqsortAutomated Reasoning10.1007/978-3-030-51054-1_18(307-323)Online publication date: 24-Jun-2020
https://doi.org/10.1007/978-3-030-51054-1_18
Blanchette JFontaine PSchulz STourret SWaldmann U(2019)Proceedings of the Second International Workshop on Automated Reasoning: Challenges, Applications, Directions, Exemplary AchievementsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.311.2311(11-17)Online publication date: 31-Dec-2019
https://doi.org/10.4204/EPTCS.311.2
Schlichtkrull ABlanchette JTraytel DMahboubi AMyreen M(2019)A verified prover based on ordered resolutionProceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3293880.3294100(152-165)Online publication date: 14-Jan-2019
https://dl.acm.org/doi/10.1145/3293880.3294100
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