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A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality.

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We created a formal framework for conflict-driven clause learning (CDCL) using Isabelle/HOL. This verified approach connects abstract calculus to functional and imperative SAT solvers, ensuring correctness and enabling experimentation.

Keywords:
CDCLDPLLIsabelle/HOLProof assistantsSAT solvers

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Area of Science:

  • Formal methods
  • Computer science
  • Automated reasoning

Background:

  • Conflict-Driven Clause Learning (CDCL) is a core technique in modern SAT solvers.
  • Formal verification of SAT solvers is crucial for ensuring their reliability.
  • Stepwise refinement is a powerful technique for developing verified software.

Purpose of the Study:

  • To develop a formally verified framework for Conflict-Driven Clause Learning (CDCL).
  • To connect an abstract CDCL calculus to concrete implementations in functional and imperative programming languages.
  • To provide a platform for proving metatheorems and experimenting with CDCL variants.

Main Methods:

  • Utilized the Isabelle/HOL proof assistant for formalization and verification.
  • Employed a chain of refinements to bridge abstract calculus and concrete SAT solver implementations.
  • Leveraged Isabelle's Refinement Framework to automate verification steps.
  • Implemented the imperative SAT solver using the two-watched-literal data structure.

Main Results:

  • A formally verified framework for CDCL, guaranteeing total correctness.
  • Successful refinement from an abstract calculus to functional and imperative SAT solvers.
  • Demonstrated the framework's utility for proving metatheorems and exploring variants like DPLL.
  • Incorporated advanced features such as forget, restart, and incremental solving rules.

Conclusions:

  • The developed framework provides a robust and verifiable foundation for CDCL solvers.
  • Stepwise refinement is effective for constructing complex, verified software components.
  • The framework facilitates the exploration and verification of novel CDCL techniques and optimizations.