Efficient Certified Resolution Proof Checking

@article{CruzFilipe2017EfficientCR,
  title={Efficient Certified Resolution Proof Checking},
  author={Lu{\'i}s Cruz-Filipe and Joao Marques-Silva and Peter Schneider-Kamp},
  journal={ArXiv},
  year={2017},
  volume={abs/1610.06984}
}
We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280… 

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References

SHOWING 1-10 OF 55 REFERENCES

Mechanical Verification of SAT Refutations with Extended Resolution

We present a mechanically-verified proof checker developed with the ACL2 theorem-proving system that is general enough to support the growing variety of increasingly complex satisfiability (SAT)

Verifying Refutations with Extended Resolution

TLDR
This work presents a new proof format for checking unsatisfiability proofs produced by SAT solvers that use techniques such as extended resolution and blocked clause addition, and shows how existing preprocessors and solvers can be modified to generate proofs in this format.

Efficiently checking propositional refutations in HOL theorem provers

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

TLDR
A formalized theory of size-optimal sorting networks is described and from this formalization a certified checker is extracted that successfully verifies computer-generated proofs of optimality on up to 8 inputs.

Bridging the gap between easy generation and efficient verification of unsatisfiability proofs

TLDR
This paper presents a practical approach that facilitates checking of unsatisfiability results in a time similar to proof discovery by embedding clause deletion information into clausal proofs.

A First Step Towards a Unified Proof Checker for QBF

TLDR
A new uniform proof format is proposed, which captures refutations and witnesses for a variety of QBF solvers, and is based on a novel extended resolution rule for QBF.

Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

TLDR
Several non-trivial optimizations of the algorithm in the checker are described, obtained by appropriately changing the formalization and capitalizing on the symbiosis with an adequate implementation of the oracle.

Validating SAT solvers using an independent resolution-based checker: practical implementations and other applications

  • Lintao ZhangS. Malik
  • Computer Science
    2003 Design, Automation and Test in Europe Conference and Exhibition
  • 2003
TLDR
The implementation of an independent resolution-based checking procedure that can check the validity of unsatisfiable claims produced by the SAT solver zchaff is described and Experimental results show low overhead for the checking process.

A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses

TLDR
A way to enjoy the power of SAT and SMT provers in Coq without compromising soundness is presented, conceived in a modular way, in order to tame the proofs' complexity and to be extendable.

Efficient Certified RAT Verification

TLDR
A new format is presented, called LRAT, which extends the DRAT format with hints that facilitate a simple and fast validation algorithm, and checking validity of LRAT proofs can be implemented using trusted systems such as the languages supported by theorem provers.
...