Certifying Parity Reasoning Efficiently Using Pseudo-Boolean Proofs

@article{Gocht2021CertifyingPR,
  title={Certifying Parity Reasoning Efficiently Using Pseudo-Boolean Proofs},
  author={Stephan Gocht and Jakob Nordstr{\"o}m},
  journal={ArXiv},
  year={2021},
  volume={abs/2209.12185}
}
The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard to verify and is sometimes wrong. For Boolean satisfiability (SAT) solvers proof logging has been introduced as a way to certify correctness, but the methods used seem hard to generalize to stronger paradigms. What is more, even for enhanced SAT techniques… 

Figures and Tables from this paper

Certified CNF Translations for Pseudo-Boolean Solving

This work shows how cutting-planes-based reasoning can provide proof logging for solvers that translate pseudo-Boolean decision problems to CNF and then run CDCL, and provides a uniform and easily extensible framework for proof logging of CNF translations.

Clausal Proofs for Pseudo-Boolean Reasoning

Working together, the two solvers can generate proofs of unsatis(cid:2)ability for problems that are intractable for other proof-generating SAT solvers.

Proofs for Propositional Model Counting

It is shown how proof traces can be generated for exact model counters based on dynamic programming, counting CDCL with component caching, and knowledge compilation to Decision-DNNF, which are the predominant techniques in today’s exact implementations.

Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

It is demonstrated that the cutting planes proof system can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes XOR and cardinality reasoning.

Non-clausal Redundancy Properties

This paper extends the redundancy framework beyond clauses to characterize redundancy for Boolean constraints in general, and shows this characterization can be instantiated to develop efficiently checkable refutation systems using redundancy properties for Binary Decision Diagrams (BDDs).

An Auditable Constraint Programming Solver

The design and implementation of a new constraint programming solver that can produce an auditable record of what problem was solved and how the solution was reached is described and an independently verifiable proof log demonstrating that the solution is correct is provided.

Logic-Based Explainability in Machine Learning

This paper overviews the ongoing research efforts on computing rigorous model-based explanations of ML models, including the actual definitions of explanations, the characterization of the complexity of computing explanations, and also how to make explanations interpretable for human decision makers, among others.

References

SHOWING 1-10 OF 71 REFERENCES

Certified CNF Translations for Pseudo-Boolean Solving

This work shows how cutting-planes-based reasoning can provide proof logging for solvers that translate pseudo-Boolean decision problems to CNF and then run CDCL, and provides a uniform and easily extensible framework for proof logging of CNF translations.

Engineering an Efficient PB-XOR Solver

This work proposes an efficient solver engineered for PB-XOR formulas, i.e., formulas consisting of a conjunction of PB and XOR constraints, and proposes three different tactics, all of which achieve significant performance improvements over the baseline.

Divide and Conquer: Towards Faster Pseudo-Boolean Solving

A modified approach to pseudo-Boolean solving based on division instead of the saturation rule used in [Chai and Kuehlmann '05] and other PB solvers, which results in a stronger conflict analysis and improves performance by keeping integer coefficient sizes down.

Extending Clause Learning SAT Solvers with Complete Parity Reasoning

A new xor-reasoning module that deduces all possible implied literals using incremental Gauss-Jordan elimination is presented and it is shown how to eliminate variables occuring only in parity constraints while preserving the decomposition.

A Cardinal Improvement to Pseudo-Boolean Solving

This work presents a technique to recover cardinality constraints from CNF on the fly during search by collecting potential building blocks of cardinality constraint constraints during propagation and combining these blocks during conflict analysis.

Clausal Proofs for Pseudo-Boolean Reasoning

Working together, the two solvers can generate proofs of unsatis(cid:2)ability for problems that are intractable for other proof-generating SAT solvers.

DRAT Proofs for XOR Reasoning

This work considers the problem of generating proofs for the XOR reasoning component in SAT solvers and proposes two methods: direct translation transforms every XOR constraint addition inference into a DRAT proof, whereas T-translation avoids the exponential blow-up in direct translations by using fresh variables.

Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

It is demonstrated that the cutting planes proof system can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes XOR and cardinality reasoning.

Justifying All Differences Using Pseudo-Boolean Reasoning

This paper demonstrates that simple, clean, and efficient proof logging is still possible for the all-different constraint, through pseudo-Boolean reasoning.

Expressing Symmetry Breaking in DRAT Proofs

This work presents a method to express the addition of symmetry-breaking predicates in DRAT, a clausal proof format supported by top-tier solvers and validated these proofs with an ACL2-based, mechanically-verified DRAT proof checker and the proof-checking tool of SAT Competition 2014.
...