# 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…

## 7 Citations

### Certified CNF Translations for Pseudo-Boolean Solving

- Computer ScienceSAT
- 2022

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

- Computer ScienceTACAS
- 2022

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

- Computer ScienceSAT
- 2022

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

- Computer ScienceAAAI
- 2022

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

- Computer ScienceCADE
- 2021

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

- Computer ScienceCP
- 2022

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

- Computer ScienceArXiv
- 2022

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.

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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.

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