Author name cluster

Andy Oertel

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

4 papers

2 author rows

AAAI Conference 2026 Conference Paper

Faster Certified Symmetry Breaking Using Orders with Auxiliary Variables

Markus Anders
Bart Bogaerts
Benjamin Bogø
Arthur Gontier
Wietze Koops
Ciaran McCreesh
Magnus O. Myreen
Jakob Nordström

Symmetry breaking is a crucial technique in modern combinatorial solving, but it is difficult to be sure it is implemented correctly. The most successful approach to deal with bugs is to make solvers certifying, so that they output not just a solution, but also a mathematical proof of correctness in a standard format, which can then be checked by a formally verified checker. This requires justifying symmetry reasoning within the proof, but developing efficient methods for this has remained a long-standing open challenge. A fully general approach was recently proposed, but it relies on encoding lexicographic orders with big integers, which quickly becomes infeasible for large symmetries. In this work, we develop a method for instead encoding orders with auxiliary variables. We show that this leads to orders-of-magnitude speed-ups in both theory and practice by running experiments on proof logging and checking for SAT symmetry breaking using the state-of-the-art satsuma symmetry breaker and the VeriPB proof checking toolchain.

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AAAI Conference 2024 Conference Paper

End-to-End Verification for Subgraph Solving

Stephan Gocht
Ciaran McCreesh
Magnus O. Myreen
Jakob Nordström
Andy Oertel
Yong Kiam Tan

Modern subgraph-finding algorithm implementations consist of thousands of lines of highly optimized code, and this complexity raises questions about their trustworthiness. Recently, some state-of-the-art subgraph solvers have been enhanced to output machine-verifiable proofs that their results are correct. While this significantly improves reliability, it is not a fully satisfactory solution, since end-users have to trust both the proof checking algorithms and the translation of the high-level graph problem into a low-level 0-1 integer linear program (ILP) used for the proofs. In this work, we present the first formally verified toolchain capable of full end-to-end verification for subgraph solving, which closes both of these trust gaps. We have built encoder frontends for various graph problems together with a 0-1 ILP (a.k.a. pseudo-Boolean) proof checker, all implemented and formally verified in the CakeML ecosystem. This toolchain is flexible and extensible, and we use it to build verified proof checkers for both decision and optimization graph problems, namely, subgraph isomorphism, maximum clique, and maximum common (connected) induced subgraph. Our experimental evaluation shows that end-to-end formal verification is now feasible for a wide range of hard graph problems.

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IJCAI Conference 2023 Conference Paper

Certified CNF Translations for Pseudo-Boolean Solving (Extended Abstract).

Stephan Gocht
Ruben Martins
Jakob Nordström
Andy Oertel

The dramatic improvements in Boolean satisfiability (SAT) solving since the turn of the millennium have made it possible to leverage conflict-driven clause learning (CDCL) solvers for many combinatorial problems in academia and industry, and the use of proof logging has played a crucial role in increasing the confidence that the results these solvers produce are correct. However, the fact that SAT proof logging is performed in conjunctive normal form (CNF) clausal format means that it has not been possible to extend guarantees of correctness to the use of SAT solvers for more expressive combinatorial paradigms, where the first step is an unverified translation of the input to CNF. In this work, we show how cutting-planes-based reasoning can provide proof logging for solvers that translate pseudo-Boolean (a. k. a. 0-1 integer linear) decision problems to CNF and then run CDCL. We are hopeful that this is just a first step towards providing a unified proof logging approach that will extend to maximum satisfiability (MaxSAT) solving and pseudo-Boolean optimization in general.

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SAT Conference 2022 Conference Paper

Certified CNF Translations for Pseudo-Boolean Solving

Stephan Gocht
Ruben Martins
Jakob Nordström
Andy Oertel

The dramatic improvements in Boolean satisfiability (SAT) solving since the turn of the millennium have made it possible to leverage state-of-the-art conflict-driven clause learning (CDCL) solvers for many combinatorial problems in academia and industry, and the use of proof logging has played a crucial role in increasing the confidence that the results these solvers produce are correct. However, the fact that SAT proof logging is performed in conjunctive normal form (CNF) clausal format means that it has not been possible to extend guarantees of correctness to the use of SAT solvers for more expressive combinatorial paradigms, where the first step is an unverified translation of the input to CNF. In this work, we show how cutting-planes-based reasoning can provide proof logging for solvers that translate pseudo-Boolean (a. k. a. 0-1 integer linear) decision problems to CNF and then run CDCL. To support a wide range of encodings, we provide a uniform and easily extensible framework for proof logging of CNF translations. We are hopeful that this is just a first step towards providing a unified proof logging approach that will also extend to maximum satisfiability (MaxSAT) solving and pseudo-Boolean optimization in general.

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