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Document
DOI: 10.4230/DagRep.15.6.1
Certifying Algorithms for Automated Reasoning (Dagstuhl Seminar 25231)

Authors: Nikolaj S. Bjørner, Marijn J. H. Heule, Daniela Kaufmann, Jakob Nordström, and Wietze Koops

Published in: Dagstuhl Reports, Volume 15, Issue 6 (2026)

Abstract
Modern automated reasoning has transformed large parts of industry and has also found numerous scientific applications. But many reasoning problems are computationally very challenging, or sometimes even undecidable. Because of this, the reasoning algorithms used are often very complex, and even the best current algorithms at times produce wrong results. As these tools are increasingly being used autonomously, sometimes even in life-critical applications, it is urgent to ensure that what they compute is valid. Software testing, while immensely useful, cannot guarantee correctness, and state-of-the-art algorithms are far beyond what techniques for producing formally verified software can handle. The focus of this Dagstuhl Seminar was the approach of addressing such issues by designing certifying algorithms using so-called proof logging, meaning that algorithms output not only a result but also a machine-verifiable proof of correctness. This proof can then be fed to a dedicated proof checker for verification. Crucially, such proofs should require low overhead to generate and be easy to check, but still supply 100% correctness guarantees. Besides ensuring correctness of outputs for complex algorithms, proof logging can also provide new tools for algorithm development and analysis, software debugging, and even research into explainability in the context of AI.
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Nikolaj S. Bjørner, Marijn J. H. Heule, Daniela Kaufmann, Jakob Nordström, and Wietze Koops. Certifying Algorithms for Automated Reasoning (Dagstuhl Seminar 25231). In Dagstuhl Reports, Volume 15, Issue 6, pp. 1-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{bjorner_et_al:DagRep.15.6.1,
  author =	{Bj{\o}rner, Nikolaj S. and Heule, Marijn J. H. and Kaufmann, Daniela and Nordstr\"{o}m, Jakob and Koops, Wietze},
  title =	{{Certifying Algorithms for Automated Reasoning (Dagstuhl Seminar 25231)}},
  pages =	{1--31},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2026},
  volume =	{15},
  number =	{6},
  editor =	{Bj{\o}rner, Nikolaj S. and Heule, Marijn J. H. and Kaufmann, Daniela and Nordstr\"{o}m, Jakob and Koops, Wietze},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.6.1},
  URN =		{urn:nbn:de:0030-drops-255798},
  doi =		{10.4230/DagRep.15.6.1},
  annote =	{Keywords: ATP, Computer Algebra, DRAT, DRUP, MIP, Propagation Redundancy, QBF, SAT, SMT}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.21
Practically Feasible Proof Logging for Pseudo-Boolean Optimization

Authors: Wietze Koops, Daniel Le Berre, Magnus O. Myreen, Jakob Nordström, Andy Oertel, Yong Kiam Tan, and Marc Vinyals

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Certifying solvers have long been standard for decision problems in Boolean satisfiability (SAT), allowing for proof logging and checking with very limited overhead, but developing similar tools for combinatorial optimization has remained a challenge. A recent promising approach covering a wide range of solving paradigms is pseudo-Boolean proof logging, but this has mostly consisted of proof-of-concept works far from delivering the performance required for real-world deployment. In this work, we present an efficient toolchain based on VeriPB and CakePB for formally verified pseudo-Boolean optimization. We implement proof logging for the full range of techniques in the state-of-the-art solvers RoundingSat and Sat4j, including core-guided search and linear programming integration with Farkas certificates and cut generation. Our experimental evaluation shows that proof logging and checking performance in this much more expressive paradigm is now quite close to the level of SAT solving, and hence is clearly practically feasible.
Cite as

Wietze Koops, Daniel Le Berre, Magnus O. Myreen, Jakob Nordström, Andy Oertel, Yong Kiam Tan, and Marc Vinyals. Practically Feasible Proof Logging for Pseudo-Boolean Optimization. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 21:1-21:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koops_et_al:LIPIcs.CP.2025.21,
  author =	{Koops, Wietze and Le Berre, Daniel and Myreen, Magnus O. and Nordstr\"{o}m, Jakob and Oertel, Andy and Tan, Yong Kiam and Vinyals, Marc},
  title =	{{Practically Feasible Proof Logging for Pseudo-Boolean Optimization}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{21:1--21:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.21},
  URN =		{urn:nbn:de:0030-drops-238825},
  doi =		{10.4230/LIPIcs.CP.2025.21},
  annote =	{Keywords: proof logging, certifying algorithms, combinatorial optimization, certification, pseudo-Boolean solving, 0-1 integer linear programming}
}
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