58 Search Results for "Heule, Marijn J. H."

Document
DOI: 10.4230/LIPIcs.CSL.2026.18
A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light

Authors: Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We extend the existing HOL Light Library for Modal Systems (HOLMS) to support a modular implementation of modal reasoning within the HOL Light proof assistant. We deeply embed axiomatic calculi and relational semantics for seven normal modal logics (K, T, B, K4, S4, S5, GL) and formalise modal adequacy theorems for these systems. We then leverage those formalisations to implement a mechanism for automated reasoning via proof-search in the associated labelled sequent calculi, which we shallowly embed in HOL Light’s goal-stack mechanism. This way, we equip the general-purpose proof assistant with (semi)decision procedures for these logics that, in case of failure to construct a proof for the input formula, return a certified countermodel within the appropriate class for the logic under consideration. On the methodological side, we propose a precise measure of the modularity of our approach by systematically adopting Christopher Strachey’s distinction between ad hoc and parametric polymorphism throughout the library.
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Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi. A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 18:1-18:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bilotta_et_al:LIPIcs.CSL.2026.18,
  author =	{Bilotta, Antonella and Maggesi, Marco and Perini Brogi, Cosimo},
  title =	{{A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{18:1--18:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.18},
  URN =		{urn:nbn:de:0030-drops-254427},
  doi =		{10.4230/LIPIcs.CSL.2026.18},
  annote =	{Keywords: Modal logic, HOL Light, Labelled sequent calculi, Logical verification, Interactive theorem proving, Automated proof-search}
}
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.FSTTCS.2025.25
On the Interplay of Cube Learning and Dependency Schemes in {QCDCL} Proof Systems

Authors: Abhimanyu Choudhury and Meena Mahajan

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Quantified Conflict Driven Clause Leaning (QCDCL) is one of the main approaches to solving Quantified Boolean Formulas (QBF). Cube-learning is employed in this approach to ensure that true formulas can be verified. Dependency Schemes help to detect spurious dependencies that are implied by the variable ordering in the quantifier prefix of QBFs but are not essential for constructing (counter)models. This detection can provably shorten refutations in specific proof systems, and is expected to speed up runs of QBF solvers. The simplest underlying proof system [BeyersdorffBöhm-LMCS2023], formalises the reasoning in the QCDCL approach on false formulas, when neither cube-learning nor dependency schemes is used. The work of [BöhmPeitlBeyersdorff-AI2024] further incorporates cube-learning. The work of [ChoudhuryMahajan-JAR2024] incorporates a limited use of dependency schemes, but without cube-learning. In this work, proof systems underlying the reasoning of QCDCL solvers which use cube learning, and which use dependency schemes at all stages, are formalised. Sufficient conditions for soundness and completeness are presented, and it is shown that using the standard and reflexive resolution path dependency schemes (𝙳^{std} and 𝙳^{rrs}) to relax the decision order provably shortens refutations. When the decisions are restricted to follow quantification order, but dependency schemes are used in propagation and learning, in conjunction with cube-learning, the resulting proof systems using the dependency schemes 𝙳^{std} and 𝙳^{rrs} are investigated in detail and their relative strengths are analysed.
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Abhimanyu Choudhury and Meena Mahajan. On the Interplay of Cube Learning and Dependency Schemes in {QCDCL} Proof Systems. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{choudhury_et_al:LIPIcs.FSTTCS.2025.25,
  author =	{Choudhury, Abhimanyu and Mahajan, Meena},
  title =	{{On the Interplay of Cube Learning and Dependency Schemes in \{QCDCL\} Proof Systems}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.25},
  URN =		{urn:nbn:de:0030-drops-251062},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.25},
  annote =	{Keywords: QBF, CDCL, Resolution, Dependency schemes}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.25
The Exchange Problem

Authors: Mohit Garg and Suneel Sarswat

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the matching are maximizing volume with dynamic pricing and maximizing volume at a uniform price. In this work, we study the algorithmic complexity of the problems arising from these matching tasks. For dynamic-price matching, we establish a lower bound of Ω(n log n) on the running time, thereby proving that the currently best-known O(n log n) algorithm is time-optimal. In contrast, for uniform-price matching, we present a linear-time algorithm, improving upon previous methods that require O(n log n) time to match n requests.
Cite as

Mohit Garg and Suneel Sarswat. The Exchange Problem. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garg_et_al:LIPIcs.AFT.2025.25,
  author =	{Garg, Mohit and Sarswat, Suneel},
  title =	{{The Exchange Problem}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.25},
  URN =		{urn:nbn:de:0030-drops-247449},
  doi =		{10.4230/LIPIcs.AFT.2025.25},
  annote =	{Keywords: Exchanges, Double Auctions, Matching Algorithms, Element Distinctness, Time Complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.56
PLS-Completeness of String Permutations

Authors: Dominik Scheder and Johannes Tantow

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Bitstrings can be permuted via permutations and compared via the lexicographic order. In this paper we study the complexity of finding a minimum of a bitstring via given permutations. As finding a global optimum is known to be NP-complete [László Babai and Eugene M. Luks, 1983], we study the local optima via the class PLS [David S. Johnson et al., 1988] and show hardness for PLS. Additionally, we show that even for one permutation the global optimization problem is NP-complete and give a formula that has these permutation as its symmetries. This answers an open question inspired from Kołodziejczyk and Thapen [Leszek Aleksander Kolodziejczyk and Neil Thapen, 2024] and stated at the SAT and interactions seminar in Dagstuhl.
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Dominik Scheder and Johannes Tantow. PLS-Completeness of String Permutations. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{scheder_et_al:LIPIcs.ESA.2025.56,
  author =	{Scheder, Dominik and Tantow, Johannes},
  title =	{{PLS-Completeness of String Permutations}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{56:1--56:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.56},
  URN =		{urn:nbn:de:0030-drops-245245},
  doi =		{10.4230/LIPIcs.ESA.2025.56},
  annote =	{Keywords: PLS, total search problems, local search, permutation groups, symmetry}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.35
Verifying an Efficient Algorithm for Computing Bernoulli Numbers

Authors: Manuel Eberl and Peter Lammich

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
The Bernoulli numbers B_k are a sequence of rational numbers that is ubiquitous in mathematics, but difficult to compute efficiently (compared to e.g. approximating π). In 2008, Harvey gave the currently fastest known practical way for computing them: his algorithm computes B_k mod p in time O(p log^{1 + o(1)} p). By doing this for O(k) many small primes p in parallel and then combining the results with the Chinese Remainder Theorem, one recovers the value of B_k as a rational number in O(k² log^{2 + o(1)} k) time. One advantage of this approach is that the expensive part of the algorithm is highly parallelisable and has very low memory requirements. This algorithm still holds the world record with its computation of B_{10⁸}. We give a verified efficient LLVM implementation of this algorithm. This was achieved by formalising the necessary mathematical background theory in Isabelle/HOL, proving an abstract version of the algorithm correct, and refining this abstract version down to LLVM using Lammich’s Isabelle-LLVM framework, including many low-level optimisations. The performance of the resulting LLVM code is comparable with Harvey’s original unverified and hand-optimised C++ implementation.
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Manuel Eberl and Peter Lammich. Verifying an Efficient Algorithm for Computing Bernoulli Numbers. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eberl_et_al:LIPIcs.ITP.2025.35,
  author =	{Eberl, Manuel and Lammich, Peter},
  title =	{{Verifying an Efficient Algorithm for Computing Bernoulli Numbers}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.35},
  URN =		{urn:nbn:de:0030-drops-246331},
  doi =		{10.4230/LIPIcs.ITP.2025.35},
  annote =	{Keywords: Bernoulli numbers, LLVM, verification, Isabelle, Chinese remainder theorem, modular arithmetic, Montgomery arithmetic}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.36
Verifying Datalog Reasoning with Lean

Authors: Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Datalog is an essential logical rule language with many applications, and modern rule engines compute logical consequences for Datalog with high performance and scalability. While Datalog is rather simple and, in principle, explainable by design, such sophisticated implementations and optimizations are hard to verify. We therefore propose a certificate-based approach to validate results of Datalog reasoners in a formally verified checker for Datalog proofs. Using the proof assistant Lean, we implement such a checker and verify its correctness against direct formalizations of the Datalog semantics. We propose two JSON encodings for Datalog proofs: one using the widely supported Datalog proof trees, and one using directed acyclic graphs for succinctness. To evaluate the practical feasibility and performance of our approach, we validate proofs that we obtain by converting derivation traces of an existing Datalog reasoner into our tool-independent format.
Cite as

Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch. Verifying Datalog Reasoning with Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tantow_et_al:LIPIcs.ITP.2025.36,
  author =	{Tantow, Johannes and Gerlach, Lukas and Mennicke, Stephan and Kr\"{o}tzsch, Markus},
  title =	{{Verifying Datalog Reasoning with Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{36:1--36:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.36},
  URN =		{urn:nbn:de:0030-drops-246342},
  doi =		{10.4230/LIPIcs.ITP.2025.36},
  annote =	{Keywords: Certifying Algorithms, Datalog, Formal Verification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.26
Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL

Authors: Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Sledgehammer is a tool that increases the level of automation in the Isabelle/HOL proof assistant by asking external automatic theorem provers (ATPs), including SMT solvers, to prove the current goal. When the external ATP succeeds it must provide enough evidence that the goal holds for Isabelle to be able to reprove it internally based on that evidence. In particular, Isabelle can do this by replaying fine-grained proof certificates from proof-producing SMT solvers as long as they are expressed in the Alethe format, which until now was supported only by the veriT SMT solver. We report on our experience adding proof reconstruction support for the cvc5 SMT solver in Isabelle by extending cvc5 to produce proofs in the Alethe format and then adapting Isabelle to reconstruct those proofs. We discuss several difficulties and pitfalls we encountered and describe a set of tools and techniques we developed to improve the process. A notable outcome of this effort is that Isabelle can now be used as an independent proof checker for SMT problems written in the SMT-LIB standard. We evaluate cvc5’s integration on a set of SMT-LIB benchmarks originating from Isabelle as well as on a set of Isabelle proofs. Our results confirm that this integration complements and improves Sledgehammer’s capabilities.
Cite as

Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli. Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lachnitt_et_al:LIPIcs.ITP.2025.26,
  author =	{Lachnitt, Hanna and Fleury, Mathias and Barbosa, Haniel and Jakpor, Jibiana and Andreotti, Bruno and Reynolds, Andrew and Schurr, Hans-J\"{o}rg and Barrett, Clark and Tinelli, Cesare},
  title =	{{Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.26},
  URN =		{urn:nbn:de:0030-drops-246243},
  doi =		{10.4230/LIPIcs.ITP.2025.26},
  annote =	{Keywords: interactive theorem proving, proof assistants, Isabelle/HOL, SMT, certification, proof certificates, proof reconstruction, proof automation}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2025.38
Sledgehammering Without ATPs (Short Paper)

Authors: Martin Desharnais and Jasmin Blanchette

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We describe an alternative architecture for "hammers," inspired by Magnushammer, in which proofs are found by the proof assistant’s built-in automation instead of by external automatic theorem provers (ATPs). We implemented this approach in Isabelle’s Sledgehammer and evaluated it. The new ATP-free approach nicely complements the traditional Sledgehammer. The two approaches in combination solve more goals than the traditional ATP-based approach alone.
Cite as

Martin Desharnais and Jasmin Blanchette. Sledgehammering Without ATPs (Short Paper). In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 38:1-38:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{desharnais_et_al:LIPIcs.ITP.2025.38,
  author =	{Desharnais, Martin and Blanchette, Jasmin},
  title =	{{Sledgehammering Without ATPs}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{38:1--38:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.38},
  URN =		{urn:nbn:de:0030-drops-246366},
  doi =		{10.4230/LIPIcs.ITP.2025.38},
  annote =	{Keywords: Interactive theorem proving, proof assistants, proof automation}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.24
Formally Verifying a Vertical Cell Decomposition Algorithm

Authors: Yves Bertot and Thomas Portet

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
The broad context of this work is the application of formal methods to geometry and robotics. We describe an algorithm to decompose a working area containing obstacles into a collection of safe cells and the formal proof that this algorithm is correct. We expect such an algorithm will be useful to compute safe trajectories. To our knowledge, this is one of the first formalization of such an algorithm to decompose a working space into elementary cells that are suitable for later applications, with the proof of correctness that guarantees that large parts of the working space are safe. Techniques to perform this proof go from algebraic reasoning on coordinates and determinants to sorting. The main difficulty comes from the possible existence of degenerate cases, which are treated in a principled way.
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Yves Bertot and Thomas Portet. Formally Verifying a Vertical Cell Decomposition Algorithm. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bertot_et_al:LIPIcs.ITP.2025.24,
  author =	{Bertot, Yves and Portet, Thomas},
  title =	{{Formally Verifying a Vertical Cell Decomposition Algorithm}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.24},
  URN =		{urn:nbn:de:0030-drops-246222},
  doi =		{10.4230/LIPIcs.ITP.2025.24},
  annote =	{Keywords: Formal Verification, Motion planning, algorithmic geometry}
}
Document
DOI: 10.4230/OASIcs.SpaceCHI.2025.24
Understanding Time in Space: Improving Timeline Understandability for Uncrewed Space Systems

Authors: Elizabeth Sloan and Kristin Yvonne Rozier

Published in: OASIcs, Volume 130, Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)

Abstract
Timelines are critical in space exploration. Timelines facilitate planning, resource management, and automation of uncrewed missions. As NASA and other space agencies increasingly rely on timelines for autonomous spacecraft operations, ensuring their understandability and verifiability is essential for mission success. However, interdisciplinary design teams face challenges in interpreting timelines due to variations in cultural and educational backgrounds, leading to communication barriers and potential system mismatches. This work-in-progress research explores time-oriented data visualizations to improve timeline comprehension in space systems. We contribute (1) a survey of visualization techniques, identifying patterns and gaps in historic time-oriented data visualizations and industry tools, (2) a focus group pilot study analyzing user interpretations of timeline visualizations, and (3) a novel method for visualizing aggregate runs of a timeline on a complex system, including identification of key features for usability of aggregate-data visuals. Our findings inform future visualization strategies for debugging and verifying timelines in uncrewed systems. While focused on space, this research has broader implications for aerospace, robotics, and emergency response systems.
Cite as

Elizabeth Sloan and Kristin Yvonne Rozier. Understanding Time in Space: Improving Timeline Understandability for Uncrewed Space Systems. In Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025). Open Access Series in Informatics (OASIcs), Volume 130, pp. 24:1-24:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sloan_et_al:OASIcs.SpaceCHI.2025.24,
  author =	{Sloan, Elizabeth and Rozier, Kristin Yvonne},
  title =	{{Understanding Time in Space: Improving Timeline Understandability for Uncrewed Space Systems}},
  booktitle =	{Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)},
  pages =	{24:1--24:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-384-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{130},
  editor =	{Bensch, Leonie and Nilsson, Tommy and Nisser, Martin and Pataranutaporn, Pat and Schmidt, Albrecht and Sumini, Valentina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SpaceCHI.2025.24},
  URN =		{urn:nbn:de:0030-drops-240143},
  doi =		{10.4230/OASIcs.SpaceCHI.2025.24},
  annote =	{Keywords: Human-Ceneterd Design, Time-Oriented Data Visualization, Uncrewed Spacecraft Operations, Formal Methods}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.31
Transformer-Based Feature Learning for Algorithm Selection in Combinatorial Optimisation

Authors: Alessio Pellegrino, Özgür Akgün, Nguyen Dang, Zeynep Kiziltan, and Ian Miguel

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

Abstract
Given a combinatorial optimisation problem, there are typically multiple ways of modelling it for presentation to an automated solver. Choosing the right combination of model and target solver can have a significant impact on the effectiveness of the solving process. The best combination of model and solver can also be instance-dependent: there may not exist a single combination that works best for all instances of the same problem. We consider the task of building machine learning models to automatically select the best combination for a problem instance. Critical to the learning process is to define instance features, which serve as input to the selection model. Our contribution is the automatic learning of instance features directly from the high-level representation of a problem instance using a transformer encoder. We evaluate the performance of our approach using the Essence modelling language via a case study of three problem classes.
Cite as

Alessio Pellegrino, Özgür Akgün, Nguyen Dang, Zeynep Kiziltan, and Ian Miguel. Transformer-Based Feature Learning for Algorithm Selection in Combinatorial Optimisation. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 31:1-31:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pellegrino_et_al:LIPIcs.CP.2025.31,
  author =	{Pellegrino, Alessio and Akg\"{u}n, \"{O}zg\"{u}r and Dang, Nguyen and Kiziltan, Zeynep and Miguel, Ian},
  title =	{{Transformer-Based Feature Learning for Algorithm Selection in Combinatorial Optimisation}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{31:1--31:22},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-238928},
  doi =		{10.4230/LIPIcs.CP.2025.31},
  annote =	{Keywords: Constraint modelling, algorithm selection, feature extraction, machine learning, transformer architecture}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.36
Balancing Latin Rectangles with LLM-Generated Streamliners

Authors: Florentina Voboril, Vaidyanathan Peruvemba Ramaswamy, and Stefan Szeider

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

Abstract
We present an integration of Large Language Models (LLMs) with streamlining techniques to find well-balanced Latin rectangles. Our approach combines LLM-generated streamlining constraints that effectively partition the search space, directing constraint solvers toward structured subspaces containing high-quality solutions. Our methodology extends LLM-generated streamliners, as Voboril et al. (2024) introduced for decision problems, to the optimization context through techniques that incrementally refine the objective function value. We propose two complementary strategies to orchestrate sets of streamliners: an incremental mechanism that utilizes improving solutions to initialize subsequent search processes, and an evolutionary framework that maintains and refines effective streamliner populations. Our experiments demonstrate that our approach successfully reduces established minimum imbalance values for partially spatially balanced Latin rectangles across multiple problem dimensions. The results validate the efficacy of combining LLMs with constraint programming methodologies for tackling problems characterized by complex global constraints.
Cite as

Florentina Voboril, Vaidyanathan Peruvemba Ramaswamy, and Stefan Szeider. Balancing Latin Rectangles with LLM-Generated Streamliners. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{voboril_et_al:LIPIcs.CP.2025.36,
  author =	{Voboril, Florentina and Peruvemba Ramaswamy, Vaidyanathan and Szeider, Stefan},
  title =	{{Balancing Latin Rectangles with LLM-Generated Streamliners}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{36:1--36:17},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-238970},
  doi =		{10.4230/LIPIcs.CP.2025.36},
  annote =	{Keywords: Balanced Latin Rectangles, Streamliners, Large Language Models, Warmstarts, Evolutionary Search}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.8
Breaking Symmetries with Involutions

Authors: Michael Codish and Mikoláš Janota

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

Abstract
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered too weak to be of practical use. Recently, the concept of graph patterns has been introduced and provides a concise representation for (large) sets of non-canonical graphs, i.e. graphs that are not lex-leaders and can be excluded from search. In particular, four (specific) graph patterns apply to identify about 3/4 of the set of all non-canonical graphs. Taking this approach further, we discover that graph patterns that derive from permutations that are involutions play an important role in the construction of symmetry breaks for graphs. We take advantage of this to guide the construction of partial and complete symmetry-breaking constraints based on graph patterns. The resulting constraints are small in size and strong in the number of symmetries they break.
Cite as

Michael Codish and Mikoláš Janota. Breaking Symmetries with Involutions. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{codish_et_al:LIPIcs.CP.2025.8,
  author =	{Codish, Michael and Janota, Mikol\'{a}\v{s}},
  title =	{{Breaking Symmetries with Involutions}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{8:1--8:17},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-238699},
  doi =		{10.4230/LIPIcs.CP.2025.8},
  annote =	{Keywords: graph symmetry, patterns, permutation, Ramsey graphs, greedy, CEGAR}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.9
Constraint Models for Klondike

Authors: Nguyen Dang, Ian P. Gent, Peter Nightingale, Felix Ulrich-Oltean, and Jack Waller

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

Abstract
Klondike is the most famous single-player card game, and remains a challenging search problem even in the "thoughtful" variant where all card locations are known. We consider the full game of Klondike except for one restriction that the unusual move of "worrying back" is disallowed. This model is able to determine the winnability of all instances of the game and in practice does so in less than 2000 secs for 10,000 instances we tested, which no other known algorithm can achieve. On some instances, however, other techniques can produce answers more quickly. We use constraint modelling to produce schedules for running our constraint model in combination with other techniques. The combination outperforms any single solver across a range of time limits. Using this combination we are able to significantly improve the best estimate of winnability of Klondike without worrying back. Finally we show how we can use this work to also improve the estimate of winnability of the regular game of Klondike.
Cite as

Nguyen Dang, Ian P. Gent, Peter Nightingale, Felix Ulrich-Oltean, and Jack Waller. Constraint Models for Klondike. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dang_et_al:LIPIcs.CP.2025.9,
  author =	{Dang, Nguyen and Gent, Ian P. and Nightingale, Peter and Ulrich-Oltean, Felix and Waller, Jack},
  title =	{{Constraint Models for Klondike}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{9:1--9:20},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-238702},
  doi =		{10.4230/LIPIcs.CP.2025.9},
  annote =	{Keywords: AI Planning, Modelling, Constraint Programming, Solitaire and Patience Games}
}
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