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Documents authored by Demirović, Emir

Document
DOI: 10.4230/LIPIcs.CP.2026.24
Formally Verified Certification of Constraint Programming Proofs

Authors: Maarten Flippo, Konstantin Sidorov, Tip ten Brink, Clément Pit-Claudel, and Emir Demirović

Published in: LIPIcs, Volume 379, 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)

Abstract
As constraint programming (CP) solvers are increasingly used in critical applications, there is a growing need for certification of solver claims of infeasibility and optimality. Recent work has demonstrated that certification is feasible for CP solvers using a multi-stage proof-generation framework; however, the underlying proof system was informal, and verification relied on translation into an external proof format, impacting the trustworthiness. We address these issues by formalising a rigorous, solver-agnostic framework for certifying CP solver claims. We present a formal definition of DRCP, a proof system for CP over integer domains that captures core solver operations, including conflict analysis and heterogeneous propagation, by modular inference rules with precise semantics. We also develop FznDrcpCheck, a formally verified proof checker in Rocq that validates DRCP proofs directly against FlatZinc models. Our evaluation shows that our framework enables practical certification across various benchmarks with negligible overhead during solving and modest proof-checking costs.
Cite as

Maarten Flippo, Konstantin Sidorov, Tip ten Brink, Clément Pit-Claudel, and Emir Demirović. Formally Verified Certification of Constraint Programming Proofs. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 24:1-24:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{flippo_et_al:LIPIcs.CP.2026.24,
  author =	{Flippo, Maarten and Sidorov, Konstantin and ten Brink, Tip and Pit-Claudel, Cl\'{e}ment and Demirovi\'{c}, Emir},
  title =	{{Formally Verified Certification of Constraint Programming Proofs}},
  booktitle =	{32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)},
  pages =	{24:1--24:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-432-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{379},
  editor =	{Beldiceanu, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.24},
  URN =		{urn:nbn:de:0030-drops-266560},
  doi =		{10.4230/LIPIcs.CP.2026.24},
  annote =	{Keywords: Constraint programming, Proof systems, Certified checking}
}
Document
DOI: 10.4230/LIPIcs.CP.2026.42
From Literals to Atomic Constraints: Generalising Conflict-Driven Clause Learning for Constraint Programming

Authors: Imko Marijnissen, Maarten Flippo, and Emir Demirović

Published in: LIPIcs, Volume 379, 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)

Abstract
Conflict‑Driven Clause Learning (CDCL) is central to the success of SAT solvers, and its adaptation to Constraint Programming (CP) through Lazy Clause Generation (LCG) has been a major breakthrough for CP solving. A core requirement of LCG is to maintain both a CP and SAT view of the problem. Because maintaining a full SAT encoding is impractical, solvers rely on partial and solver‑specific encodings - an approach that has evolved as folklore rather than formal design. We present the first systematic analysis of how leading LCG solvers maintain their SAT encodings, based on source‑code inspection and developer correspondence. Our analysis reveals substantial differences in explanation lifting, backwards explanations, linking clauses, and nogood minimisation, all driven by the need to preserve a SAT view. To overcome these compromises, we propose a native CDCL framework for CP. We replace SAT literals with atomic constraints, enabling conflict analysis, nogood learning, and nogood propagation directly at the CP level. This results in cleaner algorithmic design, eliminates SAT‑specific complications, and allows us to introduce extended nogood propagation, a generalisation of SAT‑based clause propagation, as well as CPIP nogoods, a generalisation of SAT-based learned nogoods. Our implementation of the framework in Pumpkin demonstrates competitive performance in the MiniZinc Challenge 2025. Additionally, we empirically show that extended nogood propagation combined with CPIP nogoods can significantly reduce failures, especially on problems with constraints that reason over domain holes. Overall, our framework provides a principled and semantically rich generalisation of CDCL for CP.
Cite as

Imko Marijnissen, Maarten Flippo, and Emir Demirović. From Literals to Atomic Constraints: Generalising Conflict-Driven Clause Learning for Constraint Programming. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 42:1-42:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{marijnissen_et_al:LIPIcs.CP.2026.42,
  author =	{Marijnissen, Imko and Flippo, Maarten and Demirovi\'{c}, Emir},
  title =	{{From Literals to Atomic Constraints: Generalising Conflict-Driven Clause Learning for Constraint Programming}},
  booktitle =	{32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)},
  pages =	{42:1--42:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-432-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{379},
  editor =	{Beldiceanu, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.42},
  URN =		{urn:nbn:de:0030-drops-266744},
  doi =		{10.4230/LIPIcs.CP.2026.42},
  annote =	{Keywords: LCG, CP, CDCL, Lazy Literal, Conflict Analysis, Nogood Propagation}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.4
Conflict Analysis Based on Cutting-Planes for Constraint Programming

Authors: Robbin Baauw, Maarten Flippo, and Emir Demirović

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

Abstract
This paper introduces a novel constraint learning mechanism for Constraint Programming (CP) solvers that integrates cutting planes reasoning into the conflict analysis procedure. Drawing inspiration from Lazy Clause Generation (LCG), our approach, named Lazy Linear Generation (LLG), can generate linear integer inequalities to prune the search space, rather than propositional clauses as in LCG. This combines the strengths of constraint programming (strong propagation through global constraints) with cutting-planes reasoning. We present linear constraint explanations for various arithmetic constraints and the element constraint. An experimental evaluation shows that the improved generality of linear constraints has a practical impact on a CP solver by reducing the number of encountered conflicts in 45% of our benchmark instances. Our analysis and prototype implementation show promising results and are an important step towards a new paradigm to make constraint programming solvers more effective.
Cite as

Robbin Baauw, Maarten Flippo, and Emir Demirović. Conflict Analysis Based on Cutting-Planes for Constraint Programming. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baauw_et_al:LIPIcs.CP.2025.4,
  author =	{Baauw, Robbin and Flippo, Maarten and Demirovi\'{c}, Emir},
  title =	{{Conflict Analysis Based on Cutting-Planes for Constraint Programming}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{4:1--4:19},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-238655},
  doi =		{10.4230/LIPIcs.CP.2025.4},
  annote =	{Keywords: constraint programming, learning, conflict analysis}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.35
Unite and Lead: Finding Disjunctive Cliques for Scheduling Problems

Authors: Konstantin Sidorov, Imko Marijnissen, and Emir Demirović

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

Abstract
Constraint programming solvers have seen much success in scheduling problems owing to their efficient reasoning over constraints to solve complex problems in practice. Many algorithms have been proposed for propagating information from a single constraint. However, inferring and exchanging information across multiple constraints can provide deeper insight into the global structure of a problem. In this work, we propose to exchange information amongst constraints by inferring the disjointness of tasks in scheduling problems from many constraints. We do this by (i) augmenting existing propagators, such as the Cumulative and nogoods, to report when pairs of tasks are disjoint, and (ii) leveraging this information by introducing the SelectiveDisjunctive propagator which generates a lower bound on the earliest completion time of cliques of disjoint tasks to determine conflicts. This allows us to aggregate disjointness information spanning multiple constraints to gain a better global overview of the problem, as well as more precise local information. We also identify a problem structure where an LCG solver reasoning over Cumulative constraints separately, without any reformulations, requires an exponential amount of time to prove infeasibility, which we both justify theoretically and show empirically; on the other hand, our approach solves those instances in polynomial time. On particular known RCPSP and RCPSP/max benchmarks, our approach significantly reduces the number of conflicts required to prove optimality when resource contention is high. Additionally, we discover new lower bounds for 16 RCPSP/max instances (closing six of them) and four RCPSP instances (closing one), as well as new upper bounds for two RCPSP/max instances and four RCPSP instances. Furthermore, we empirically analyse our proposed approach to determine which features are beneficial for performance, showing that finding cliques is one of the main bottlenecks and that detecting disjointness during search can lead to improved bounds on certain instances, but it generally negatively impacts learning. This work paves the way for reasoning over the disjointness of tasks inferred from a variety of standard constraints to discover novel information sourced from multiple constraints during search.
Cite as

Konstantin Sidorov, Imko Marijnissen, and Emir Demirović. Unite and Lead: Finding Disjunctive Cliques for Scheduling Problems. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 35:1-35:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sidorov_et_al:LIPIcs.CP.2025.35,
  author =	{Sidorov, Konstantin and Marijnissen, Imko and Demirovi\'{c}, Emir},
  title =	{{Unite and Lead: Finding Disjunctive Cliques for Scheduling Problems}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{35:1--35:24},
  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.2025.35},
  URN =		{urn:nbn:de:0030-drops-238969},
  doi =		{10.4230/LIPIcs.CP.2025.35},
  annote =	{Keywords: Constraint Programming, Lazy Clause Generation, Propagation, Scheduling, Cumulative, Disjunctive}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.9
Pseudo-Boolean Reasoning About States and Transitions to Certify Dynamic Programming and Decision Diagram Algorithms

Authors: Emir Demirović, Ciaran McCreesh, Matthew J. McIlree, Jakob Nordström, Andy Oertel, and Konstantin Sidorov

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Pseudo-Boolean proof logging has been used successfully to provide certificates of optimality from a variety of constraint- and satisifability-style solvers that combine reasoning with a backtracking or clause-learning search. Another paradigm, occurring in dynamic programming and decision diagram solving, instead reasons about partial states and possible transitions between them. We describe a framework for generating clean and efficient pseudo-Boolean proofs for these kinds of algorithm, and use it to produce certifying algorithms for knapsack, longest path, and interval scheduling. Because we use a common proof system, we can also reason about hybrid solving algorithms: we demonstrate this by providing proof logging for a dynamic programming based knapsack propagator inside a constraint programming solver.
Cite as

Emir Demirović, Ciaran McCreesh, Matthew J. McIlree, Jakob Nordström, Andy Oertel, and Konstantin Sidorov. Pseudo-Boolean Reasoning About States and Transitions to Certify Dynamic Programming and Decision Diagram Algorithms. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{demirovic_et_al:LIPIcs.CP.2024.9,
  author =	{Demirovi\'{c}, Emir and McCreesh, Ciaran and McIlree, Matthew J. and Nordstr\"{o}m, Jakob and Oertel, Andy and Sidorov, Konstantin},
  title =	{{Pseudo-Boolean Reasoning About States and Transitions to Certify Dynamic Programming and Decision Diagram Algorithms}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.9},
  URN =		{urn:nbn:de:0030-drops-206948},
  doi =		{10.4230/LIPIcs.CP.2024.9},
  annote =	{Keywords: Proof logging, dynamic programming, decision diagrams}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.11
A Multi-Stage Proof Logging Framework to Certify the Correctness of CP Solvers

Authors: Maarten Flippo, Konstantin Sidorov, Imko Marijnissen, Jeff Smits, and Emir Demirović

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Proof logging is used to increase trust in the optimality and unsatisfiability claims of solvers. However, to this date, no constraint programming solver can practically produce proofs without significantly impacting performance, which hinders mainstream adoption. We address this issue by introducing a novel proof generation framework, together with a CP proof format and proof checker. Our approach is to divide the proof generation into three steps. At runtime, we require the CP solver to only produce a proof sketch, which we call a scaffold. After the solving is done, our proof processor trims and expands the scaffold into a full CP proof, which is subsequently verified. Our framework is agnostic to the solver and the verification approach. Through MiniZinc benchmarks, we demonstrate that with our framework, the overhead of logging during solving is often less than 10%, significantly lower than other approaches, and that our proof processing step can reduce the overall size of the proof by orders of magnitude and by extension the proof checking time. Our results demonstrate that proof logging has the potential to become an integral part of the CP community.
Cite as

Maarten Flippo, Konstantin Sidorov, Imko Marijnissen, Jeff Smits, and Emir Demirović. A Multi-Stage Proof Logging Framework to Certify the Correctness of CP Solvers. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{flippo_et_al:LIPIcs.CP.2024.11,
  author =	{Flippo, Maarten and Sidorov, Konstantin and Marijnissen, Imko and Smits, Jeff and Demirovi\'{c}, Emir},
  title =	{{A Multi-Stage Proof Logging Framework to Certify the Correctness of CP Solvers}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.11},
  URN =		{urn:nbn:de:0030-drops-206969},
  doi =		{10.4230/LIPIcs.CP.2024.11},
  annote =	{Keywords: proof logging, formal verification, constraint programming}
}
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