Polynomial-time Computation: Opening the Blackboxes in Constraint Problems

Project Information

POCOCOP

Grant agreement ID: 101071674

DOI

10.3030/101071674

EC signature date 19 January 2023

Start date 1 March 2023

End date 28 February 2029

Funded under

• European Research Council (ERC)

Total cost

€ 7 932 935,00

EU contribution

€ 7 932 935,00

Coordinated by

TECHNISCHE UNIVERSITAET DRESDEN
Germany

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (40)

On the non-measurability of $$\omega $$-categorical Hrushovski constructions

Author(s): Paolo Marimon
Published in: Archive for Mathematical Logic, Issue 64, 2024, ISSN 0933-5846
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00153-024-00943-4

Mal’cev complexes

Author(s): Andrew Moorhead
Published in: International Journal of Algebra and Computation, Issue 34, 2024, ISSN 0218-1967
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0218196724500371

An Algebraic Proof of the Dichotomy for Graph Orientation Problems with Forbidden Tournaments

Author(s): Roman Feller; Michael Pinsker
Published in: SIAM Journal on Discrete Mathematics, Issue 40/1, 2026, ISSN 1095-7146
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.48550/ARXIV.2405.20263

The Sherali–Adams and Weisfeiler–Leman Hierarchies in (Promise Valued) Constraint Satisfaction Problems

Author(s): Libor Barto; Silvia Butti; Victor Dalmau
Published in: ACM Transactions on Computation Theory, Issue 18/1, 2026, ISSN 1942-3462
Publisher: Association for Computing Machinery
DOI: 10.48550/ARXIV.2401.16998

Network satisfaction problems solved by <i>k</i> -consistency

Author(s): Manuel Bodirsky, Simon Knäuer
Published in: International Journal of Algebra and Computation, Issue 36, 2025, ISSN 0218-1967
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0218196726500013

Forbidden Tournaments and the Orientation Completion Problem

Author(s): Manuel Bodirsky, Santiago Guzmán-Pro
Published in: SIAM Journal on Discrete Mathematics, Issue 39, 2025, ISSN 0895-4801
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M1604849

Big Ramsey degrees and infinite languages

Author(s): Samuel Braunfeld, David Chodounský, Noé de Rancourt, Jan Hubička, Jamal Kawach, Matěj Konečný
Published in: Advances in Combinatorics, 2024, ISSN 2517-5599
Publisher: Alliance of Diamond Open Access Journals
DOI: 10.19086/aic.2024.4

Twenty years of Nešetřil’s classification programme of Ramsey classes

Author(s): Jan Hubička, Matěj Konečný
Published in: Computer Science Review, Issue 59, 2026, ISSN 1574-0137
Publisher: Elsevier BV
DOI: 10.1016/J.COSREV.2025.100814

Multisorted Boolean clones determined by binary relations up to minion homomorphisms

Author(s): Libor Barto, Maryia Kapytka
Published in: Algebra universalis, Issue 86, 2024, ISSN 0002-5240
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00012-024-00878-0

Testing Isomorphism of Chordal Graphs of Bounded Leafage is Fixed-Parameter Tractable

Author(s): Vikraman Arvind, Roman Nedela, Ilia Ponomarenko, Peter Zeman
Published in: Algorithmica, Issue 88, 2026, ISSN 0178-4617
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00453-026-01374-8

Algebra Universalis

Author(s): Barto, Libor; Kapytka, Maryia
Published in: Algebra universalis, Issue 86, 2024, ISSN 0002-5240
Publisher: Birkhauser Verlag
DOI: 10.48550/ARXIV.2407.16513

Forbidden Tournaments and the Orientation Completion Problem

Author(s): Manuel Bodirsky, Santiago Guzmán-Pro
Published in: SIAM Journal on Discrete Mathematics, Issue 39, 2025, ISSN 0895-4801
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M1604849

Submaximal clones over a three-element set up to minor-equivalence

Author(s): Albert Vucaj, Dmitriy Zhuk
Published in: Algebra universalis, Issue 85, 2024, ISSN 0002-5240
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s00012-024-00852-w

Generalisations of matrix partitions: Complexity and obstructions

Author(s): Alexey Barsukov, Mamadou Moustapha Kanté
Published in: Theoretical Computer Science, Issue 1007, 2024, ISSN 0304-3975
Publisher: Elsevier BV
DOI: 10.1016/j.tcs.2024.114652

SIAM Journal on Computing

Author(s): Antoine Mottet; Tomáš Nagy; Michael Pinsker; Michał Wrona
Published in: SIAM Journal on Computing, Issue 53/6, 2024, ISSN 0097-5397
Publisher: SIAM
DOI: 10.1137/22M1538934

Ramsey expansions of metrically homogeneous graphs

Author(s): Andrés Aranda, David Bradley-Williams, Jan Hubička, Miltiadis Karamanlis, Michael Kompatscher, Matěj Konečný, Micheal Pawliuk
Published in: European Journal of Combinatorics, Issue 132, 2026, ISSN 0195-6698
Publisher: Elsevier BV
DOI: 10.1016/J.EJC.2025.104255

MIXED IDENTITIES FOR OLIGOMORPHIC AUTOMORPHISM GROUPS

Author(s): MANUEL BODIRSKY, JAKOB SCHNEIDER, ANDREAS THOM
Published in: The Journal of Symbolic Logic, 2025, ISSN 0022-4812
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/JSL.2025.10123

A Complexity Dichotomy in Spatial Reasoning via Ramsey Theory

Author(s): Manuel Bodirsky, Bertalan Bodor
Published in: ACM Transactions on Computation Theory, Issue 16, 2024, ISSN 1942-3454
Publisher: Association for Computing Machinery (ACM)
DOI: 10.1145/3649445

GMSNP and Finite Structures

Author(s): Santiago Guzmán-Pro
Published in: ACM Transactions on Computation Theory, Issue 18, 2026, ISSN 1942-3454
Publisher: Association for Computing Machinery (ACM)
DOI: 10.1145/3774645

The Generic Circular Triangle‐Free Graph

Author(s): Manuel Bodirsky, Santiago Guzmán‐Pro
Published in: Journal of Graph Theory, Issue 109, 2025, ISSN 0364-9024
Publisher: Wiley
DOI: 10.1002/JGT.23235

Computational complexity of covering coloured mixed multigraphs with simple degree partitions

Author(s): Jan Bok, Jiří Fiala, Nikola Jedličková, Jan Kratochvíl, Michaela Seifrtová
Published in: Discrete Applied Mathematics, Issue 385, 2026, ISSN 0166-218X
Publisher: Elsevier BV
DOI: 10.1016/J.DAM.2026.01.019

International Journal of Algebra and Computation

Author(s): Moorhead, Andrew
Published in: International Journal of Algebra and Computation, Issue Volume 34 (2024), 2024, ISSN 0218-1967
Publisher: World Scientific Publishing
DOI: 10.1142/S0218196724500371

Collapsing the Bounded Width Hierarchy for Infinite-Domain Constraint Satisfaction Problems: When Symmetries Are Enough

Author(s): Antoine Mottet, Tomáš Nagy, Michael Pinsker, Michał Wrona
Published in: SIAM Journal on Computing, Issue 53, 2024, ISSN 0097-5397
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/22M1538934

ON THE ZARISKI TOPOLOGY ON ENDOMORPHISM MONOIDS OF OMEGA-CATEGORICAL STRUCTURES

Author(s): MICHAEL PINSKER, CLEMENS SCHINDLER
Published in: The Journal of Symbolic Logic, 2024, ISSN 0022-4812
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/jsl.2023.81

The lattice of clones of self-dual operations collapsed

Author(s): Manuel Bodirsky, Albert Vucaj, Dmitriy Zhuk
Published in: International Journal of Algebra and Computation, Issue 33, 2023, ISSN 0218-1967
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0218196723500327

INVARIANT KEISLER MEASURES FOR $\omega $-CATEGORICAL STRUCTURES

Author(s): PAOLO MARIMON
Published in: The Journal of Symbolic Logic, Issue 90, 2025, ISSN 0022-4812
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/JSL.2024.39

Smooth approximations: An algebraic approach to CSPs over finitely bounded homogeneous structures

Author(s): Antoine Mottet, Michael Pinsker
Published in: Journal of the ACM, Issue 71, 2024, ISSN 0004-5411
Publisher: Association for Computing Machinery (ACM)
DOI: 10.1145/3689207

Unifying the Three Algebraic Approaches to the CSP via Minimal Taylor Algebras

Author(s): Libor Barto, Zarathustra Brady, Andrei Bulatov, Marcin Kozik, Dmitriy Zhuk
Published in: TheoretiCS, Issue Volume 3, 2024, ISSN 2751-4838
Publisher: Centre pour la Communication Scientifique Directe (CCSD)
DOI: 10.46298/theoretics.24.14

Polish topologies on endomorphism monoids of relational structures

Author(s): L. Elliott, J. Jonušas, J.D. Mitchell, Y. Péresse, M. Pinsker
Published in: Advances in Mathematics, Issue 431, 2023, ISSN 0001-8708
Publisher: Elsevier BV
DOI: 10.1016/j.aim.2023.109214

EPPA numbers of graphs

Author(s): David Bradley-Williams, Peter J. Cameron, Jan Hubička, Matěj Konečný
Published in: Journal of Combinatorial Theory, Series B, Issue 170, 2025, ISSN 0095-8956
Publisher: Elsevier BV
DOI: 10.1016/J.JCTB.2024.09.003

SIAM Journal on Discrete Mathematics

Author(s): Manuel Bodirsky; Santiago Guzmán-Pro
Published in: SIAM Journal on Discrete Mathematics, Issue 39/1, 2025, ISSN 0895-4801
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.48550/ARXIV.2309.08327

Archive for Mathematical Logic

Author(s): Marimon, Paolo
Published in: Archive for Mathematical Logic, 2024, ISSN 0933-5846
Publisher: Springer
DOI: 10.1007/S00153-024-00943-4

Infinitary primitive positive definability over the real numbers with convex relations

Author(s): Sebastian Meyer
Published in: Algebra universalis, Issue 86, 2025, ISSN 0002-5240
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00012-025-00893-9

Complexity Classification Transfer for CSPs via Algebraic Products

Author(s): Manuel Bodirsky, Peter Jonsson, Barnaby Martin, Antoine Mottet, Žaneta Semanišinová
Published in: SIAM Journal on Computing, Issue 53, 2024, ISSN 0097-5397
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/22M1534304

\(\boldsymbol{\Pi_2^P}\) vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem

Author(s): Dmitriy Zhuk
Published in: SIAM Journal on Computing, Issue 54-6, 2025, ISSN 1095-7111
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/25M1725747

"Primitive elements of finite fields <mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML"" altimg=""si1.svg""><mml:msub><mml:mrow><mml:mi mathvariant=""double-struck"">F</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub></mml:math> avoiding affine hyperplanes for q = 4 and q = 5"

Author(s): Philipp A. Grzywaczyk, Arne Winterhof
Published in: Finite Fields and Their Applications, Issue 96, 2024, ISSN 1071-5797
Publisher: Elsevier BV
DOI: 10.1016/J.FFA.2024.102416

On guarded extensions of MMSNP

Author(s): Alexey Barsukov, Florent R. Madelaine
Published in: Logical Methods in Computer Science, Issue Volume 21, Issue 4, 2025, ISSN 1860-5974
Publisher: Centre pour la Communication Scientifique Directe (CCSD)
DOI: 10.46298/LMCS-21(4:15)2025

Primitive elements of finite fields avoiding affine hyperplanes for q = 4 and q = 5

Author(s): Grzywaczyk, Philipp Alexander; Winterhof, Arne
Published in: Finite Fields and Their Applications, Issue Volume 96, 2024, ISSN 1071-5797
Publisher: Elsevier
DOI: 10.1016/j.ffa.2024.102416

NPA Hierarchy for Quantum Isomorphism and Homomorphism Indistinguishability

Author(s): Prem Nigam Kar; David E. Roberson; Tim Seppelt; Peter Zeman
Published in: Quantum, Issue 10, 2026, ISSN 2521-327X
Publisher: "{Verein zur F{\""{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}"
DOI: 10.48550/ARXIV.2407.10635

Finite algebras with Hom-sets of polynomial size

Author(s): Libor Barto, Antoine Mottet
Published in: Transactions of the American Mathematical Society, 2024, ISSN 0002-9947
Publisher: American Mathematical Society (AMS)
DOI: 10.1090/TRAN/9262

Conference proceedings (19)

Nonuniform Deterministic Finite Automata over Finite Algebraic Structures

Author(s): Paweł M. Idziak, Piotr Kawałek, and Jacek Krzaczkowski
Published in: 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025), 2025, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.ICALP.2025.161

Violating Constant Degree Hypothesis Requires Breaking Symmetry

Author(s): Piotr Kawałek, Armin Weiss
Published in: 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025), 2025, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.STACS.2025.58

NPA Hierarchy for Quantum Isomorphism and Homomorphism Indistinguishability

Author(s): Prem Nigam Kar, David E. Roberson, Tim Seppelt, and Peter Zeman
Published in: 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025), 2025, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.ICALP.2025.105

The Complexity of Resilience Problems via Valued Constraint Satisfaction Problems

Author(s): Manuel Bodirsky, Žaneta Semanišinová, Carsten Lutz
Published in: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science, Issue 27, 2024
Publisher: ACM
DOI: 10.1145/3661814.3662071

An Order out of Nowhere: A New Algorithm for Infinite-Domain CSPs

Author(s): Antoine Mottet, Tomáš Nagy, Michael Pinsker
Published in: 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024), 2024
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.48550/ARXIV.2301.12977

Symmetric Linear Arc Monadic Datalog and Gadget Reductions

Author(s): Manuel Bodirsky, Florian Starke
Published in: 28th International Conference on Database Theory (ICDT 2025), 2025, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.ICDT.2025.13

Network Satisfaction Problems Solved by k-Consistency

Author(s): Manuel Bodirsky, Simon Knäuer
Published in: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023), 2023, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPIcs.ICALP.2023.116

Algebraic Approach to Approximation

Author(s): Libor Barto; Silvia Butti; Alexandr Kazda; Caterina Viola; Stanislav Živný
Published in: LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science, 2024, ISBN 9798400706608
Publisher: Association for Computing Machinery
DOI: 10.48550/ARXIV.2401.15186

Temporal Valued Constraint Satisfaction Problems

Author(s): Manuel Bodirsky, Édouard Bonnet, and Žaneta Semanišinová
Published in: 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025), 2025, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.MFCS.2025.24

Binary symmetries of tractable non-rigid structures

Author(s): Paolo Marimon, Michael Pinsker
Published in: 2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2025
Publisher: IEEE
DOI: 10.1109/LICS65433.2025.00036

Circuit Equivalence in 2-Nilpotent Algebras

Author(s): Piotr Kawałek, Michael Kompatscher, Jacek Krzaczkowski
Published in: 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024), 2024, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPIcs.STACS.2024.45

$\prod_{2}^{P}$ vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem

Author(s): Dmitriy Zhuk
Published in: 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS), 2024
Publisher: IEEE
DOI: 10.1109/FOCS61266.2024.00043

Reducing Stochastic Games to Semidefinite Programming

Author(s): Manuel Bodirsky, Georg Loho, and Mateusz Skomra
Published in: 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025), 2025, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.ICALP.2025.145

Containment for Guarded Monotone Strict NP

Author(s): Alexey Barsukov, Michael Pinsker, and Jakub Rydval
Published in: 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025), 2025, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.ICALP.2025.140

Hereditary First-Order Logic: the Tractable Quantifier Prefix Classes

Author(s): Manuel Bodirsky and Santiago Guzmán-Pro
Published in: 34th EACSL Annual Conference on Computer Science Logic (CSL 2026), 2026, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.CSL.2026.6

Identifying Tractable Quantified Temporal Constraints Within Ord-Horn

Author(s): Jakub Rydval, Žaneta Semanišinová, Michał Wrona
Published in: 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024), 2024, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPIcs.ICALP.2024.151

A CSP approach to Graph Sandwich Problems

Author(s): Manuel Bodirsky, Santiago Guzmán-Pro
Published in: Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2026
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/1.9781611978971.85

The sorrows of a smooth digraph: the first hardness criterion for infinite directed graph-colouring problems

Author(s): Johanna Brunar, Marcin Kozik, Tomáš Nagy, Michael Pinsker
Published in: 2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2025
Publisher: IEEE
DOI: 10.1109/LICS65433.2025.00037

Restricted CSPs and F-Free Digraph Algorithmics

Author(s): Santiago Guzmán-Pro and Barnaby Martin
Published in: 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025), 2025, ISSN 1868-8969
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/LIPICS.ICALP.2025.158

Book chapters (2)

Resolving Sets in Temporal Graphs

Author(s): Jan Bok, Antoine Dailly, Tuomo Lehtilä
Published in: Lecture Notes in Computer Science, Combinatorial Algorithms, 2024, ISBN 978-3-031-63020-0
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-63021-7_22

A topological proof of the Hell-Nešetřil dichotomy

Author(s): Sebastian Meyer, Jakub Opršal
Published in: Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2025
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/1.9781611978322.154