POCOCOP

Team Papers Conferences Visitors Visits Abstract

POCOCOP is an ERC Synergy Grant (ERC SyG No. 101071674) funded by the European Research Council (ERC)
POCOCOP starts 1 Mar 2023 and ends 28 Feb 2029

The goal of POCOCOP is to systematically explore polynomial-time tractability in the field of constraint satisfaction and its extensions, in particular promise CSPs, valued CSPs, and CSPs over infinite domains. The project is jointly led by three principal investigators: Manuel Bodirsky (TU Dresden), Michael Pinsker (TU Vienna), and Libor Barto (Charles University, Prague).

2nd POCOCOP meeting, Dec 2023

Team

For applications use the email jobs(at)acronym_of_the_grant(dot)eu. The applicants should have a strong background in at least one of the following fields: theoretical computer science, model theory, or universal algebra. Informal inquiries are very welcome.

PIs Libor Barto
CU Manuel Bodirsky
TU Dresden Michael Pinsker
TU Wien

postdocs Dmitriy Zhuk: since 1 Mar 2023 Santiago Guzmán Pro: since 22 May 2023 Paolo Marimon: since 1 Aug 2023

Alexey Barsukov: since 1 May 2023 Matěj Konečný: since 1 Oct 2023 Albert Vucaj: since 1 Oct 2023

Andrew Moorhead: since 1 Oct 2023

PhD students Kaan Doğanay: since 1 May 2023 Sebastian Meyer: since 1 Mar 2023 Albert Vucaj: 1 May 2023 - 30 Sep 2023

Maximilian Hadek: since 15 Jan 2024 Žaneta Semanišinová: since 1 May 2023 Paolo Marimon: 1 Jul 2023 - 31 Jul 2023

Philipp Grzywaczyk: since 1 Oct 2023 Piotr Kawałek: since 1 Sep 2023

Johanna Brunar: since 1 Oct 2023

Roman Feller: since 15 Oct 2023

Papers

K. Asimi, L. Barto, V. Dalmau: The Complexity of Promise Constraint Satisfaction Problem Seen from the Other Side [arXiv]
J. Rydval, Ž. Semanišinová, M. Wrona: Identifying Tractable Quantified Temporal Constraints within Ord-Horn [arXiv]
P. Grzywaczyk, A. Winterhof: Primitive elements of finite fields F_q^r avoiding affine hyperplanes for q=4 and q=5 [arXiv]
L. Barto, S. Butti, A. Kazda, C. Viola, S. Živný: Algebraic Approach to Approximation [arXiv]
L. Barto, S. Butti, V. Dalmau: The Sherali-Adams and Weisfeiler-Leman hierarchies in (Promise Valued) Constraint Satisfaction Problems [arXiv]
L. Barto, Z. Brady, A. Bulatov, M. Kozik, D. Zhuk, Unifying the Three Algebraic Approaches to the CSP via Minimal Taylor Algebras [arXiv]
S. Guzmán-Pro: Local expressions of hereditary classes [arXiv]
D. Bradley-Williams, P. J. Cameron, J. Hubička, M. Konečný: EPPA numbers of graphs [arXiv]
M. Bodirsky, Ž. Semanišinová, C. Lutz: The Complexity of Resilience Problems via Valued Constraint Satisfaction Problems [arXiv]
M. Bodirsky, S. Guzmán Pro: Forbidden Tournaments and the Orientation Completion Problem [arXiv]
M. Pinsker, C. Schindler: On the Zariski topology on endomorphism monoids of omega-categorical structures [arXiv]
L. Barto, A. Mottet: Finite Algebras with Hom-Sets of Polynomial Size [arXiv]
M. Pinsker, C. Schindler: The semigroup of increasing functions on the rational numbers has a unique Polish topology [arXiv]
A. Vucaj, D. Zhuk: Submaximal clones over a three-element set up to minor-equivalence [arXiv]

L. Elliott, J. Jonušas, J. D. Mitchell, Y. Péresse, M. Pinsker: Polish topologies on endomorphism monoids of relational structures, Advances in Mathematics 431 (2023), 109214 [DOI] [arXiv]
M. Bodirsky, S. Knaeuer: Network Satisfaction Problems Solvable by k-Consistency, ICALP'23, 116:1--116:20 [DOI] [arXiv]
M. Bodirsky, J. Bulín, F. Starke, M. Wernthaler: The smallest hard trees, Constraints 28 (2023), 105-137 [DOI] [arXiv]
M. Bodirsky, A. Vucaj, D. Zhuk: The lattice of clones of self-dual operations collapsed, International Journal of Algebra and Computation 30/4 (2023), 717-749 [DOI] [arXiv]

Conferences, workshops, seminars

8 Feb 2024, Ž. Semanišinová, seminar talk Constraint satisfaction problems: an algebraic approach to classifying computational complexity at Algebra seminar, P. J. Šafárik University, Košice, Slovakia [Slides]
29 Jan 2024, M. Bodirsky, seminar talk (Concrete and Abstract) Minions and Applications at Seminar Geometric Methods in Mathematics, TU Dresden, Germany
16 Jan 2024, L. Barto, talk Symetrie ve výpočetní složitosti (in Czech) for Learned Society of the Czech Republic, Prague, Czechia [Slides] [YouTube video]
4 Jan 2024, M. Konečný, seminar talk Extending partial automorphisms at AGK Seminar, TU Dresden, Germany
18 Dec 2023, M. Pinsker, talk Maximal clones on omega at Colloquium for Martin Goldstern’s 60th birthday, TU Wien, Austria
6 Dec 2023, S. G. Pro, online seminar talk Forbidden tournaments and the orientation (completion) problem at Atlantic Graph Theory Seminar, AARMS [Slides]
27 Nov 2023, M. Konečný, seminar talk EPPA numbers of graphs at G^2OAT Monday Seminar, Czech Technical University, Prague, Czechia [Slides]
6-8 Nov 2023, P. Marimon, M. Pinsker, Ž. Semanišinová attending workshop Combinatorial Problems in Model Theory and Computer Science, Leeds, UK
1. M. Pinsker: invited talk Constraint Satisfaction Problems: algebraic and model-theoretic challenges to distinguish the easy from the hard (7 Nov) [slides]
2. Ž. Semanišinová: invited talk Valued Constraint Satisfaction Problem and Resilience in Database Theory (7 Nov) [slides]
23-28 Oct 2023, M. Bodirsky, M. Pinsker attending Conference on Generic Structures, Będlewo, Poland
1. M. Bodirsky: invited talk Generic Structures for Monotone Sentences in Monadic Second-Order Logic (27 Oct) [slides]
2. M. Pinsker: invited talk Topologies on endomorphism monoids of generic structures (27 Oct) [slides]
19 Oct 2023, M. Konečný, invited talk EPPA numbers of graphs at Annual DYNASNET meeting (16-20 Oct 2023), Lednice, Czechia [Slides]
17 Oct 2023, A. Vucaj, seminar talk Clones over finite sets and Minor Conditions at Seminar: Algebra and Discrete Mathematics, JKU, Linz, Austria [Slides]
13 Oct 2023, S. G. Pro, talk Forbidden tournaments and the orientation (completion) problem at KOLKOM 2023 (13-14 Oct 2023), Heidelberg, Germany [Slides]
28 Sep 2023, M. Bodirsky, invited talk Model theoretic challenges in constraint satisfaction at Mathematical Logic section of DMV Meeting (25-28 Sep 2023), Ilmenau, Germany [Slides]
16 Sep 2023, P. Marimon, invited talk Measures in homogeneous 3-hypergraphs at Model Theory Workshop (15-18 Sep 2023), Warsaw, Poland [Slides]
18-22 Sep 2023, POCOCOP attending CWC, Weissensee, Austria
28 Aug - 1 Sep 2023, S. G. Pro attending EUROCOMB'23, Prague, Czechia
10-14 Jul 2023, M. Bodirsky attending ICALP, Paderborn, Germany
4-7 Jul 2023, Ž. Semanišinová, M. Pinsker, A. Vucaj attending Algebra Week, Siena, Italy
1. Ž. Semanišinová: invited talk Valued Constraint Satisfaction Problem and Resilience in Database Theory (5 Jul) [slides]
2. M. Pinsker: invited talk Loop conditions (6 Jul) [slides]
3. A. Vucaj: invited talk Clones over finite sets up to minor-equivalence (7 Jul) [slides]
29 Jun 2023, S. G. Pro, seminar talk Structural Graph Theory, finite bounds, and some CSPs at AGK Seminar, TU Dresden, Germany [Slides]
28 Jun 2023, M. Pinsker, talk Symmetries of graphs and structures that fail to interpret a finite thing at LICS'23 (26-29 Jun 2023), Boston, USA [Slides]
9-11 Jun 2023, S. Meyer, Ž. Semanišinová, M. Pinsker, D. Zhuk, attending AAA 103, Tartu, Estonia
1. S. Meyer: talk Infinitary pp-definabillity over the real numbers with convex relations (9 Jun) [slides]
2. Ž. Semanišinová: talk Valued Constraint Satisfaction Problem and Resilience in Database Theory (10 Jun) [slides]
3. M. Pinkser: talk The semigroup of increasing functions on the rationals and its unique Polish topology (9 Jun)
4. D. Zhuk: talk On symmetric term operations in finite Taylor algebras (9 Jun) [slides]
1 Jun 2023, M. Pinsker, outreach talk POCOCOP at TU Wien Faculty meeting
18 May 2023, M. Pinsker, outreach talk Universal algebra, the Sudoku revolution, and POCOCOP at Austrian Mathematical Society Early Student Awards
30 Mar 2023, M. Pinsker, seminar talk Constraint Satisfaction Problems: algebraic and model-theoretic challenges to distinguish the easy from the hard at Logic Colloquium, University of Vienna, KGRC [slides]
23-26 Mar 2023, L. Barto, attending Spring school, Department of Algebra (with A. Krokhin)
14 Mar 2023, D. Zhuk, online seminar talk Clones on 3 Elements: A New Hope at PALS [slides]
14 Mar 2023, M. Bodirsky, seminar talk Valued Constraint Satisfaction Problems and Resilience in Database Theory at Algebra Colloquium, Charles University [slides]

Visitors

22-26 Jan 2024, Andy Zucker visiting TU Dresden. Gave a talk Ultracoproducts and weak containment for flows of topological groups at AGK Seminar
13-14 Dec 2023, Jan Hubička visiting TU Dresden
3-12 Dec 2024m Colin Jahel visiting TU Dresden. Gave a talk Asymptotic theories and homomorphically avoided structures
3-9 Dec 2023, Édouard Bonnet visiting TU Dresden
14-20 Aug 2023, Bertalan Bodor visiting TU Dresden
7-12 Aug 2023, Marcin Kozik, Michał Wrona visiting TU Wien
19-22 Jun 2023, Jakub Opršal visiting CU
4-8 Jun 2023, Bertalan Bodor visiting CU
28 May - 2 Jun 2023, Colin Jahel visiting TU Dresden
10-20 Apr 2023, Silvia Butti visiting CU
3-5 Apr 2023, Andrei Krokhin visiting TU Wien
20 Mar - 1 Apr 2023, Andrei Krokhin visiting CU

Visits

28 Jan - 2 Feb 2024: L. Barto visiting Marcin Kozik at Jagiellonian University
10-16 Dec 2023: L. Barto visiting Andrei Krokhin at Durham University

Team visits

29 Nov - 2 Dec 2023 2nd POCOCOP meeting: M. Bodirsky, S. Meyer, A. Moorhead, P. Grzywaczyk, S. Guzmán Pro, Ž. Semanišinová, M. Konečný, M. Pinsker, P. Marimon, A. Vucaj, P. Kawalek, J. Brunar, R. Feller visiting CU
28-30 May 2023 1st POCOCOP meeting: M. Pinsker, A. Vucaj, M. Bodirsky, Z. Semanišinová, S. Meyer visiting CU
4-8 May 2023: Z. Semanišinová visiting TU Wien
13-15 Mar 2023: M. Bodirsky, S. Meyer visiting CU

Abstract

The class P of polynomial-time computable computational problems is the most important and robust complexity class for the study of efficient computation. Answering what problems belong to P will lead to groundbreaking applications in science and modern society where computation is omnipresent. Moreover, P is a relatively recent mathematical object and radically different from classical notions studied for centuries; thus, capturing it promises the discovery of new fundamental theorems in mathematics.

Our current understanding of P is limited; for instance, the P=NP millennium problem is wide open. There neither exists a uniform reduction technique, nor a single algorithmic scheme capturing the power of P, nor a description of P in purely logical terms. We intend to provide these in a context which is so rich and vast that it requires the unification of some of the most important techniques, and will enhance our general understanding of P.

Within the microcosm of finite-domain constraint satisfaction problems (CSPs), the recent resolution of the Feder-Vardi conjecture by Bulatov and by Zhuk provides a satisfactory picture of P. Our goal is a vast and uniform generalisation of this result in three directions: towards approximation via Promise CSPs, towards optimisation via Valued CSPs, and towards infinite domains via omega-categorical CSPs and CSPs over numeric domains. In particular, our setting includes the linear programming problem as a numeric Valued CSP, the approximate graph coloring problem as a Promise CSP, and many problems from qualitative reasoning as infinite-domain CSPs. Our methods range from universal algebra, model theory, Ramsey theory, to complexity theory. Building on cross-connections between these extensions, we will provide a uniform description of P within this diverse and applicable universe, thus making a revolutionary leap in the resolution of the general problem.

Funding statement: Funded by the European Union (ERC, POCOCOP, 101071674). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.