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).

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
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

  1. M. Bodirsky, Ž. Semanišinová, C. Lutz: The Complexity of Resilience Problems via Valued Constraint Satisfaction Problems [arXiv]
  2. M. Bodirsky, S. Guzmán Pro: Forbidden Tournaments and the Orientation Completion Problem [arXiv]
  3. M. Pinsker, C. Schindler: On the Zariski topology on endomorphism monoids of omega-categorical structures [arXiv]
  4. L. Barto, A. Mottet: Finite Algebras with Hom-Sets of Polynomial Size [arXiv]
  5. M. Pinsker, C. Schindler: The semigroup of increasing functions on the rational numbers has a unique Polish topology [arXiv]
  6. A. Vucaj, D. Zhuk: Submaximal clones over a three-element set up to minor-equivalence [arXiv]

  7. 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]
  8. M. Bodirsky, S. Knaeuer: Network Satisfaction Problems Solvable by k-Consistency, ICALP'23, 116:1--116:20 [DOI] [arXiv]
  9. M. Bodirsky, J. Bulín, F. Starke, M. Wernthaler: The smallest hard trees, Constraints 28 (2023), 105-137 [DOI] [arXiv]
  10. 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

  1. 18-22 Sep 2023, POCOCOP attending CWC, Weissensee, Austria
  2. 10-14 Jul 2023, M. Bodirsky attending ICALP, Paderborn, Germany
  3. 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]
  4. 29 Jun 2023, S. G. Pro, seminar talk Structural Graph Theory, finite bounds, and some CSPs at AGK Seminar, TU Dresden [Slides]
  5. 28 Jun 2023, M. Pinsker, talk Symmetries of graphs and structures that fail to interpret a finite thing LICS'23 (26-29 Jun 2023), Boston, USA [Slides]
  6. 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]
  7. 1 Jun 2023, M. Pinsker, outreach talk POCOCOP at TU Wien Faculty meeting
  8. 18 May 2023, M. Pinsker, outreach talk Universal algebra, the Sudoku revolution, and POCOCOP at Austrian Mathematical Society Early Student Awards
  9. 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]
  10. 23-26 Mar 2023, L. Barto, attending Spring school, Department of Algebra (with A. Krokhin)
  11. 14 Mar 2023, D. Zhuk, online seminar talk Clones on 3 Elements: A New Hope at PALS [slides]
  12. 14 Mar 2023, M. Bodirsky, seminar talk Valued Constraint Satisfaction Problems and Resilience in Database Theory at Algebra Colloquium, Charles University [slides]

Visitors

  1. 14-20 August 2023, Bertalan Bodor visiting TU Dresden
  2. 7-12 August 2023, Marcin Kozik, Michał Wrona visiting TU Wien
  3. 19-22 Jun 2023, Jakub Opršal visiting CU
  4. 4-8 Jun 2023, Bertalan Bodor visiting CU
  5. 28 May - 2 Jun 2023, Colin Jahel visiting TU Dresden
  6. 10-20 Apr 2023, Silvia Butti visiting CU
  7. 3-5 Apr 2023, Andrei Krokhin visiting TU Wien
  8. 20 Mar - 1 Apr 2023, Andrei Krokhin visiting CU

Visits

Team visits

  1. 28-30 May 2023: M. Pinsker, A. Vucaj, M. Bodirsky, Z. Semanišinová, S. Meyer visiting CU (1st POCOCOP meeting)
  2. 4-8 May 2023: Z. Semanišinová visiting TU Wien
  3. 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.

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