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).
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.
- L. Barto, A. Mottet: Finite Algebras with Hom-Sets of Polynomial Size
- M. Pinsker, C. Schindler: The semigroup of increasing functions on the rational numbers has a unique Polish topology
- A. Vucaj, D. Zhuk: Submaximal clones over a three-element set up to minor-equivalence
- L. Elliott, J. Jonušas, J. D. Mitchell, Y. Péresse, M. Pinsker: Polish topologies on endomorphism monoids of relational structures, to appear in Advances in Mathematics
- M. Bodirsky, S. Knaeuer: Network Satisfaction Problems Solvable by k-Consistency, to appear in ICALP'23
- M. Bodirsky, J. Bulín, F. Starke, M. Wernthaler: The smallest hard trees, Constraints, 2023
Conferences, workshops, seminars
- 4-7 Jul 2023, Ž. Semanišinová, M. Pinsker attending Algebra Week, Siena, Italy
- Ž. Semanišinová: invited talk Valued Constraint Satisfaction Problem and Resilience in Database Theory (5 Jul)
- M. Pinsker: invited talk Loop conditions (6 Jul)
- 29 Jun 2023, S. G. Pro, seminar talk Structural Graph Theory, finite bounds, and some CSPs at AGK Seminar, TU Dresden
- 28 Jun 2023, M. Pinsker, LICS'23 (26-29 Jun 2023), Boston, USA
- 9-11 Jun 2023, S. Meyer, Ž. Semanišinová, M. Pinsker, attending AAA 103, Tartu, Estonia
- S. Meyer: talk Infinitary pp-definabillity over the real numbers with convex relations (9 Jun)
- Ž. Semanišinová: talk Valued Constraint Satisfaction Problem and Resilience in Database Theory (10 Jun)
- M. Pinkser: talk The semigroup of increasing functions on the rationals and its unique Polish topology (9 Jun)
- 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
- 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
- 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
- 28-30 May 2023: M. Pinsker, A. Vucaj, M. Bodirsky, Z. Semanišinová, S. Meyer visiting CU (1st POCOCOP meeting)
- 4-8 May 2023: Z. Semanišinová visiting TU Wien
- 13-15 Mar 2023: M. Bodirsky, S. Meyer visiting CU
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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