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).

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

Alexey Barsukov: since 1 May 2023

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

Žaneta Semanišinová: since 1 May 2023

Papers

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]

M. Bodirsky, J. Bulín, F. Starke, M. Wernthaler: The smallest hard trees, Constraints, 2023 [DOI] [arXiv]

Conferences, workshops, seminars

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 [slides]

Visitors

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

Team visits

4-8 May 2023: Z. Semanišinová visiting TU Wien
13-15 Mar 2023: M. Bodirsky 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.