English
Related papers

Related papers: A dichotomy theorem for conservative general-value…

200 papers

A famous result by Jeavons, Cohen, and Gyssens shows that every constraint satisfaction problem (CSP) where the constraints are preserved by a semi-lattice operation can be solved in polynomial time. This is one of the basic facts for the…

Computational Complexity · Computer Science 2011-11-30 Manuel Bodirsky , Dugald Macpherson , Johan Thapper

A counting constraint satisfaction problem (#CSP) asks for the number of ways to satisfy a given list of constraints, drawn from a fixed constraint language \Gamma. We study how hard it is to evaluate this number approximately. There is an…

Computational Complexity · Computer Science 2012-04-26 Colin McQuillan

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP…

Computational Complexity · Computer Science 2016-05-03 Marcin Kozik , Joanna Ochremiak

Finite-domain constraint satisfaction problems are either solvable by Datalog, or not even expressible in fixed-point logic with counting. The border between the two regimes coincides with an important dichotomy in universal algebra; in…

Logic · Mathematics 2022-06-08 Manuel Bodirsky , Jakub Rydval

The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias,…

Computational Complexity · Computer Science 2022-02-02 Clement Carbonnel , Miguel Romero , Stanislav Zivny

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a fixed domain to the variables so that all constraints are satisfied. In…

Data Structures and Algorithms · Computer Science 2018-12-06 Víctor Dalmau , Marcin Kozik , Andrei Krokhin , Konstantin Makarychev , Yury Makarychev , Jakub Opršal

The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special…

Computational Complexity · Computer Science 2017-06-20 Peter Jonsson , Victor Lagerkvist , Biman Roy

We give a surprising classification for the computational complexity of the Quantified Constraint Satisfaction Problem over a constraint language $\Gamma$, QCSP$(\Gamma)$, where $\Gamma$ is a finite language over $3$ elements which contains…

Computational Complexity · Computer Science 2022-07-28 Dmitriy Zhuk , Barnaby Martin

Many natural decision problems can be formulated as constraint satisfaction problems for reducts $\mathbb{A}$ of finitely bounded homogeneous structures. This class of problems is a large generalisation of the class of CSPs over finite…

Logic · Mathematics 2023-06-22 Manuel Bodirsky , Antoine Mottet

We study Constraint Satisfaction Problems (CSPs) in an infinite context. We show that the dichotomy between easy and hard problems -- established already in the finite case -- presents itself as the strength of the corresponding De…

Logic · Mathematics 2024-10-30 Tamás Kátay , László Márton Tóth , Zoltán Vidnyánszky

The classifications of temporal and phylogeny constraint languages stand among the most seminal complexity classifications within infinite-domain Constraint Satisfaction Problems (CSPs), yet remain the most mysterious in terms of algorithms…

Logic in Computer Science · Computer Science 2026-05-07 Johanna Brunar , Michael Pinsker , Moritz Schöbi

One of the central open problems to classify the computational complexity of finite-domain constraint satisfaction problems within P is to prove better algorithmic results for CSPs with a Maltsev polymorphism; we do not even know whether…

Rings and Algebras · Mathematics 2026-02-10 Manuel Bodirsky , Andrew Moorhead

We study the computational complexity of planar valued constraint satisfaction problems (VCSPs), which require the incidence graph of the instance be planar. First, we show that intractable Boolean VCSPs have to be self-complementary to be…

Computational Complexity · Computer Science 2017-04-12 Peter Fulla , Stanislav Zivny

We study the parameterized complexity of MinCSP for so-called equality languages, i.e., for finite languages over an infinite domain such as $\mathbb{N}$, where the relations are defined via first-order formulas whose only predicate is $=$.…

Data Structures and Algorithms · Computer Science 2023-05-19 George Osipov , Magnus Wahlström

A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…

Computational Complexity · Computer Science 2018-10-30 Manuel Bodirsky , Marcello Mamino

A continuous constraint satisfaction problem (CCSP) is a constraint satisfaction problem (CSP) with an interval domain $U \subset \mathbb{R}$. We engage in a systematic study to classify CCSPs that are complete of the Existential Theory of…

Computational Complexity · Computer Science 2024-08-07 Tillmann Miltzow , Reinier F. Schmiermann

For a large class of optimization problems, namely those that can be expressed as finite-valued constraint satisfaction problems (VCSPs), we establish a dichotomy on the number of levels of the Lasserre hierarchy of semi-definite programs…

Logic in Computer Science · Computer Science 2016-09-27 Anuj Dawar , Pengming Wang

To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…

Logic · Mathematics 2016-09-14 Ian Payne

The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…

Logic in Computer Science · Computer Science 2007-05-23 Hubie Chen

We study methods for transforming valued constraint satisfaction problems (VCSPs) to binary VCSPs. First, we show that the standard dual encoding preserves many aspects of the algebraic properties that capture the computational complexity…

Discrete Mathematics · Computer Science 2017-10-31 David A. Cohen , Martin C. Cooper , Peter G. Jeavons , Andrei Krokhin , Robert Powell , Stanislav Zivny