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Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…

Data Structures and Algorithms · Computer Science 2014-07-30 Amey Bhangale , Swastik Kopparty , Sushant Sachdeva

We study the complexity of valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a \emph{constraint language}, a fixed set of cost functions over a finite domain. An instance of the problem is specified by…

Computational Complexity · Computer Science 2010-08-25 Vladimir Kolmogorov

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

We present a definition of the class NP in combinatorial context as the set of languages of structures defined by finitely many forbidden lifted substructures. We apply this to special syntactically defined subclasses and show how they…

Combinatorics · Mathematics 2007-06-13 Gabor Kun , Jaroslav Nesetril

We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…

Computational Complexity · Computer Science 2010-02-22 Andrew Drucker

A temporal (constraint) language is a relational structure with a first-order definition in the rational numbers with the order. We study here the complexity of the Quantified Constraint Satisfaction Problem (QCSP) for temporal constraint…

Logic in Computer Science · Computer Science 2021-09-08 Michał Wrona

In pursuit of a deeper understanding of Boolean Promise Constraint Satisfaction Problems (PCSPs), we identify a class of problems with restricted structural complexity, which could serve as a promising candidate for complete…

Computational Complexity · Computer Science 2025-10-01 Katzper Michno

We study constraint satisfaction problems (CSPs) in the presence of counting quantifiers $\exists^{\geq j}$, asserting the existence of $j$ distinct witnesses for the variable in question. As a continuation of our previous (CSR 2012) paper,…

Logic in Computer Science · Computer Science 2013-12-31 Barnaby Martin , Juraj Stacho

In this paper we provide an extended formulation for the class of constraint satisfaction problems and prove that its size is polynomial for instances whose constraint graph has bounded treewidth. This implies new upper bounds on extension…

Computational Complexity · Computer Science 2015-04-29 Petr Kolman , Martin Koutecký

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

A constraint satisfaction problem (CSP), $\textsf{Max-CSP}(\mathcal{F})$, is specified by a finite set of constraints $\mathcal{F} \subseteq \{[q]^k \to \{0,1\}\}$ for positive integers $q$ and $k$. An instance of the problem on $n$…

Computational Complexity · Computer Science 2024-02-27 Chi-Ning Chou , Alexander Golovnev , Madhu Sudan , Santhoshini Velusamy

We consider the problem of approximately solving constraint satisfaction problems with arity $k > 2$ ($k$-CSPs) on instances satisfying certain expansion properties, when viewed as hypergraphs. Random instances of $k$-CSPs, which are also…

Data Structures and Algorithms · Computer Science 2019-07-19 Vedat Levi Alev , Fernando Granha Jeronimo , Madhur Tulsiani

Given a constraint satisfaction problem (CSP) on $n$ variables, $x_1, x_2, \dots, x_n \in \{\pm 1\}$, and $m$ constraints, a global cardinality constraint has the form of $\sum_{i = 1}^{n} x_i = (1-2p)n$, where $p \in (\Omega(1), 1 -…

Data Structures and Algorithms · Computer Science 2016-10-21 Xue Chen , Yuan Zhou

Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to…

Discrete Mathematics · Computer Science 2017-01-24 Colin Wei , Stefano Ermon

A Constraint Satisfaction Problem (CSP) is a framework used for modeling and solving constrained problems. Tree-search algorithms like backtracking try to construct a solution to a CSP by selecting the variables of the problem one after…

Artificial Intelligence · Computer Science 2014-10-06 Muhammad Rezaul Karim

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

Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…

Logic · Mathematics 2024-05-13 Manuel Bodirsky , Bertalan Bodor

We study minimum cost constraint satisfaction problems (MinCostCSP) through the algebraic lens. We show that for any constraint language $\Gamma$ which has the dual discriminator operation as a polymorphism, there exists a…

Data Structures and Algorithms · Computer Science 2025-07-14 Ian DeHaan , Neng Huang , Euiwoong Lee

The quantified constraint satisfaction problem (QCSP) is the problem of deciding, given a structure and a first-order prenex sentence whose quantifier-free part is the conjunction of atoms, whether or not the sentence holds on the…

Logic in Computer Science · Computer Science 2015-03-20 Hubie Chen

In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…

Data Structures and Algorithms · Computer Science 2020-12-03 Joshua Brakensiek , Venkatesan Guruswami , Marcin Wrochna , Stanislav Živný