English
Related papers

Related papers: Low-level dichotomy for Quantified Constraint Sati…

200 papers

We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is a reflexive tournament. It is well-known that reflexive tournaments can be split into a sequence of strongly connected components…

Computational Complexity · Computer Science 2022-04-13 Benoit Larose , Petar Markovic , Barnaby Martin , Daniel Paulusma , Siani Smith , Stanislav Zivny

The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…

Computational Complexity · Computer Science 2017-01-09 Hubie Chen , Benoit Larose

The $\mathcal{H}$-coloring problem for undirected simple graphs is a computational problem from a huge class of the constraint satisfaction problems (CSP): an $\mathcal{H}$-coloring of a graph $\mathcal{G}$ is just a homomorphism from…

Logic · Mathematics 2020-10-07 Azza Gaysin

We study the use of local consistency methods as reductions between constraint satisfaction problems (CSPs), and promise version thereof, with the aim to classify these reductions in a similar way as the algebraic approach classifies gadget…

Logic in Computer Science · Computer Science 2024-05-20 Victor Dalmau , Jakub Opršal

We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction -- a refinement of the Hrushosvki-encoding -- to $\omega$-categorical structures in a possibly infinite signature. We…

Logic in Computer Science · Computer Science 2021-01-12 Pierre Gillibert , Julius Jonušas , Michael Kompatscher , Antoine Mottet , Michael Pinsker

We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a…

Computational Complexity · Computer Science 2015-04-17 Christian Glasser , Peter Jonsson , Barnaby Martin

For $n\geq 3$, let $(H_n, E)$ denote the $n$-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on $n$ vertices. We show that for all…

Logic in Computer Science · Computer Science 2021-01-12 Manuel Bodirsky , Barnaby Martin , Michael Pinsker , András Pongrácz

The algebraic approach to the Constraint Satisfaction Problem (CSP) uses high order symmetries of relational structures -- polymorphisms -- to study the complexity of the CSP. In this paper we further develop one of the methods the…

Logic in Computer Science · Computer Science 2020-07-21 Andrei A. Bulatov

We prove that an $\omega$-categorical core structure primitively positively interprets all finite structures with parameters if and only if some stabilizer of its polymorphism clone has a homomorphism to the clone of projections, and that…

Logic in Computer Science · Computer Science 2016-02-16 Libor Barto , Michael Pinsker

An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…

Computational Complexity · Computer Science 2015-01-08 Jonah Brown-Cohen , Prasad Raghavendra

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 define and explore a notion of unique prime factorization for constraint functions, and use this as a new tool to prove a complexity classification for counting weighted Eulerian orientation problems with arrow reversal symmetry (ARS).…

Computational Complexity · Computer Science 2021-04-13 Jin-Yi Cai , Zhiguo Fu , Shuai Shao

In the Constraint Satisfaction Problem (CSP for short) the goal is to decide the existence of a homomorphism from a given relational structure $G$ to a given relational structure $H$. If the structure $H$ is fixed and $G$ is the only input,…

Logic in Computer Science · Computer Science 2025-10-14 Andrei A. Bulatov , Amirhossein Kazeminia

This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to…

Computational Complexity · Computer Science 2024-08-07 Libor Barto , Zarathustra Brady , Andrei Bulatov , Marcin Kozik , Dmitriy Zhuk

A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…

Artificial Intelligence · Computer Science 2015-02-10 Evgenij Thorstensen

Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism $\mbox{$\bR \rightarrow \bGamma$}$ between two relational…

Computational Complexity · Computer Science 2015-10-27 Vladimir Kolmogorov , Michal Rolinek , Rustem Takhanov

For relational structures A, B of the same signature, the Promise Constraint Satisfaction Problem PCSP(A,B) asks whether a given input structure maps homomorphically to A or does not even map to B. We are promised that the input satisfies…

Computational Complexity · Computer Science 2023-06-22 Alexandr Kazda , Peter Mayr , Dmitriy Zhuk

Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…

Artificial Intelligence · Computer Science 2012-07-19 Manuel Bodirsky , Martin Hils , Alex Krimkevich

We study the complexity of constraint satisfaction problems for templates $\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with the successor relation. Assuming a widely believed conjecture from finite domain…

Computational Complexity · Computer Science 2016-04-27 Manuel Bodirsky , Victor Dalmau , Barnaby Martin , Antoine Mottet , Michael Pinsker

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