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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

For general input automata, there exist regular constraint languages such that asking if a given input automaton admits a synchronizing word in the constraint language is PSPACE-complete or NP-complete. Here, we investigate this problem for…

Formal Languages and Automata Theory · Computer Science 2021-09-08 Stefan Hoffmann

In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…

Computational Complexity · Computer Science 2007-05-23 Peter Jonsson , Mikael Klasson , Andrei Krokhin

The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…

Logic in Computer Science · Computer Science 2026-02-23 Antoine Cuvelier , Rémi Morvan

This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…

Computational Complexity · Computer Science 2018-07-23 Grigoriy V. Bokov

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

We determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted Boolean constraint satisfaction problem (or CSP) with any number of additional unary (i.e., arity 1)…

Computational Complexity · Computer Science 2015-05-19 Tomoyuki Yamakami

Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…

Computational Complexity · Computer Science 2021-05-25 Manoj Kumar

The logic MMSNP is a well-studied fragment of Existential Second-Order logic that, from a computational perspective, captures finite-domain Constraint Satisfaction Problems (CSPs) modulo polynomial-time reductions. At the same time, MMSNP…

Computational Complexity · Computer Science 2026-05-12 Demian Banakh , Alexey Barsukov , Tamio-Vesa Nakajima

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

Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well-known problems can be cast as promise CSPs including approximate graph…

Computational Complexity · Computer Science 2018-07-16 Joshua Brakensiek , Venkatesan Guruswami

In the constraint satisfaction problem ($CSP$), the aim is to find an assignment of values to a set of variables subject to specified constraints. In the minimum cost homomorphism problem ($MinHom$), one is additionally given weights…

Machine Learning · Computer Science 2010-04-06 Rustem Takhanov

This paper describes an extension to the constraint satisfaction problem (CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of…

Artificial Intelligence · Computer Science 2014-11-17 R. A Helzerman , M. P. Harper

The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints, where a surjective assignment is an assignment…

Computational Complexity · Computer Science 2021-04-30 Dmitriy Zhuk

Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…

Computational Complexity · Computer Science 2026-04-28 Manuel Bodirsky

In this paper we determine the complexity of a broad class of problems that extends the temporal constraint satisfaction problems. To be more precise we study the problems Poset-SAT($\Phi$), where $\Phi$ is a given set of quantifier-free…

Computational Complexity · Computer Science 2016-09-27 Michael Kompatscher , Trung Van Pham

The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about…

Computational Complexity · Computer Science 2021-07-19 Libor Barto , Jakub Bulín , Andrei Krokhin , Jakub Opršal

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 develop a new theory of strong subalgebras and linear congruences that are defined globally. Using this theory we provide a new proof of the correctness of Zhuk's algorithm for all tractable CSPs on a finite domain, and therefore a new…

Computational Complexity · Computer Science 2024-10-22 Dmitriy Zhuk

A natural strengthening of an algorithm for the (promise) constraint satisfaction problem is its singleton version: we first fix a variable to an element from its domain, then run the algorithm, and remove the element from the domain if the…

Logic in Computer Science · Computer Science 2026-03-31 Dmitriy Zhuk