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A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the…
A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…
Finite valued constraint satisfaction problems are a formalism for describing many natural optimization problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of…
The constraint satisfaction problem, parameterized by a relational structure, provides a general framework for expressing computational decision problems. Already the restriction to the class of all finite structures forms an interesting…
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…
The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full…
In this paper the computational complexity of the (bi)simulation problem over restricted graph classes is studied. For trees given as pointer structures or terms the (bi)simulation problem is complete for logarithmic space or NC$^1$,…
In this document, we introduce PyCSP$3$, a Python library that allows us to write models of combinatorial constrained problems in a declarative manner. Currently, with PyCSP$3$, you can write models of constraint satisfaction and…
We prove a complexity classification theorem that classifies all counting constraint satisfaction problems ($\#$CSP) over Boolean variables into exactly three categories: (1) Polynomial-time tractable; (2) $\#$P-hard for general instances,…
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 -…
We present a structural classification of constraint satisfaction problems (CSP) described by reflexive complete $2$-edge-coloured graphs. In particular, this classification extends the structural dichotomy for graph homomorphism problems…
Holant problems are a general framework to study the computational complexity of counting problems. It is a more expressive framework than counting constraint satisfaction problems (CSP) which are in turn more expressive than counting graph…
The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures.…
Conjunctive Regular Path Queries, or CRPQs for short, are an essential construct in graph query languages. In this paper, we propose the first output-sensitive algorithm for evaluating acyclic CRPQs. It is output-sensitive in the sense that…
We propose a major revision of the format XCSP 2.1, called XCSP3, to build integrated representations of combinatorial constrained problems. This new format is able to deal with mono/multi optimization, many types of variables, cost…
We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting. Specifically, given a Boolean constraint language $\Gamma$ and a degree bound $\Delta$, we study the complexity of…
The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…
Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and artificial intelligence. Forbidding patterns (generic sub-instances) provides a means of defining…