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We study the time complexity of the weighted first-order model counting (WFOMC) over the logical language with two variables and counting quantifiers. The problem is known to be solvable in time polynomial in the domain size. However, the…
Constraint languages that arise from finite algebras have recently been the object of study, especially in connection with the Dichotomy Conjecture of Feder and Vardi. An important class of algebras are those that generate congruence…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
We consider the dichotomy conjecture for consistent query answering under primary key constraints. It states that, for every fixed Boolean conjunctive query q, testing whether q is certain (i.e. whether it evaluates to true over all repairs…
Constraint Satisfaction Problems (CSPs, for short) make up a class of problems with applications in many areas of computer science. The first classification of these problems was given by Schaeffer who showed that every CSP over the domain…
The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in…
Holant problems capture a class of Sum-of-Product computations such as counting matchings. It is inspired by holographic algorithms and is equivalent to tensor networks, with counting CSP being a special case. A classification for Holant…
In this paper, we define the reoptimization variant of the closest substring problem (CSP) under sequence addition. We show that, even with the additional information we have about the problem instance, the problem of finding a closest…
The \emph{Workflow Satisfiability Problem (WSP)} is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether…
Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of…
Conservative constraint satisfaction problems (CSPs) constitute an important particular case of the general CSP, in which the allowed values of each variable can be restricted in an arbitrary way. Problems of this type are well studied for…
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…
Let \Gamma be a structure with a finite relational signature and a first-order definition in (R;*,+) with parameters from R, that is, a relational structure over the real numbers where all relations are semi-algebraic sets. In this article,…
Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…
The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable if the model-complete core of the template…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…
A natural and established way to restrict the constraint satisfaction problem is to fix the relations that can be used to pose constraints; such a family of relations is called a constraint language. In this article, we study arc…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its…