Related papers: Proof complexity of Mal'tsev CSP
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable…
A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective…
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…
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…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…
The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…
We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a…
A conservative class of constraint satisfaction problems CSPs is a class for which membership is preserved under arbitrary domain reductions. Many well-known tractable classes of CSPs are conservative. It is well known that lexleader…
The logic MMSNP is a restricted fragment of existential second-order logic which allows to express many interesting queries in graph theory and finite model theory. The logic was introduced by Feder and Vardi who showed that every MMSNP…
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,…
We study the Constraint Satisfaction Problem CSP(A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.
The constraint satisfaction problem (CSP) on a relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the…
We define a class of algebras, the semilattices of Mal'cev blocks (for short, SMB algebras). In a nutshell, these algebras are semilattices in which each element gets blown up into a Mal'cev algebra. We publish for the first time our old…
We study optimisation problems that can be formulated as valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a \emph{constraint language}, a fixed set of cost functions taking finite and infinite costs…
Constraint Satisfaction Problem (CSP) is a framework for modeling and solving a variety of real-world problems. Once the problem is expressed as a finite set of constraints, the goal is to find the variables' values satisfying them. Even…
Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a…
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of…
A dichotomy theorem for counting problems due to Creignou and Hermann states that or any nite set S of logical relations, the counting problem #SAT(S) is either in FP, or #P-complete. In the present paper we show a dichotomy theorem for…
It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy…