相关论文: Satisfaction, Restriction and Amalgamation of Cons…
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…
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…
This is the report-version of a mini-series of two articles on the foundations of satisfiability of conjunctive normal forms with non-boolean variables, to appear in Fundamenta Informaticae, 2011. These two parts are here bundled in one…
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…
Data constraints are fundamental for practical data modelling, and a verifiable conformance of a data instance to a safety-critical constraint (satisfaction relation) is a corner-stone of safety assurance. Diagrammatic constraints are…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
Adhesive categories provide an abstract framework for the algebraic approach to rewriting theory, where many general results can be recast and uniformly proved. However, checking that a model satisfies the adhesivity properties is sometimes…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
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 present a generic construction of finite realisations of amalgamation patterns. An amalgamation pattern is specified by a finite collection of finite template structures together with a collection of partial isomorphisms between them. A…
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;…
For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…
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…
We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…
The article considers one of the possible generalizations of constraint satisfaction problems where relations are replaced by multivalued membership functions. In this case operations of disjunction and conjunction are replaced by maximum…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
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…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…