相关论文: CD(4) has bounded width
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…
A temporal constraint language is a set of relations that are first-order definable over (Q;<). We show that several temporal constraint languages whose constraint satisfaction problem is maximally tractable are also maximally tractable for…
Every CSP(B) for a finite structure B is either in P or it is NP-complete but the proofs of the finite-domain CSP dichotomy by Andrei Bulatov and Dimitryi Zhuk not only show the computational complexity separation but also confirm the…
Query evaluation on probabilistic databases is generally intractable (#P-hard). Existing dichotomy results have identified which queries are tractable (or safe), and connected them to tractable lineages. In our previous work, using…
A famous result by Jeavons, Cohen, and Gyssens shows that every constraint satisfaction problem (CSP) where the constraints are preserved by a semi-lattice operation can be solved in polynomial time. This is one of the basic facts for the…
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…
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…
We study the tractability of conjunctive query answering for queries with unbounded arity. It is well known that tractability of the problem can be characterised in terms of the queries treewidth under the assumption of bounded arity. We…
We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…
Given a diagram D of a knot K, we give easily computable bounds for Rasmussen's concordance invariant s(K). The bounds are not independent of the diagram D chosen, but we show that for diagrams satisfying a given condition the bounds are…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…
We prove two results about width of words in $SL_n(\mathbb{Z})$. The first is that, for every $n \geq 3$, there is a constant $C(n)$ such that the width of any word in $SL_n(\mathbb{Z})$ is less than $C(n)$. The second result is that, for…
We prove that every congruence distributive variety has directed J\'{o}nsson terms, and every congruence modular variety has directed Gumm terms. The directed terms we construct witness every case of absorption witnessed by the original…
Many natural decision problems can be formulated as constraint satisfaction problems for reducts $\mathbb{A}$ of finitely bounded homogeneous structures. This class of problems is a large generalisation of the class of CSPs over finite…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of…
Several important decision problems on conjunctive queries (CQs) are NP-complete in general but become tractable, and actually highly parallelizable, if restricted to acyclic or nearly acyclic queries. Examples are the evaluation of Boolean…
The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main…
The simplest toroidally compactified string theories exhibit a duality between large and small radii: compactification on a circle, for example, is invariant under R goes to 1/R. Compactification on more general Lorentzian lattices (i.e.…