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35
Datalog and constraint satisfaction with infinite templates
 In Proceedings of the 23rd International Symposium on Theoretical Aspects of Computer Science (STACS’06), LNCS 3884
, 2006
"... Abstract. On finite structures, there is a wellknown connection between the expressive power of Datalog, finite variable logics, the existential pebble game, and bounded hypertree duality. We study this connection for infinite structures. This has applications for constraint satisfaction with infin ..."
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Cited by 39 (21 self)
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Abstract. On finite structures, there is a wellknown connection between the expressive power of Datalog, finite variable logics, the existential pebble game, and bounded hypertree duality. We study this connection for infinite structures. This has applications for constraint satisfaction with infinite templates, i.e., for all computational problems that are closed under disjoint unions and whose complement is closed under homomorphisms. If the template Γ is ωcategorical, we obtain alternative characterizations of bounded Datalog width. We also show that CSP(Γ) can be solved in polynomial time if Γ is ωcategorical and the input is restricted to instances of bounded treewidth. Finally, we prove algebraic characterisations of those ωcategorical templates whose CSP has Datalog width (1, k), and for those whose CSP has strict Datalog width k.
Dualities for constraint satisfaction problems
"... In a nutshell, a duality for a constraint satisfaction problem equates the existence of one homomorphism to the nonexistence of other homomorphisms. In this survey paper, we give an overview of logical, combinatorial, and algebraic aspects of the following forms of duality for constraint satisfact ..."
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Cited by 22 (8 self)
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In a nutshell, a duality for a constraint satisfaction problem equates the existence of one homomorphism to the nonexistence of other homomorphisms. In this survey paper, we give an overview of logical, combinatorial, and algebraic aspects of the following forms of duality for constraint satisfaction problems: finite duality, bounded pathwidth duality, and bounded treewidth duality.
Recent results on the algebraic approach to the CSP
 In The Same Volume
, 2008
"... Abstract. We describe an algebraic approach to the constraint satisfaction problem (CSP) and present recent results on the CSP that make use of, in an essential way, this algebraic framework. 1 ..."
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Cited by 21 (4 self)
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Abstract. We describe an algebraic approach to the constraint satisfaction problem (CSP) and present recent results on the CSP that make use of, in an essential way, this algebraic framework. 1
Ontologybased data access: a study through disjunctive datalog, csp, and mmsnp
 IN: PODS
, 2014
"... Ontologybased data access is concerned with querying incomplete data sources in the presence of domainspecific knowledge provided by an ontology. A central notion in this setting is that of an ontologymediated query, which is a database query coupled with an ontology. In this article, we study se ..."
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Cited by 20 (2 self)
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Ontologybased data access is concerned with querying incomplete data sources in the presence of domainspecific knowledge provided by an ontology. A central notion in this setting is that of an ontologymediated query, which is a database query coupled with an ontology. In this article, we study several classes of ontologymediated queries, where the database queries are given as some form of conjunctive query and the ontologies are formulated in description logics or other relevant fragments of firstorder logic, such as the guarded fragment and the unary negation fragment. The contributions of the article are threefold. First, we show that popular ontologymediated query languages have the same expressive power as natural fragments of disjunctive datalog, and we study the relative succinctness of ontologymediated queries and disjunctive datalog queries. Second, we establish intimate connections between ontologymediated queries and constraint satisfaction problems (CSPs) and their logical generalization, MMSNP formulas. Third, we exploit these connections to obtain new results regarding: (i) firstorder rewritability and datalog rewritability of ontologymediated queries; (ii) P/NP dichotomies for ontologymediated queries; and (iii) the query containment problem for ontologymediated queries.
Affine systems of equations and counting infinitary logic
 In ICALP’07, volume 4596 of LNCS
, 2007
"... Abstract We consider the definability of constraint satisfaction problems (CSP) in various fixedpoint andinfinitary logics. We show that testing the solvability of systems of equations over a finite Abelian group, ..."
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Cited by 17 (7 self)
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Abstract We consider the definability of constraint satisfaction problems (CSP) in various fixedpoint andinfinitary logics. We show that testing the solvability of systems of equations over a finite Abelian group,
On the scope of the universalalgebraic approach to constraint satisfaction
, 2009
"... The universalalgebraic approach has proved a powerful tool in the study of the computational complexity of constraint satisfaction problems (CSPs). This approach has previously been applied to the study of CSPs with finite or (infinite) ωcategorical templates. Our first result is an exact charact ..."
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Cited by 12 (9 self)
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The universalalgebraic approach has proved a powerful tool in the study of the computational complexity of constraint satisfaction problems (CSPs). This approach has previously been applied to the study of CSPs with finite or (infinite) ωcategorical templates. Our first result is an exact characterization of those CSPs that can be formulated with (a finite or) an ωcategorical template. The universalalgebraic approach relies on the fact that in finite or ωcategorical structures A, a relation is primitive positive definable if and only if it is preserved by the polymorphisms of A. In this paper, we present results that can be used to study the computational complexity of CSPs with arbitrary infinite templates. Specifically, we prove that every CSP can be formulated with a template A such that a relation is primitive positive definable in A if and only if it is firstorder definable on A and preserved by the infinitary polymorphisms of A. We present applications of our general results to the description and analysis of the computational complexity of CSPs. In particular, we present a polymorphismbased description of those CSPs that are firstorder definable (and therefore can be solved in polynomialtime), and give general hardness criteria based on the absence of polymorphisms that depend on more than one argument.
Generalised dualities and finite maximal antichains
 GraphTheoretic Concepts in Computer Science (Proceedings of WG 2006), volume 4271 of Lecture Notes in Comput. Sci
, 2006
"... We fully characterise the situations where the existence of a homomorphism from a digraph G to at least one of a finite set H of directed graphs is determined by a finite number of forbidden subgraphs. We prove that these situations, called generalised dualities, are characterised by the nonexisten ..."
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Cited by 11 (3 self)
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We fully characterise the situations where the existence of a homomorphism from a digraph G to at least one of a finite set H of directed graphs is determined by a finite number of forbidden subgraphs. We prove that these situations, called generalised dualities, are characterised by the nonexistence of a homomorphism to G from a finite set of forests. Furthermore, we characterise all finite maximal antichains in the partial order of directed graphs ordered by the existence of homomorphism. We show that these antichains correspond exactly to the