Results 1  10
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71
Minimal Deductive Systems for RDF
 In ESWC
, 2007
"... Abstract This paper presents a minimalist program for RDF, by showing how one can do without several predicates and keywords of the RDF Schema vocabulary, obtaining a simpler language which preserves the original semantics. This approach is beneficial in at least two directions: (a) To have a simple ..."
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Cited by 75 (9 self)
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Abstract This paper presents a minimalist program for RDF, by showing how one can do without several predicates and keywords of the RDF Schema vocabulary, obtaining a simpler language which preserves the original semantics. This approach is beneficial in at least two directions: (a) To have a simple abstract fragment of RDFS easy to formalize and to reason about, which captures the essence of RDFS; (b) To obtain algorithmic properties of deduction and optimizations that are relevant for particular fragments. Among our results are: the identification of a simple fragment of RDFS; the proof that it encompasses the main features of RDFS; a formal semantics and a deductive system for it; sound and complete deductive systems for their subfragments; and an O(n log n) complexity bound for ground entailment in this fragment. 1
On Digraph Coloring Problems and Treewidth Duality
 20th IEEE Symposium on Logic in Computer Science (LICS
, 2005
"... It is known that every constraintsatisfaction problem (CSP) reduces, and is in fact polynomially equivalent, to a digraph coloring problem. By carefully analyzing the constructions, we observe that the reduction is quantifierfree. Using this, we illustrate the power of the logical approach to CSPs ..."
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Cited by 53 (2 self)
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It is known that every constraintsatisfaction problem (CSP) reduces, and is in fact polynomially equivalent, to a digraph coloring problem. By carefully analyzing the constructions, we observe that the reduction is quantifierfree. Using this, we illustrate the power of the logical approach to CSPs by resolving two conjectures about treewidth duality in the digraph case. The point is that the analogues of these conjectures for general CSPs were resolved long ago by proof techniques that break down for digraphs. We also completely characterize those CSPs that are firstorder definable and show that they coincide with those that have finitary tree duality. The combination of this result with an older result by Neˇsetˇril and Tardif shows that there is a computable listing of all template structures whose CSP is definable in full firstorder logic. Finally, we provide new width lower bounds for some tractable CSPs. The novelty is that our bounds are a tight function of the treewidth of the underlying instance. As a corollary we get a new proof that there exist tractable CSPs without bounded treewidth duality. ∗ This work was partially supported by CICYT TIN200404343 and by the European Commision through the RTN COMBSTRU HPRNCT200200278. 1 1
A Combinatorial Characterization of Resolution Width
 In 18th IEEE Conference on Computational Complexity
, 2002
"... We provide a characterization of the resolution width introduced in the context of propositional proof complexity in terms of the existential pebble game introduced in the context of finite model theory. The characterization is tight and purely combinatorial. Our first application of this result i ..."
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Cited by 52 (6 self)
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We provide a characterization of the resolution width introduced in the context of propositional proof complexity in terms of the existential pebble game introduced in the context of finite model theory. The characterization is tight and purely combinatorial. Our first application of this result is a surprising proof that the minimum space of refuting a 3CNF formula is always bounded from below by the minimum width of refuting it (minus 3). This solves a wellknown open problem. The second application is the unification of several width lower bound arguments, and a new width lower bound for the Dense Linear Order Principle. Since we also show that this principle has resolution refutations of polynomial size, this provides yet another example showing that the sizewidth relationship is tight.
Constraint solving via fractional edge covers
 In Proceedings of the of the 17th Annual ACMSIAM Symposium on Discrete Algorithms
, 2006
"... Many important combinatorial problems can be modelled as constraint satisfaction problems, hence identifying polynomialtime solvable classes of constraint satisfaction problems received a lot of attention. In this paper, we are interested in structural properties that can make the problem tractable ..."
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Cited by 51 (9 self)
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Many important combinatorial problems can be modelled as constraint satisfaction problems, hence identifying polynomialtime solvable classes of constraint satisfaction problems received a lot of attention. In this paper, we are interested in structural properties that can make the problem tractable. So far, the largest structural class that is known to be polynomialtime solvable is the class of bounded hypertree width instances introduced by Gottlob et al. [20]. Here we identify a new class of polynomialtime solvable instances: those having bounded fractional edge cover number. Combining hypertree width and fractional edge cover number, we then introduce the notion of fractional hypertree width. We prove that constraint satisfaction problems with bounded fractional hypertree width can be solved in polynomial time (provided that a the tree decomposition is given in the input). We also prove that certain parameterized constraint satisfaction, homomorphism, and embedding problems are fixedparameter tractable on instances having bounded fractional hypertree width. 1.
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.
Can you beat treewidth?
, 2007
"... It is wellknown that constraint satisfaction problems (CSP) can be solved in time n O(k) if the treewidth of the primal graph of the instance is at most k and n is the size of the input. We show that no algorithm can be significantly better than this treewidthbased algorithm, even if we restrict t ..."
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Cited by 38 (8 self)
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It is wellknown that constraint satisfaction problems (CSP) can be solved in time n O(k) if the treewidth of the primal graph of the instance is at most k and n is the size of the input. We show that no algorithm can be significantly better than this treewidthbased algorithm, even if we restrict the problem to some special class of primal graphs. Formally, let G be an arbitrary class of graphs and assume that there is an algorithm A solving binary CSP for instances whose primal graph is in G. We prove that if the running time of A is f(G)n o(k/logk) , where k is the treewidth of the primal graph G and f is an arbitrary function, then the Exponential Time Hypothesis fails. We prove the result also in the more general framework of the homomorphism problem for boundedarity relational structures. For this problem, the treewidth of the core of the lefthand side structure plays the same role as the treewidth of the primal graph above.
A characterisation of firstorder constraint satisfaction problems
 LOGICAL METHODS COMPUT. SCI
, 2007
"... We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction problem is firstorder definable: we show the general problem to ..."
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Cited by 35 (11 self)
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We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction problem is firstorder definable: we show the general problem to be NPcomplete, and give a polynomialtime algorithm in the case of cores. A slight modification of this algorithm provides, for firstorder definable CSP’s, a simple polytime algorithm to produce a solution when one exists. As an application of our algebraic characterisation of first order CSP’s, we describe a large family of Lcomplete CSP’s.
Clauselearning algorithms with many restarts and boundedwidth resolution
, 2009
"... We offer a new understanding of some aspects of practical SATsolvers that are based on DPLL with unitclause propagation, clauselearning, and restarts. On the theoretical side, we do so by analyzing a concrete algorithm which we claim is faithful to what practical solvers do. In particular, befo ..."
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Cited by 34 (3 self)
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We offer a new understanding of some aspects of practical SATsolvers that are based on DPLL with unitclause propagation, clauselearning, and restarts. On the theoretical side, we do so by analyzing a concrete algorithm which we claim is faithful to what practical solvers do. In particular, before making any new decision or restart, the solver repeatedly applies the unitresolution rule until saturation, and leaves no component to the mercy of nondeterminism except for some internal randomness. We prove the perhaps surprising fact that, although the solver is not explicitely designed for it, it ends up behaving as widthk resolution after no more than n 2k+1 conflicts and restarts, where n is the number of variables. In other words, widthk resolution can be thought as n 2k+1 restarts of the unitresolution rule with learning. On the experimental side, we give evidence for the claim that this theoretical result describes real world solvers. We do so by running some of the most prominent solvers on some CNF formulas that we designed to have resolution refutations of width k. It turns out that the upper bound of the theoretical result holds for these solvers and that the true performance appears to be not very far from it.
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
, 2010
"... An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP instances (i.e., where each constraint involves only two variables ..."
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Cited by 31 (4 self)
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An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP instances (i.e., where each constraint involves only two variables), the situation is well understood: the complexity of the problem essentially depends on the treewidth of the graph of the constraints [19, 24]. However, this is not the correct answer if constraints with unbounded number of variables are allowed, and in particular, for CSP instances arising from query evaluation problems in database theory. Formally, if H is a class of hypergraphs, then let CSP(H) be CSP restricted to instances whose hypergraph is in H. Our goal is to characterize those classes of hypergraphs for which CSP(H) is polynomialtime solvable or fixedparameter tractable, parameterized by the number of variables. In the applications related to database query evaluation, we usually assume that the number of variables is much smaller than the size of the instance, thus parameterization by the number of variables is a meaningful question. The most general known property of H that makes CSP(H) polynomialtime solvable is bounded fractional hypertree width. Here we introduce a new hypergraph measure called submodular width, and show that bounded submodular width of H (which is a strictly more general property than bounded fractional hypertree width) implies that CSP(H) is fixedparameter tractable. In a matching hardness result, we show that if H has unbounded submodular width, then CSP(H) is not fixedparameter tractable (and hence not polynomialtime solvable), unless the Exponential Time Hypothesis (ETH) fails. The algorithmic result uses tree decompositions in a novel way: instead of using a single decomposition depending on the hypergraph, the instance is split into a set of
Generalized majorityminority operations are tractable
 In LICS
, 2005
"... Vol. 2 (4:1) 2006, pp. 1–15 www.lmcsonline.org ..."
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