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44
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 50 (7 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 37 (1 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 34 (4 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.
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 32 (18 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.
Symbolic Decision Procedures for QBF
 Proceedings of 10th Int. Conf. on Principles and Practice of Constraint Programming (CP 2004
, 2004
"... Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are searchbased. In this work we explore an alternative approach to QBF solving, based on symb ..."
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Cited by 24 (1 self)
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Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are searchbased. In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination. We extend some recent symbolic approaches for SAT solving to symbolic QBF solving, using various decisiondiagram formalisms such as OBDDs and ZDDs. In both approaches, QBF formulas are solved by eliminating all their quantifiers. Our first solver, QMRES, maintains a set of clauses represented by a ZDD and eliminates quantifiers via multiresolution. Our second solver, QBDD, maintains a set of OBDDs, and eliminate quantifier by applying them to the underlying OBDDs. We compare our symbolic solvers to several competitive searchbased solvers. We show that QBDD is not competitive, but QMRES compares favorably with searchbased solvers on various benchmarks consisting of nonrandom formulas.
Generalized majorityminority operations are tractable
 In LICS
, 2005
"... Vol. 2 (4:1) 2006, pp. 1–15 www.lmcsonline.org ..."
Tardif: A characterisation of firstorder constraint satisfaction problems
 Logical Methods Comput. Sci
"... Abstract. 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 pr ..."
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Cited by 23 (6 self)
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Abstract. 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. 1.
Search vs. symbolic techniques in satisfiability solving
 in Proceedings 7th International Conference on Theory and Applications of Satisfiability Testing
, 2004
"... Abstract. Recent work has shown how to use OBDDs for satisfiability solving. The idea of this approach, which we call symbolic quantifier elimination, is to view an instance of propositional satisfiability as an existentially quantified propositional formula. Satisfiability solving then amounts to q ..."
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Cited by 19 (3 self)
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Abstract. Recent work has shown how to use OBDDs for satisfiability solving. The idea of this approach, which we call symbolic quantifier elimination, is to view an instance of propositional satisfiability as an existentially quantified propositional formula. Satisfiability solving then amounts to quantifier elimination; once all quantifiers have been eliminated we are left with either 1 or 0. Our goal in this work is to study the effectiveness of symbolic quantifier elimination as an approach to satisfiability solving. To that end, we conduct a direct comparison with the DPLLbased ZChaff, as well as evaluate a variety of optimization techniques for the symbolic approach. In comparing the symbolic approach to ZChaff, we evaluate scalability across a variety of classes of formulas. We find that no approach dominates across all classes. While ZChaff dominates for many classes of formulas, the symbolic approach is superior for other classes of formulas. Once we have demonstrated the viability of the symbolic approach, we focus on optimization techniques for this approach. We study techniques from constraint satisfaction for finding a good plan for performing the symbolic operations of conjunction and of existential quantification. We also study various variableordering heuristics, finding that while no heuristic seems to dominate across all classes of formulas, the maximumcardinality search heuristic seems to offer the best overall performance. 1
Constraint Propagation as a Proof System
 10th Int.Conf. on Principles and Practice of Constraint Programing, LN in Computer Science vol.3258
, 2004
"... Refutation proofs can be viewed as a special case of constraint propagation, which is a fundamental technique in solving constraintsatisfaction problems. ..."
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Cited by 19 (1 self)
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Refutation proofs can be viewed as a special case of constraint propagation, which is a fundamental technique in solving constraintsatisfaction problems.
Can You Beat Treewidth?
 THEORY OF COMPUTING, VOLUME 6 (2010), PP. 85–112
, 2010
"... It is wellknown that constraint satisfaction problems (CSP) over an unbounded domain 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 do significantly better than this treewidthbased algor ..."
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Cited by 13 (5 self)
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It is wellknown that constraint satisfaction problems (CSP) over an unbounded domain 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 do significantly better than this treewidthbased algorithm, even if we restrict the problem to some special class of primal graphs. Formally, let A be an algorithm solving binary CSP (i. e., CSP where every constraint involves two variables). We prove that if there is a class G of graphs with unbounded treewidth such that the running time of algorithm A is f (G)n o(k/logk) on instances whose primal graph G is in G, where k is the treewidth of the primal graph G and f is an arbitrary function, then the Exponential Time Hypothesis (ETH) 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. Finally, we use the results to obtain corollaries on the complexity of (Colored/Partitioned) Subgraph Isomorphism.