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45
Constraint Solving in Uncertain and Dynamic Environments: A Survey
 Constraints
, 2005
"... Abstract. This article follows a tutorial, given by the authors on dynamic constraint solving at CP 2003 [87]. It aims at offering an overview of the main approaches and techniques that have been proposed in the domain of constraint satisfaction to deal with uncertain and dynamic environments. Keywo ..."
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Cited by 36 (3 self)
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Abstract. This article follows a tutorial, given by the authors on dynamic constraint solving at CP 2003 [87]. It aims at offering an overview of the main approaches and techniques that have been proposed in the domain of constraint satisfaction to deal with uncertain and dynamic environments. Keywords: constraint satisfaction problem, uncertainty, change, stability, robustness, flexibility
Efficient solving of quantified inequality constraints over the real numbers
 ACM Transactions on Computational Logic
"... Let a quantified inequality constraint over the reals be a formula in the firstorder predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. Solving such constraints is an undecidable problem when allowing function symbols such sin or cos. In t ..."
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Cited by 31 (9 self)
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Let a quantified inequality constraint over the reals be a formula in the firstorder predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. Solving such constraints is an undecidable problem when allowing function symbols such sin or cos. In the paper we give an algorithm that terminates with a solution for all, except for very special, pathological inputs. We ensure the practical efficiency of this algorithm by employing constraint programming techniques. 1
QCSP made practical by virtue of restricted quantification
 In Manuela Veloso, editor, International Joint Conference on Artificial Intelligence
, 2007
"... The QCSP + language we introduce extends the framework of Quantified Constraint Satisfaction Problems (QCSPs) by enabling us to neatly express restricted quantifications via a chain of nested CSPs to be interpreted as alternately conjuncted and disjuncted. Restricted quantifiers turn out to be a con ..."
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Cited by 25 (2 self)
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The QCSP + language we introduce extends the framework of Quantified Constraint Satisfaction Problems (QCSPs) by enabling us to neatly express restricted quantifications via a chain of nested CSPs to be interpreted as alternately conjuncted and disjuncted. Restricted quantifiers turn out to be a convenient solution to the crippling modeling issues we encounter in QCSP and—surprisingly— they help to reuse propagation technology and to prune the search space. Our QCSP + solver—which also handles arithmetic and global constraints— exhibits stateoftheart performances. 1
Algorithms for quantified constraint satisfaction problems
 In Proceedings of CP2004
, 2004
"... Abstract. Many propagation and search algorithms have been developed for constraint satisfaction problems (CSPs). In a standard CSP all variables are existentially quantified. The CSP formalism can be extended to allow universally quantified variables, in which case the complexity of the basic reaso ..."
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Cited by 22 (2 self)
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Abstract. Many propagation and search algorithms have been developed for constraint satisfaction problems (CSPs). In a standard CSP all variables are existentially quantified. The CSP formalism can be extended to allow universally quantified variables, in which case the complexity of the basic reasoning tasks rises from NPcomplete to PSPACEcomplete. Such problems have, so far, been studied mainly in the context of quantified Boolean formulae. Little work has been done on problems with discrete nonBoolean domains. We attempt to fill this gap by extending propagation and search algorithms from standard CSPs to the quantified case. We also show how the notion of value interchangeability can be exploited to break symmetries and speed up search by orders of magnitude. Finally, we test experimentally the algorithms and methods proposed. 1
CSP properties for quantified constraints: Definitions and complexity
 In Proceedings 20th National Conference on Artificial Intelligence (AAAI 2005
, 2005
"... Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the simple, classical notion of solution inappropriate. As a consequence, even such essential CSP properties as consistency or s ..."
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Cited by 19 (3 self)
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Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the simple, classical notion of solution inappropriate. As a consequence, even such essential CSP properties as consistency or substitutability are not completely understood in the quantified case. In this paper, we show that most of the properties which are used by solvers for CSP can be generalized to Quantified CSP. We propose a systematic study of the relations which hold between these properties, as well as complexity results regarding the decision of these properties. Finally, and since these problems are typically intractable, we generalise the approach used in CSP and propose weakenings of these notions based on locality, which allow for a tractable, albeit incomplete detecting of these properties.
The Complexity of Constraint Satisfaction Games and QCSP
"... We study the complexity of twoperson constraint satisfaction games. An instance of such a game is given by a collection of constraints on overlapping sets of variables, and the two players alternately make moves assigning values from a finite domain to the variables in a specified order. The first ..."
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Cited by 18 (7 self)
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We study the complexity of twoperson constraint satisfaction games. An instance of such a game is given by a collection of constraints on overlapping sets of variables, and the two players alternately make moves assigning values from a finite domain to the variables in a specified order. The first player tries to satisfy all constraints, while the other tries to break at least one constraint; the goal is to decide whether the first player has a winning strategy. We show that such games can be conveniently represented by a logical form of quantified constraint satisfaction, where an instance is given by a firstorder sentence in which quantifiers alternate and the quantifierfree part is a conjunction of atomic formulas; the goal is to decide whether the sentence is true. While the problem of deciding such a game is PSPACEcomplete in general, by restricting the set of allowed constraint predicates, one can obtain infinite classes of constraint satisfaction games of lower complexity. We use the quantified constraint satisfaction framework to study how the complexity of deciding such a game depends on the parameter set of allowed predicates. With every predicate, one can associate certain predicatepreserving operations, called polymorphisms. We show that the complexity of our games is determined by the surjective polymorphisms of the constraint predicates. We illustrate how this result can be used by identifying the complexity of a wide variety of constraint satisfaction games.
QBFBased Formal Verification: Experience and Perspectives
 JSAT
"... The language of Quantified Boolean Formulas (QBF) has a lot of potential applications to Formal Verification (FV) tasks, as it captures many of these tasks in a natural and compact way. Practical experience has been disappointing though. When compared with contending approaches such as SAT, QBFbase ..."
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Cited by 17 (0 self)
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The language of Quantified Boolean Formulas (QBF) has a lot of potential applications to Formal Verification (FV) tasks, as it captures many of these tasks in a natural and compact way. Practical experience has been disappointing though. When compared with contending approaches such as SAT, QBFbased FV has invariably yielded unfavorable experimental results. This paper makes two contributions. We first provide an account of the status quo in QBFbased FV. We examine commonly adopted formalizations and the relative strengths of different decision procedures. In the second part of this paper, we investigate for the first time the relevance of some advanced QBF techniques to FV tasks. In particular, we describe the use and the benefits of restricted quantifiers, QBF certificates, alternative encodings for classical model checking problems, and encodings with free variables. These promising research perspectives seem to reverse the negative standing of QBF applied to FV, as confirmed by the experimental evidence we discuss. Experiments are conducted by extending the publicly available solver sKizzo in several ways, and they include the first case studies where QBF compares favorably to SAT, its traditional competitor. QBF turns out to be an order of magnitude faster than SAT in some tasks (e.g., automated design debugging of large circuits). Moreover, as the size of the problems grows, the SAT encodings result in excessive memory requirements leading to outofmemory conditions, while the more compact QBF encodings continue to be manageable and solvable.
Encoding Quantified CSPs as Quantified Boolean Formulae
 In Proceedings of ECAI2004
, 2004
"... Quantified Constraint Satisfaction Problems (QCSPs) are CSPs in which some variables are universally quantified. For each possible value of such variables, we have to find ways to set the remaining, existentially quantified, variables so that the constraints are all satisfied. Interest in this topic ..."
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Cited by 17 (1 self)
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Quantified Constraint Satisfaction Problems (QCSPs) are CSPs in which some variables are universally quantified. For each possible value of such variables, we have to find ways to set the remaining, existentially quantified, variables so that the constraints are all satisfied. Interest in this topic is increasing following recent advances in Quantified Boolean Formulae (QBFs), the analogous generalisation of satisfiability (SAT). We show that we can encode QCSPs as QBFs. We introduce a simple generalisation of the direct encoding of CSPs into SAT. We then introduce some adaptations of this encoding to make it effective in a QBF solver. We solve some QCSP test instances orders of magnitude faster than using a specialised QCSP solver, taking advantage of the more advanced state of the art in QBF solving. Our conclusions are twofold. First, there is considerably more subtlety required in encodings in QBF than in SAT. Second, in an area such as QCSP where algorithmic techniques are not yet highly developed, encodings into a better understood problem can give access to extremely advanced search methods with very little implementation effort.
Consistency and the Quantified Constraint Satisfaction Problem
, 2007
"... Constraint satisfaction is a very well studied and fundamental artificial intelligence technique. Various forms of knowledge can be represented with constraints, and reasoning techniques from disparate fields can be encapsulated within constraint reasoning algorithms. However, problems involving unc ..."
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Cited by 16 (1 self)
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Constraint satisfaction is a very well studied and fundamental artificial intelligence technique. Various forms of knowledge can be represented with constraints, and reasoning techniques from disparate fields can be encapsulated within constraint reasoning algorithms. However, problems involving uncertainty, or which have an adversarial nature (for example, games), are difficult to express and solve in the classical constraint satisfaction problem. This thesis is concerned with an extension to the classical problem: the Quantified Constraint Satisfaction Problem (QCSP). QCSP has recently attracted interest. In QCSP, quantifiers are allowed, facilitating the expression of uncertainty. I examine whether QCSP is a useful formalism. This divides into two questions: whether QCSP can be solved efficiently; and whether realistic problems can be represented in QCSP. In attempting to answer these questions, the main contributions of this thesis are the following: • the definition of two new notions of consistency; • four new constraint propagation algorithms (with eight variants in total), along with empirical evaluations;
Xml representation of constraint networks format
 XCSP 2.1. http://www.cril.univartois.fr/CPAI08/XCSP2_ 1Competition.pdf
, 2008
"... We propose a new extended format to represent constraint networks using XML. This format allows us to represent constraints defined either in extension or in intension. It also allows us to reference global constraints. Any instance of the problems CSP (Constraint Satisfaction Problem), QCSP (Quanti ..."
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Cited by 13 (1 self)
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We propose a new extended format to represent constraint networks using XML. This format allows us to represent constraints defined either in extension or in intension. It also allows us to reference global constraints. Any instance of the problems CSP (Constraint Satisfaction Problem), QCSP (Quantified CSP) and WCSP (Weighted CSP) can be represented using this format. A subset of this format will be used for the third international competition of CSP solvers which will be held during summer 2008 (deadline: