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Strong controllability of disjunctive temporal problems with uncertainty
 In Proc. CP
, 2007
"... Abstract. The Disjunctive Temporal Problem with Uncertainty (DTPU) is an extension of the Disjunctive Temporal Problem (DTP) that accounts for events not under the control of the executing agent. We investigate the semantics of DTPU constraints, refining the existing notion that they are simply disj ..."
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Abstract. The Disjunctive Temporal Problem with Uncertainty (DTPU) is an extension of the Disjunctive Temporal Problem (DTP) that accounts for events not under the control of the executing agent. We investigate the semantics of DTPU constraints, refining the existing notion that they are simply disjunctions of STPU constraints. We then develop the first sound and complete algorithm to determine whether Strong Controllability holds for a DTPU. We analyze the complexity of our algorithm with respect to the number of constraints in different classes, showing that, for several common subclasses of DTPUs, determining Strong Controllability has the same complexity as solving DTPs. 1
Repairbased methods for quantified CSPs
 In CP
, 2005
"... Abstract. The Quantified CSP (QCSP) is a generalization of the CSP which allows for universally quantified variables. For each possible sequence of assignments to such variables, we have to find a way to set the values of the remaining, existentially quantified, variables so that all the constraints ..."
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Abstract. The Quantified CSP (QCSP) is a generalization of the CSP which allows for universally quantified variables. For each possible sequence of assignments to such variables, we have to find a way to set the values of the remaining, existentially quantified, variables so that all the constraints are satisfied. Such problems arise in areas such as planning under uncertainty, model checking, and adversary game playing. QCSPs are starting to attract interest following the development of numerous efficient solvers for the closely related area of QBF. Two approaches have been studied so far; the encoding of QCSPs into QBF, and the generalization of wellknown search procedures for CSPs, like FC and MAC, to the quantified case. In this paper we introduce a new approach which utilizes repairbased techniques. We describe a framework for a QCSP solver in which complete and incomplete repairbased methods can be incorporated. We also evaluate such a solver that applies backtracking and local search methods based on the minconflicts heuristic. Experimental results demonstrate that even simple repairbased techniques can outperform the stateoftheart solver QCSPSolve. 1
Blocksolve: a BottomUp Approach for Solving Quantified CSPs
 In Proceedings of CP2006
, 2006
"... Abstract. Thanks to its extended expressiveness, the quantified constraint satisfaction problem (QCSP) can be used to model problems that are difficult to express in the standard CSP formalism. This is only recently that the constraint community got interested in QCSP and proposed algorithms to solv ..."
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Abstract. Thanks to its extended expressiveness, the quantified constraint satisfaction problem (QCSP) can be used to model problems that are difficult to express in the standard CSP formalism. This is only recently that the constraint community got interested in QCSP and proposed algorithms to solve it. In this paper we propose BlockSolve, an algorithm for solving QCSPs that factorizes computations made in branches of the search tree. Instead of following the order of the variables in the quantification sequence, our technique searches for combinations of values for existential variables at the bottom of the tree that will work for (several) values of universal variables earlier in the sequence. An experimental study shows the good performance of BlockSolve compared to a state of the art QCSP solver. 1
A solver for quantified Boolean and linear constraints
 In Proc. of Int. Symp. on Applied Computing (SAC). ACM
, 2007
"... We make a number of contributions to the understanding and practical resolution of quantified constraints. Unlike previous work in the CP literature that was essentially focused on constraints expressed as binary tables, we focus on Presburger Arithmetics, i.e., Boolean combinations of linear constr ..."
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We make a number of contributions to the understanding and practical resolution of quantified constraints. Unlike previous work in the CP literature that was essentially focused on constraints expressed as binary tables, we focus on Presburger Arithmetics, i.e., Boolean combinations of linear constraints. From a theoretical perspective, we clarify the problem of the treatment of universal quantifiers by proposing a “symmetric ” version of the notion of quantified consistency. This notion imposes to maintain two constraint stores, which will be used to reason on universal and existential variables, respectively. We then describe a branch & bound algorithm that integrates both forms of propagation. Its implementation is, to the best of our knowledge, the first CP solver for this class of quantified constraints. 1.
Solving Existentially Quantified Constraints with One Equality and Arbitrarily Many Inequalities
 In Proc. of CP’03, LNCS 2833
, 2003
"... This paper contains the first algorithm that can solve disjunctions of constraints of the form g1 . . . ..."
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This paper contains the first algorithm that can solve disjunctions of constraints of the form g1 . . .
Solution directed backjumping for QCSP
 In Proc. of Int. Conf. on Principles and Practice of Constraint Programming (CP
, 2007
"... Abstract. In this paper we present new techniques for improving backtracking based Quantified Constraint Satisfaction Problem (QCSP) solvers. QCSP is a generalization of CSP in which variables are either universally or existentially quantified and these quantifiers can be alternated in arbitrary way ..."
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Abstract. In this paper we present new techniques for improving backtracking based Quantified Constraint Satisfaction Problem (QCSP) solvers. QCSP is a generalization of CSP in which variables are either universally or existentially quantified and these quantifiers can be alternated in arbitrary ways. Our main new technique is solution directed backjumping (SBJ). In analogue to conflict directed backjumping, SBJ allows the solver to backtrack out of solved subtrees without having to find all of the distinct solutions normally required to validate the universal variables. Experiments with the solver QCSPSolve demonstrate that SBJ can improve its performance on random instances by orders of magnitude. In addition to this contribution, we demonstrate that performing varying levels of propagation for universal vs. existential variables can also be useful for enhancing performance. Finally, we discuss some techniques that are technically interesting but do not yet yield empirical improvements. 1
An Algebraic Graphical Model for Decision with Uncertainties, Feasibilities, and Utilities
, 2005
"... Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express “simple ” decision problems, while others are designed to take into account uncertainties, unfeasible decisions, ..."
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Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express “simple ” decision problems, while others are designed to take into account uncertainties, unfeasible decisions, and utilities. Even in a single formalism, several variants are often proposed to model different types of uncertainty (probability, possibility...) or utility (additive or not). In this article, we introduce an algebraic graphical model that encompasses a large number of such formalisms: (1) we first adapt previous structures from Friedman, Chu and Halpern for representing uncertainty, utility, and expected utility in order to deal with generic forms of sequential decision making; (2) on these structures, we then introduce composite graphical models that express information via variables linked by “local ” functions, thanks to conditional independence; (3) on these graphical models, we finally define a simple class of queries which can represent various scenarios in terms of observabilities and controllabilities. A natural decisiontree semantics for such queries is completed by an equivalent operational semantics, which induces generic algorithms. The proposed framework, called the PlausibilityFeasibilityUtility (PFU) framework, not only provides a better understanding of the links between existing formalisms, but it also covers yet unpublished frameworks (such as possibilistic influence diagrams) and unifies formalisms such as quantified boolean formulas and influence diagrams. Our backtrack and variable elimination generic algorithms are a first step towards unified algorithms. 1.
Realtime Online Solving of Quantified CSPs
 In Proceedings of CP
, 2009
"... Abstract. We define Realtime Online solving of Quantified Constraint Satisfaction Problems (QCSPs) as a model for realtime online CSP solving. We use a combination of propagation, lookahead and heuristics and show how all three improve performance. For adversarial opponents we show that we can achie ..."
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Abstract. We define Realtime Online solving of Quantified Constraint Satisfaction Problems (QCSPs) as a model for realtime online CSP solving. We use a combination of propagation, lookahead and heuristics and show how all three improve performance. For adversarial opponents we show that we can achieve promising results through good lookahead and heuristics and that a version of alpha beta pruning performs strongly. For random opponents, we show that we can frequently achieve solutions even on problems which lack a winning strategy and that we can improve our success rate by using Existential Quantified Generalised Arc Consistency, a lower level of consistency than SQGAC, to maximise pruning without removing solutions. We also consider the power of the universal opponent and show that through good heuristic selection we can generate a significantly stronger player than a static heuristic provides. 1
Value Ordering for Quantified CSPs
"... We investigate the use of value ordering in backtracking search for Quantified Constraint Satisfaction problems (QCSPs). We consider two approaches for ordering heuristics. The first approach is solutionfocused and is inspired by adversarial search: on existential variables we prefer values that ..."
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We investigate the use of value ordering in backtracking search for Quantified Constraint Satisfaction problems (QCSPs). We consider two approaches for ordering heuristics. The first approach is solutionfocused and is inspired by adversarial search: on existential variables we prefer values that maximise the chances of leading to a solution, while on universal variables we prefer values that minimise those chances. The second approach is verificationfocused, where we prefer values that are easier to verify whether or not they lead to a solution. In particular, we give instantiations of this approach using QCSPSolve’s purevalue rule [1]. We show that on dense 3block problems, using QCSPSolve, the solutionfocused adversarial heuristics are up to 50 % faster than lexicographic ordering, while on sparse loose interleaved problems, the verificationfocused purevalue heuristics are up to 50 % faster. Both types are up to 50 % faster on dense interleaved problems, with one purevalue heuristic approaching an order of magnitude improvement.
Strategic constraint satisfaction problems
 In Proc. of CP’06 Workshop on Modelling and Reformulation
, 2006
"... Abstract. The Quantified constraint satisfaction problem (QCSP) has been introduced to express situations in which we are not able to decide the value of some of the variables (the universal ones). Despite the expressiveness of QCSP, many problems, such as twoplayer games or motion planning of robo ..."
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Abstract. The Quantified constraint satisfaction problem (QCSP) has been introduced to express situations in which we are not able to decide the value of some of the variables (the universal ones). Despite the expressiveness of QCSP, many problems, such as twoplayer games or motion planning of robots, remain difficult to express. In this paper, we propose Strategic CSP, an extension of QCSP where universal variables adapt their domain to be compatible with previous choices. This new framework permits an easy encoding of many twoplayer games. We give examples of such encodings and provide a preliminary experimental evaluation. 1