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QuickXplain: preferred explanations and relaxations for overconstrained problems
 In Proceedings of AAAI’04
, 2004
"... Overconstrained problems can have an exponential number of conflicts, which explain the failure, and an exponential number of relaxations, which restore the consistency. A user of an interactive application, however, desires explanations and relaxations containing the most important constraints. To ..."
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Cited by 118 (1 self)
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Overconstrained problems can have an exponential number of conflicts, which explain the failure, and an exponential number of relaxations, which restore the consistency. A user of an interactive application, however, desires explanations and relaxations containing the most important constraints. To address this need, we define preferred explanations and relaxations based on user preferences between constraints and we compute them by a generic method which works for arbitrary CP, SAT, or DL solvers. We significantly accelerate the basic method by a divideandconquer strategy and thus provide the technological basis for the explanation facility of a principal industrial constraint programming tool, which is, for example, used in numerous configuration applications.
Extracting MUCs from constraint networks
 In Proceedings of ECAI’06
, 2006
"... Abstract. We address the problem of extracting Minimal Unsatisfiable Cores (MUCs) from constraint networks. This computationally hard problem has a practical interest in many application domains such as configuration, planning, diagnosis, etc. Indeed, identifying one or several disjoint MUCs can hel ..."
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Cited by 17 (6 self)
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Abstract. We address the problem of extracting Minimal Unsatisfiable Cores (MUCs) from constraint networks. This computationally hard problem has a practical interest in many application domains such as configuration, planning, diagnosis, etc. Indeed, identifying one or several disjoint MUCs can help circumscribe different sources of inconsistency in order to repair a system. In this paper, we propose an original approach that involves performing successive runs of a complete backtracking search, using constraint weighting, in order to surround an inconsistent part of a network, before identifying all transition constraints belonging to a MUC using a dichotomic process. We show the effectiveness of this approach, both theoretically and experimentally. 1
Modelbased debugging using multiple abstract models
 In Proceedings of International Workshop on Automated and AnalysisDriven Debugging (AADEBUG’03
, 2003
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Coupling csp decomposition methods and diagnosis algorithms for treestructured systems
 In In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI
, 2003
"... Decomposition methods are used to convert general constraint satisfaction problems into an equivalent treestructured problem that can be solved more effectively. Recently, diagnosis algorithms for treestructured systems have been introduced, but the prerequisites of coupling these algorithms to the ..."
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Cited by 8 (2 self)
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Decomposition methods are used to convert general constraint satisfaction problems into an equivalent treestructured problem that can be solved more effectively. Recently, diagnosis algorithms for treestructured systems have been introduced, but the prerequisites of coupling these algorithms to the outcome of decomposition methods have not been analyzed in detail, thus limiting their diagnostic applicability. In this paper we generalize the TREE* algorithm and show how to use hypertree decomposition outcomes as input to the algorithm to compute the diagnoses of a general diagnosis problem. 1
Preferring maximum confirmation diagnoses
"... Models used for ModelBased Diagnosis usually assume that the inaccuracy of data is smaller than the precision with which the data is described. In some domains, however, this assumption is invalid. Observations may not be accurate or the behavior model of the system does not allow for accurate pred ..."
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Cited by 1 (0 self)
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Models used for ModelBased Diagnosis usually assume that the inaccuracy of data is smaller than the precision with which the data is described. In some domains, however, this assumption is invalid. Observations may not be accurate or the behavior model of the system does not allow for accurate predictions. Therefore, the accuracy of predictions, which is a function of the accuracy of the observed system inputs and the behavior model of the system, may differ from the accuracy of the observed system outputs. This paper investigates the consequences of using inaccurate values. The paper will show that traditional notions of preferred diagnoses such as abductive diagnosis and minimum consistencybased diagnosis are no longer suited if the available data has different accuracies. A new notion of preferred diagnoses, called maximum confirmation diagnoses, is introduced. 1
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"... aast sed urat avio s, w tem he diag he a dia iagnos d on t fers to is usua n easi data lues su d [9,10 ic prec activities by temporal constraints specifying lower and upper bounds on the temporal distance between two events. Fig. 1 gives an illustration. In order to apply ModelBased Diagnosis, the ..."
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aast sed urat avio s, w tem he diag he a dia iagnos d on t fers to is usua n easi data lues su d [9,10 ic prec activities by temporal constraints specifying lower and upper bounds on the temporal distance between two events. Fig. 1 gives an illustration. In order to apply ModelBased Diagnosis, the temporal constraints are viewed as behavioral constraints of sis. However, in order to apply abductive diagnoses, knowledge of how components of a system may fail is required. If only partial knowledge about the normal and abnormal behavior of components is available, a weaker form of abductive diagnosis, called maximuminformative diagnosis [17,18] can be used. A maximuminformative diagnosis tries to explain as many observed system outputs as possible. In all cases, unlikely diagnoses may be preferred if inaccurate values are used. To give an illustration of the problem with minimum/minimal diagnoses, consider a minimal diagnosis D that enables us to
A New Heuristicbased albeit Complete Method to Extract MUCs from Unsatisfiable CSPs
"... When a Constraint Satisfaction Problem (CSP) admits no solution, most current solvers express that the whole search space has been explored unsuccessfully but do not exhibit which constraints are actually contradicting one another and make the problem infeasible. In this paper, we improve a recent h ..."
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When a Constraint Satisfaction Problem (CSP) admits no solution, most current solvers express that the whole search space has been explored unsuccessfully but do not exhibit which constraints are actually contradicting one another and make the problem infeasible. In this paper, we improve a recent heuristicbased approach to compute infeasible minimal subparts of CSPs, also called Minimally Unsatisfiable Cores (MUCs). The approach is based on the heuristic exploitation of the number of times each constraint has been falsified during previous failed search steps. It appears to improve the performance of the initial technique, which was the most efficient one until now.
Journal on Satisfiability, Boolean Modeling and Computation 1 (2007) 147–167 Recording and Minimizing Nogoods from Restarts
, 2006
"... In this paper 1., nogood recording is investigated for CSP within the randomization and restart framework. Our goal is to avoid the same situations to occur from one run to the next ones. More precisely, nogoods are recorded when the current cutoff value is reached, i.e. before restarting the search ..."
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In this paper 1., nogood recording is investigated for CSP within the randomization and restart framework. Our goal is to avoid the same situations to occur from one run to the next ones. More precisely, nogoods are recorded when the current cutoff value is reached, i.e. before restarting the search algorithm. Such a set of nogoods is extracted from the last branch of the current search tree and exploited using the structure of watched literals originally proposed for SAT. We prove that the worstcase time complexity of extracting such nogoods at the end of each run is only O(n 2 d) where n is the number of variables of the constraint network and d the size of the greatest domain, whereas for any node of the search tree, the worstcase time complexity of exploiting these nogoods to enforce Generalized Arc Consistency (GAC) is O(nB) where B  denotes the number of recorded nogoods. As the number of nogoods recorded before each new run is bounded by the length of the last branch, the total number of recorded nogoods is polynomial in the number of restarts. Interestingly, we show that when the minimization of the nogoods is envisioned with respect to an inference operator φ, it is possible to directly identify some nogoods that cannot be minimized. For φ = AC (i.e. for MAC), the worstcase time complexity of extracting minimal nogoods is slightly increased to O(en 2 d 3) where e is the number of constraints of the network. Experimentation over a wide range of CSP instances using a generic stateoftheart CSP solver demonstrates the effectiveness of this approach. Recording nogoods (and in particular, minimal nogoods) from restarts significantly improves the robustness of the solver.
Revised (Day Month Year)
, 2012
"... When a Constraint Satisfaction Problem (CSP) admits no solution, it can be useful to pinpoint which constraints are actually contradicting one another and make the problem infeasible. In this paper, a recent heuristicbased approach to compute infeasible minimal subparts of discrete CSPs, also calle ..."
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When a Constraint Satisfaction Problem (CSP) admits no solution, it can be useful to pinpoint which constraints are actually contradicting one another and make the problem infeasible. In this paper, a recent heuristicbased approach to compute infeasible minimal subparts of discrete CSPs, also called Minimally Unsatisfiable Cores (MUCs), is improved. The approach is based on the heuristic exploitation of the number of times each constraint has been falsified during previous failed search steps. It appears to enhance the performance of the initial technique, which was the most efficient one until now.