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362
The Model Evolution Calculus
, 2003
"... The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quanti ..."
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Cited by 87 (14 self)
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The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The recent FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the firstorder level without resorting to ground instantiations. FDPLL lifts to the firstorder case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful litfing of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, one of FDPLL's optimizations, and so has the potential of leading to much faster implementations.
Solution reuse in dynamic constraint satisfaction problems
 In Proceedings of the 12th National Conference on Artificial Intelligence
, 1994
"... Many AI problems can be modeled as constraint satisfaction problems (CSP), but many of them are actually dynamic: the set of constraints to consider evolves because of the environment, the user or other agents in the framework of a distributed system. In this context, computing a new solution from s ..."
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Cited by 86 (6 self)
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Many AI problems can be modeled as constraint satisfaction problems (CSP), but many of them are actually dynamic: the set of constraints to consider evolves because of the environment, the user or other agents in the framework of a distributed system. In this context, computing a new solution from scratch after each problem change is possible, but has two important drawbacks: inefficiency and instability of the successive solutions. In this paper, we propose a method for reusing any previous solution and producing a new one by local changes on the previous one. First we give the key idea and the corresponding algorithm. Then we establish
Lazy Satisfiability Modulo Theories
 Journal on Satisfiability, Boolean Modeling and Computation
, 2007
"... Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingl ..."
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Cited by 85 (34 self)
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Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingly important due to its applications in many domains in different communities, in particular in formal verification. An amount of papers with novel and very efficient techniques for SMT has been published in the last years, and some very efficient SMT tools are now available. Typical SMT (T) problems require testing the satisfiability of formulas which are Boolean combinations of atomic propositions and atomic expressions in T, so that heavy Boolean reasoning must be efficiently combined with expressive theoryspecific reasoning. The dominating approach to SMT (T), called lazy approach, is based on the integration of a SAT solver and of a decision procedure able to handle sets of atomic constraints in T (Tsolver), handling respectively the Boolean and the theoryspecific components of reasoning. Unfortunately, neither the problem of building an efficient SMT solver, nor even that of acquiring a comprehensive background knowledge in lazy SMT, is of simple solution. In this paper we present an extensive survey of SMT, with particular focus on the lazy approach. We survey, classify and analyze from a theoryindependent perspective the most effective techniques and optimizations which are of interest for lazy SMT and which have been proposed in various communities; we discuss their relative benefits and drawbacks; we provide some guidelines about their choice and usage; we also analyze the features for SAT solvers and Tsolvers which make them more suitable for an integration. The ultimate goals of this paper are to become a source of a common background knowledge and terminology for students and researchers in different areas, to provide a reference guide for developers of SMT tools, and to stimulate the crossfertilization of techniques and ideas among different communities.
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 78 (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.
A complexity analysis of spacebounded learning algorithms for the constraint satisfaction problem
 In Proceedings of the Thirteenth National Conference on Artificial Intelligence
, 1996
"... Learning during backtrack search is a spaceintensive process that records information (such as additional constraints) in order to avoid redundant work. In this paper, we analyze the effects of polynomialspacebounded learning on runtime complexity of backtrack search. One spacebounded learning sc ..."
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Cited by 77 (2 self)
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Learning during backtrack search is a spaceintensive process that records information (such as additional constraints) in order to avoid redundant work. In this paper, we analyze the effects of polynomialspacebounded learning on runtime complexity of backtrack search. One spacebounded learning scheme records only those constraints with limited size, and another records arbitrarily large constraints but deletes those that become irrelevant to the portion of the search space being explored. We find that relevancebounded learning allows better runtime bounds than sizebounded learning on structurally restricted constraint satisfaction problems. Even when restricted to linear space, our relevancebounded learning algorithm has runtime complexity near that of unrestricted (exponential spaceconsuming) learning schemes.
Backjumping for Quantified Boolean Logic Satisfiability
 ARTIFICIAL INTELLIGENCE
, 2001
"... The implementation of effective reasoning tools for deciding the satisfiability of Quantified Boolean Formulas (QBFs) is an important research issue in Artificial Intelligence. Many decision procedures have been proposed in the last few years, most of them based on the Davis, Logemann, Loveland ..."
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Cited by 76 (5 self)
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The implementation of effective reasoning tools for deciding the satisfiability of Quantified Boolean Formulas (QBFs) is an important research issue in Artificial Intelligence. Many decision procedures have been proposed in the last few years, most of them based on the Davis, Logemann, Loveland procedure (DLL) for propositional satisfiability (SAT). In this paper we show how it is possible to extend the conflictdirected backjumping schema for SAT to QBF: when applicable, it allows to jump over existentially quantified literals while backtracking. We introduce solutiondirected backjumping, which allows the same for universally quantified literals. Then, we show how it is possible to incorporate both conflictdirected and solutiondirected backjumping in a DLLbased decision procedure for QBF satisfiability. We also implement and test the procedure: The experimental analysis shows that, because of backjumping, significant speedups can be obtained. While there have been several proposals for backjumping in SAT, this is the first time as far as we know this idea has been proposed, implemented and experimented for QBFs.
An Empirical Study of Dynamic Variable Ordering Heuristics for the Constraint Satisfaction Problem
 In Proceedings of CP96
, 1996
"... . The constraint satisfaction community has developed a number of heuristics for variable ordering during backtracking search. For example, in conjunction with algorithms which check forwards, the FailFirst (FF) and Brelaz (Bz) heuristics are cheap to evaluate and are generally considered to be ver ..."
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Cited by 69 (15 self)
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. The constraint satisfaction community has developed a number of heuristics for variable ordering during backtracking search. For example, in conjunction with algorithms which check forwards, the FailFirst (FF) and Brelaz (Bz) heuristics are cheap to evaluate and are generally considered to be very effective. Recent work to understand phase transitions in NPcomplete problem classes enables us to compare such heuristics over a large range of different kinds of problems. Furthermore, we are now able to start to understand the reasons for the success, and therefore also the failure, of heuristics, and to introduce new heuristics which achieve the successes and avoid the failures. In this paper, we present a comparison of the Bz and FF heuristics in forward checking algorithms applied to randomlygenerated binary CSP's. We also introduce new and very general heuristics and present an extensive study of these. These new heuristics are usually as good as or better than Bz and FF, and we id...
QuickXPlain: Conflict Detection for Arbitrary Constraint Propagation Algorithms
, 2001
"... Existing conflict detection methods for CSP's such as [de Kleer, 1989; Ginsberg, 1993] cannot make use of powerful propagation which makes them unusable for complex realworld problems. On the other hand, powerful constraint propagation methods lack the ability to extract dependencies or confli ..."
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Cited by 68 (0 self)
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Existing conflict detection methods for CSP's such as [de Kleer, 1989; Ginsberg, 1993] cannot make use of powerful propagation which makes them unusable for complex realworld problems. On the other hand, powerful constraint propagation methods lack the ability to extract dependencies or conflicts, which makes them unusable for many advanced AI reasoning methods that require conflicts, as well as for interactive applications that require explanations. In this paper, we present a nonintrusive conflict detection algorithm called QUICKXPLAIN that tackles those problems. It can be applied to any propagation or inference algorithm as powerful as it may be. Our algorithm improves the efficiency of direct nonintrusive conflict detectors by recursively partitioning the problem into subproblems of half the size and by immediately skipping those subproblems that do not contain an element of the conflict. QUICKXPLAIN is used as explanation component of an advanced industrial constraintbased configuration tool.
Local Search With Constraint Propagation and ConflictBased Heuristics
, 2002
"... Search algorithms for solving CSP (Constraint Satisfaction Problems) usually fall into one of two main families: local search algorithms and systematic algorithms. Both families have their advantages. Designing hybrid approaches seems promising since those advantages may be combined into a single ap ..."
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Cited by 67 (17 self)
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Search algorithms for solving CSP (Constraint Satisfaction Problems) usually fall into one of two main families: local search algorithms and systematic algorithms. Both families have their advantages. Designing hybrid approaches seems promising since those advantages may be combined into a single approach. In this paper, we present a new hybrid technique. It performs a local search over partial assignments instead of complete assignments, and uses filtering techniques and conflictbased techniques to efficiently guide the search. This new technique benefits from both classical approaches: aprioripruning of the search space from filteringbased search and possible repair of early mistakes from local search. We focus on a specific version of this technique: tabu decisionrepair.Experiments done on openshop scheduling problems show that our approach competes well with the best highly specialized algorithms. 2002 Elsevier Science B.V. All rights reserved.
The PaLM system: explanationbased constraint programming
 In Proceedings of TRICS: Techniques foR Implementing Constraint programming Systems, a postconference workshop of CP 2000
, 2000
"... Explanationbased constraint programming is a new way of solving constraint problems: it allows to propagate constraints of the problem, learning from failure and from the solver (thanks to recording explanations) and finally allows to get rid of backtrackbased complete searches by allowing more fr ..."
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Cited by 63 (13 self)
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Explanationbased constraint programming is a new way of solving constraint problems: it allows to propagate constraints of the problem, learning from failure and from the solver (thanks to recording explanations) and finally allows to get rid of backtrackbased complete searches by allowing more free moves in the search space (while remaining complete). This paper presents the PaLM system, an implementation of an explanationbased constraint programming system in CHOCO a constraint programming layer on top of CLAIRE.