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388
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 110 (19 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.
Building decision procedures for modal logics from propositional decision procedures  The case study of modal K(m)
, 1996
"... The goal of this paper is to propose a new technique for developing decision procedures for propositional modal logics. The basic idea is that propositional modal decision procedures should be developed on top of propositional decision procedures. As a case study, we consider satisfiability in m ..."
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Cited by 98 (29 self)
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The goal of this paper is to propose a new technique for developing decision procedures for propositional modal logics. The basic idea is that propositional modal decision procedures should be developed on top of propositional decision procedures. As a case study, we consider satisfiability in modal K(m), that is modal K with m modalities, and develop an algorithm, called Ksat, on top of an implementation of the DavisPutnamLongemannLoveland procedure. Ksat is thoroughly tested and compared with various procedures and in particular with the stateoftheart tableaubased system Kris. The experimental results show that Ksat outperforms Kris and the other systems of orders of magnitude, highlight an intrinsic weakness of tableaubased decision procedures, and provide partial evidence of a phase transition phenomenon for K(m).
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 96 (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
On the conversion between nonbinary and binary constraint satisfaction problems
, 1998
"... It is well known that any nonbinary discrete constraint satisfaction problem (CSP) can be translated into an equivalent binary CSP. Two translations are known: the dual graph translation and the hidden variable translation. However, there has been little theoretical or experimental work on how well ..."
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Cited by 95 (6 self)
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It is well known that any nonbinary discrete constraint satisfaction problem (CSP) can be translated into an equivalent binary CSP. Two translations are known: the dual graph translation and the hidden variable translation. However, there has been little theoretical or experimental work on how well backtracking algorithms perform on these binary representations in comparison to their performance on the corresponding nonbinary CSP. We present both theoretical and empirical results to help understand the tradeoffs involved. In particular, we show that translating a nonbinary CSP into a binary representation can be a viable solution technique in certain circumstances. The ultimate aim of this research is to give guidance for when one should consider translating between nonbinary and binary representations. Our results supply some initial answers to this question.
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 86 (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...
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 85 (3 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.
Efficient solving of large nonlinear arithmetic constraint systems with complex boolean structure
 Journal on Satisfiability, Boolean Modeling and Computation
, 2007
"... In order to facilitate automated reasoning about large Boolean combinations of nonlinear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with intervalbased arithmetic constraint solving. Our approach deviates substantially f ..."
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Cited by 85 (11 self)
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In order to facilitate automated reasoning about large Boolean combinations of nonlinear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with intervalbased arithmetic constraint solving. Our approach deviates substantially from lazy theorem proving approaches in that it directly controls arithmetic constraint propagation from the SAT solver rather than delegating arithmetic decisions to a subordinate solver. Through this tight integration, all the algorithmic enhancements that were instrumental to the enormous performance gains recently achieved in propositional SAT solving carry over smoothly to the rich domain of nonlinear arithmetic constraints. As a consequence, our approach is able to handle large constraint systems with extremely complex Boolean structure, involving Boolean combinations of multiple thousand arithmetic constraints over some thousands of variables.
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 81 (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.
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 80 (6 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.
Conflictdirected A* and Its Role in Modelbased Embedded Systems
 Journal of Discrete Applied Mathematics
, 2003
"... Artificial intelligence has traditionally used constraint satisfaction and logic to frame a wide range of problems, including planning, diagnosis, cognitive robotics and embedded systems control. However, many decision making problems are now being reframed as optimization problems, involving a sea ..."
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Cited by 77 (27 self)
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Artificial intelligence has traditionally used constraint satisfaction and logic to frame a wide range of problems, including planning, diagnosis, cognitive robotics and embedded systems control. However, many decision making problems are now being reframed as optimization problems, involving a search over a discrete space for the best solution that satisfies a set of constraints. The best methods for finding optimal solutions, such as A*, explore the space of solutions one state at a time. This paper introduces conflictdirected A*, a method for solving optimal constraint satisfaction problems. Conflictdirected A* searches the state space in best first order, but accelerates the search process by eliminating subspaces around each state that are inconsistent. This elimination process builds upon the concepts of conflict and kernel diagnosis used in modelbased diagnosis[1,2] and in dependencydirected search[36]. Conflictdirected A* is a fundamental tool for building modelbased embedded systems, and has been used to solve a range of problems, including fault isolation[1], diagnosis[7], mode estimation and repair[8], modelcompilation[9] and modelbased programming[10].