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106
HENTENRYCK: Helios: A modeling language for global optimization and its implementation in Newton
 Theoretical Computer Science
, 1997
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Practical Applications of Constraint Programming
 CONSTRAINTS
, 1996
"... Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples, ..."
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Cited by 109 (1 self)
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Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples,
Universally Quantified Interval Constraints
 PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 2000
"... Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decompo ..."
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Cited by 51 (0 self)
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Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decomposition (CAD). However, CAD restricts its input to be conjunctions and disjunctions of polynomial constraints with rational coefficients, while some applications such as camera control involve systems with arbitrary forms where time is the only universally quantified variable. In this paper, the handling of universally quantified variables is first related to the computation of innerapproximation of real relations.
Heterogeneous Constraint Solving
 PROCEEDINGS OF ALP'96, VOLUME 1139 OF LNCS
, 1996
"... Most CLP languages designed in the past few years feature at least some combination of constraint solving capabilities. These combinations can take multiple forms since they achieve either the mixing of di erent domains or the use of di erent algorithms over the same domain. These solvers are also v ..."
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Cited by 48 (10 self)
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Most CLP languages designed in the past few years feature at least some combination of constraint solving capabilities. These combinations can take multiple forms since they achieve either the mixing of di erent domains or the use of di erent algorithms over the same domain. These solvers are also very di erent in nature. Some of them perform complete constraint solving while others are based on propagation methods. This paper is an attempt to design a uni ed framework describing the cooperation of constraint solving methods. Most techniques used in constraintbased systems are shown to be implementations of operators called constraint narrowing operators. A generalized notion of arcconsistency, called weak arcconsistency is proposed and is used to model heterogeneous constraint solving. We provide conditions on the constraint solving algorithms which guarantee termination, correctness and con uence of the resulting combined solver. This framework is shown to be general enough to describe the operational semantics of the basic constraint solving mechanisms in a number of current CLP systems. 1
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 29 (8 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
Dynamic domain splitting for numeric CSPs
, 1998
"... In this paper, a new search technique over numeric csps is presented: dynamic domain splitting. The usual search technique over numeric csps is a dichotomic search interleaved with a consistency filtering, which is called domain splitting. This paper proposes to replace chronological backtracking ..."
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Cited by 26 (11 self)
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In this paper, a new search technique over numeric csps is presented: dynamic domain splitting. The usual search technique over numeric csps is a dichotomic search interleaved with a consistency filtering, which is called domain splitting. This paper proposes to replace chronological backtracking at the core of domain splitting by a non destructive backtracking technique.
Comparing Partial Consistencies
, 1999
"... Global search algorithms have been widely used in the constraint programming framework to solve constraint systems over continuous domains. This paper precisely states the relations among the different partial consistencies which are main emphasis of these algorithms. The ..."
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Cited by 23 (4 self)
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Global search algorithms have been widely used in the constraint programming framework to solve constraint systems over continuous domains. This paper precisely states the relations among the different partial consistencies which are main emphasis of these algorithms. The
A Constraint Satisfaction Approach to a Circuit Design Problem
, 1998
"... A classical circuitdesign problem from Ebers and Moll [6] features a system of nine nonlinear equations in nine variables that is very challenging both for local and global methods. This system was solved globally using an interval method by Ratschek and Rokne [23] in the box [0; 10] 9 . Their ..."
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Cited by 23 (1 self)
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A classical circuitdesign problem from Ebers and Moll [6] features a system of nine nonlinear equations in nine variables that is very challenging both for local and global methods. This system was solved globally using an interval method by Ratschek and Rokne [23] in the box [0; 10] 9 . Their algorithm had enormous costs (i.e., over 14 months using a network of 30 Sun Sparc1 workstations) but they state that "at this time, we know no other method which has been applied to this circuit design problem and which has led to the same guaranteed result of locating exactly one solution in this huge domain, completed with a reliable error estimate." The present paper gives a novel branchandprune algorithm that obtains a unique safe box for the above system within reasonable computation times. The algorithm combines traditional interval techniques with an adaptation of discrete constraintsatisfaction techniques to continuous problems. Of particular interest is the simplicity o...