Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Artificial Intelligence
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A theory of diagnosis from first principles
Artificial Intelligence
Artificial Intelligence
The CLP( R ) language and system
ACM Transactions on Programming Languages and Systems (TOPLAS)
Readings in model-based diagnosis
Readings in model-based diagnosis
Diagnosis with behavioral modes
Readings in model-based diagnosis
Back to defaults: characterizing and computing diagnoses as coherent assumption sets
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Constraint logic programming: selected research
Constraint logic programming: selected research
On the handling of disequations in CLP over linear rational arithmetic
Constraint logic programming
Building problem solvers
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
Remote Agent: to boldly go where no AI system has gone before
Artificial Intelligence - Special issue: artificial intelligence 40 years later
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Diagnosing tree-structured systems
Artificial Intelligence
Consistency restoriation and explanations in dynamic CSPs----application to configuration
Artificial Intelligence
Compiling Knowledge into Decomposable Negation Normal Form
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Local Search with Constraint Propagation and Conflict-Based Heuristics
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
A Comparison of Structural CSP Decomposition Methods
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
SyDeR—System design for reusability
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Theory of Relational Databases
Theory of Relational Databases
Model-based diagnosis using structured system descriptions
Journal of Artificial Intelligence Research
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Model-based applications in engineering, such as configuration, diagnosis or interactive decision-support systems, require embedded constraint solvers with challenging capabilities. They do not only demand classical services as consistency checking and solving, but also the computation of minimal conflicts and explanations. Moreover, modelling engineered systems makes often use of expressive constraint languages, which mix continuous and discrete variable domains, linear and non-linear equations, inequalities, and even procedural constraints. A positive feature of typical engineered systems is, however, that their corresponding constraint models have a bounded and even relatively small density (induced width).We present here a relational framework for constraint solving $\mathbb{RCS}$ that has been specifically designed to address these requirements. $\mathbb{RCS}$ is based on problem decomposition and variable elimination, exploiting the low-density property. To analyse a set of constraints $\mathbb{RCS}$ builds a so-called aggregation tree by joining the input constraints and eliminating certain variables after every single join. The aggregation tree is used by a set of conceptually simple algorithms to incrementally check consistency, compute solutions, minimal conflicts and explanations. We also report experimental results obtained with a prototype implementation of this framework.