POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Communications of the ACM
Constraint arithmetic on real intervals
Constraint logic programming
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Intelligent camera control for graphical environments
Intelligent camera control for graphical environments
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
A Constraint Satisfaction Approach to a Circuit Design Problem
Journal of Global Optimization
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An Algorithm to Compute Inner Approximations of Relations for Interval Constraints
PSI '99 Proceedings of the Third International Andrei Ershov Memorial Conference on Perspectives of System Informatics
Numerica: a modeling language for global optimization
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Extending the constraint propagation of intervals
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
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Reliably solving non-linear real constraints on computer is a challenging task due to the approximation induced by the resort to floating-point numbers. Interval constraints have consequently gained some interest from the scientific community since they are at the heart of complete algorithms that permit enclosing all solutions with an arbitrary accuracy. Yet, soundness is beyond reach of present-day interval constraint-based solvers, while it is sometimes a strong requirement. What is more, many applications involve constraint systems with some quantified variables these solvers are unable to handle. Basic facts on interval constraints and local consistency algorithms are first surveyed in this paper; then, symbolic and numerical methods used to compute inner approximations of real relations and to solve constraints with quantified variables are briefly presented, and directions for extending interval constraint techniques to solve these problems are pointed out.