Chemical equilibrium systems as numerical test problems
ACM Transactions on Mathematical Software (TOMS)
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Intelligent camera control for graphical environments
Intelligent camera control for graphical environments
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
Interval Constraint Logic Programming
Selected Papers from Constraint Programming: Basics and Trends
Extending the constraint propagation of intervals
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Extending consistent domains of numeric CSP
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Approximation Techniques for Non-linear Problems with Continuum of Solutions
Proceedings of the 5th International Symposium on Abstraction, Reformulation and Approximation
Search Techniques for Non-linear Constraint Satisfaction Problems with Inequalities
AI '01 Proceedings of the 14th Biennial Conference of the Canadian Society on Computational Studies of Intelligence: Advances in Artificial Intelligence
Beyond NP: Arc-Consistency for Quantified Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Modeling Camera Control with Constrained Hypertubes
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Continuous First-Order Constraint Satisfactionwith Equality and Disequality Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
On Constraint Problems with Incompleteor Erroneous Data
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Continuous First-Order Constraint Satisfaction
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
Satisfiability solving and model generation for quantified first-order logic formulas
FoVeOOS'10 Proceedings of the 2010 international conference on Formal verification of object-oriented software
Solving CSP including a universal quantification
MOZ'04 Proceedings of the Second international conference on Multiparadigm Programming in Mozart/Oz
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
Combining CSP and constraint-based mining for pattern discovery
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
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Non-linear 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 quantifier-free 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 inner-approximation of real relations. Algorithms for solving non-linear real constraint systems with universally quantified variables are then presented along with the theoretical framework on inner-approximation of relations supporting them. These algorithms are based on the computation of outer-approximations of the solution set of the negation of involved constraints. An application to the devising of a declarative modeller for expressing camera motion using a cinematic language is sketched, and results from a prototype are presented.