The complexity of linear problems in fields
Journal of Symbolic Computation
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Guaranteed tuning, with application to robust control and motion planning
Automatica (Journal of IFAC)
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
Robust analysis and design of control systems using interval arithmetic
Automatica (Journal of IFAC)
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Quantified constraints under perturbation
Journal of Symbolic Computation
Constraint Programming: Basics and Trends: 1994 Chatillon Spring School, Chantillon-Sur-Seine, France, May 16-20, 1994: Selected Papers
The Versatility of Handling Disjunctions as Constraints
PLILP '93 Proceedings of the 5th International Symposium on Programming Language Implementation and Logic Programming
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Design, Implementation, and Evaluation of the Constraint Language cc(FD)
Selected Papers from Constraint Programming: Basics and Trends
Interval Constraint Logic Programming
Selected Papers from Constraint Programming: Basics and Trends
Universally Quantified Interval Constraints
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Solving Disjunctive Constraints for Interactive Graphical Applications
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
On the combinatorial and algebraic complexity of quantifier elimination
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Search Heuristics for Box Decomposition Methods
Journal of Global Optimization
Beyond NP: Arc-Consistency for Quantified Constraints
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
Automated test generation for engineering applications
Proceedings of the 20th IEEE/ACM international Conference on Automated software engineering
Efficient solving of quantified inequality constraints over the real numbers
ACM Transactions on Computational Logic (TOCL)
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
Language-based abstraction refinement for hybrid system verification
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
SIAM Journal on Control and Optimization
Safety verification of hybrid systems by constraint propagation based abstraction refinement
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
A robust interpretation of duration calculus
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Predicate abstraction of programs with non-linear computation
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Computing equilibria using interval constraints
CSCLP'04 Proceedings of the 2004 joint ERCIM/CoLOGNET international conference on Recent Advances in Constraints
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This paper shows how to use constraint programming techniques for solving first-order constraints over the reals (i.e., formulas in the first-order predicate language over the structure of the real numbers). More specifically, based on a narrowing operator that implements an arbitrary notion of consistency for atomic constraints over the reals (e.g., box-consistency), the paper provides a narrowing operator for first-order constraints that implements a corresponding notion of first-order consistency, and a solver based on such a narrowing operator. As a consequence, this solver can take over various favorable properties from the field of constraint programming.