Abstract
We report on a new way of handling non-linear arithmetic constraints and its implementation into the QUAD-CLP(R) language. Important properties of the problem at hand are a discretization through geometric equivalence classes and decomposition into convex pieces. A case analysis of those equivalence classes leads to a relaxation (and sometimes recasting) of the original constraints into linear constraints, much easier to handle. Complementing earlier expositions in [18] and [19], the present focus is on applications upholding its worth.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Colmerauer. Prolog II Reference Manual and Theoretical Model. Rep. groupe d'intelligence artificielle, Université d'Aix-Marseille II, Luminy, October 1982.
S. Donikian and G. Hégron. Constraint Management in a Declarative Design Method for 3D Scene Sketch Modeling. In P. Kanellakis, J.-L. Lassez, C. Lau, V. Saraswat, R. Wachter, and D. Wagner, editors, PPCP'93, Newport, RI, April 1993.
T. Dubé and C.-K. Yap. The Geometry in Constraint Logic Programs. In P. Kanellakis, J.-L. Lassez, C. Lau, V. Saraswat, R. Wachter, and D. Wagner, editors, PPCP'93, Newport, RI, April 1993.
M. Gleicher. Practical Issues in Graphical Constraints. In P. Kanellakis, J.-L. Lassez, C. Lau, V. Saraswat, R. Wachter, and D. Wagner, editors, PPCP'93, Newport, RI, April 1993.
N. Heintze, S. Michaylov, and P. J. Stuckey. CLP(ℜ) and Some Electrical Engineering Problems. In J.-L. Lassez, editor, Proceedings of the 4th International Conference on Logic Programming, pages 675–703, Melbourne, May 1987. MIT Press.
C.M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, Inc., 1989.
H. Hong. Non-linear Constraints Solving over Real Numbers in Constraint Logic Programming (Introducing RISC-CLP). Technical Report 92-16, RISC-Link, January 1992.
J.-L. Imbert. Simplification des systèmes de contraintes numériques linéaires. PhD thesis, Faculté des Sciences de Luminy, Université Aix-Marseilles II, 1989.
J. Jaffar, S. Michaylov, P. J. Stuckey, and R. H. C. Yap. The CLP(ℜ) Language and System. ACM Transactions on Programming Languages and Systems, 14(3):339–395, July 1992.
J. Jaffar, S. Michaylov, and R. H. C. Yap. A Methodology for Managing Hard Constraints in CLP Systems. ACM SIGPLAN-PLDI, 26(6):306–316, 1991.
G. Kuper. Aggregation in Constraint Databases. In P. Kanellakis, J.-L. Lassez, C. Lau, V. Saraswat, R. Wachter, and D. Wagner, editors, PPCP'93, Newport, RI, April 1993.
C. Lassez and J.-L. Lassez. Quantifier Elimination for Conjunctions of Linear Constraints via a Convex Hull Algorithm. IBM Research Report, IBM T.J. Watson Research Center, 1991.
J.-L. Lassez, T. Huynh, and K. McAloon. Simplification and Elimination of Redundant Linear Arithmetic Constraints. In Proceedings of NA CLP 89, pages 37–51. MIT Press, 1989.
F. Major, M. Turcotte, D. Gautheret, G. Lapalme, E. Fillion, and R. Cedergren. The combination of symbolic and numerical computation for three-dimensional modeling of RNA. Science, 253, September 1991.
B. A. Nadel, X. Wu, and D. Kagan. Multiple abstraction levels in automobile transmission design: constraint satisfaction formulations and implementations. Int. J. Expert Systems: Research and Applications. (to appear).
W. Older and A. Vellino. Constraint Arithmetic on Real Intervals. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993.
G. Pesant and M. Boyer. Linear Approximations of Quadratic Constraints, (submitted for publication).
G. Pesant and M. Boyer. A Geometric Approach to Quadratic Constraints in Constraint Logic Programming. In F. Benhamou, A. Colmerauer, and G. Smolka, editors, Third Workshop on Constraint Logic Programming, Marseilles, France, March 1993.
G. Pesant and M. Boyer. Handling Quadratic Constraints Through Geometry. In D. Miller, editor, International Logic Programming Symposium, Vancouver, Canada, October 1993. MIT Press.
K. Sakai and A. Aiba. CAL: A Theoretical Background of Constraint Logic Programming and its Applications. Journal of Symbolic Computation, 8:589–603, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pesant, G., Boyer, M. (1994). QUAD-CLP(R): Adding the power of quadratic constraints. In: Borning, A. (eds) Principles and Practice of Constraint Programming. PPCP 1994. Lecture Notes in Computer Science, vol 874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58601-6_93
Download citation
DOI: https://doi.org/10.1007/3-540-58601-6_93
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58601-2
Online ISBN: 978-3-540-49032-6
eBook Packages: Springer Book Archive