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Projecting CLPR constraints

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Abstract

The presentation of constraints in a usable form is an essential aspect of Constraint Logic Programming (CLP) systems. It is needed both in the output of constraints, as well as in the production of an internal representation of constraints for meta-level manipulation. Typically, only a small subset\(\tilde x\) of the variables in constraints is of interest, and so an informal statement of the problem at hand is: given a conjunction\(c(\tilde x,\tilde y)\) of constraints, express the projection\(\exists \tilde y c(\tilde x,\tilde y)\) ofc onto\(\tilde x\) in the simplest form.

In this paper, we consider the constraints of the CLP(R) system and describe the essential features of its projection module. One main part focuses on the well-known problem of projection inlinear arithmetic constraints. We start with a classical algorithm and augment it with a procedure for eliminating redundant constraints generated by the algorithm. A second part discusses projection of the other object-level constraints: equations over trees and nonlinear equations. The final part deals with producing a manipulable form of the constraints, which complicates the projection problem.

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References

  1. Černikov, S. N., “Contraction of Finite Systems of Linear Inequalities (In Russian),”Doklady Akademiia Nauk SSSR, 152, 5, pp. 1075–1078, 1963. (English translation inSoviet Mathematics Doklady, 4, 5, pp. 1520–1524, 1963.)

    Google Scholar 

  2. Collins, G. E., “Quantifier Elimination for Real Closed Fields: A Guide to the Literature,” inComputer Algebra: Symbolic and Algebraic Computation, Computing Supplement #4 (B. Buchberger, R. Loos and G. E. Collins eds.), Springer-Verlag, pp. 79–81, 1982.

  3. Duffin, R. J., “On Fourier’s Analysis of Linear Inequality Systems,”Mathematical Programming Study, 1, pp. 71–95, 1974.

    MathSciNet  Google Scholar 

  4. Fourier, J-B. J.,Histoire de l’Academie Royale des Sciences de l’Institut de France, 7, pp. xlvii-lv, 1827. Reported in: Analyse des travaux de l’Academie Royale des Sciences, pendant l’annee 1824, Partie mathematique, (Partial English translation in: Kohler, D. A., “Translation of a Report by Fourier on his work on Linear Inequalities,”Opsearch, 10, pp. 38–42, 1973.)

    Google Scholar 

  5. Heintze, N. C., Michaylov, S., Stuckey, P. J. and Yap, R., “Meta-Programming in CLP(R),” inProc. North American Conf. on Logic Programming, Cleveland, pp. 1–19, 1989. (Full version in:Technical Report, 92/14, Department of Computer Science, University of Melbourne, 1992).

  6. Huynh, T., Lassez, C. and Lassez, J-L., “Practical Issues on the Projection of Polyhedral Sets,”Annals of Mathematics and Artificial Intelligence 6, pp. 295–316, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  7. Jaffar, J. and Lassez, J-L., “Constraint Logic Programming,”Technical Report, 86/73, Dept. of Computer Science, Monash University, June 1986. (An abstract appears in:Proc. 14th Principles of Programming Languages, Munich, pp. 111–119, 1987).

  8. Jaffar, J., Michaylov, S., Stuckey, P. and Yap, R., “The CLP(R) Language and System,”ACM Transactions on Programming Languages, 14, 3, pp. 339–395, July 1992.

    Article  Google Scholar 

  9. Kohler, D. A., “Projections of Polyhedral Sets,”Ph. D. thesis, Technical Report, ORC-67-29, Operations Research Center, University of California at Berkeley, August 1967

  10. Lassez, J-L., Huynh, T. and McAloon, K., “Simplification and Elimination of Redundant Linear Arithmetic Constraints,” inProc. North American Conference on Logic Programming, Cleveland, pp. 35–51, 1989.

  11. Lassez, J-L. and McAloon, K., “Generalized Canonical Forms for Linear Constraints and Applications,” inProc. Int. Conf. on Fifth Generation Computer Systems, ICOT, Tokyo, pp. 703–710, 1988.

  12. Lassez, J-L. and Maher, M., “On Fourier’s Algorithm for Linear Arithmetic Constraints,”Journal of Automated Reasoning, 9, pp. 373–379, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  13. Paterson, M. S. and Wegman, M. N., “Linear Unification,”Journal of Computer and System Sciences, 16, 2, pp. 158–167, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  14. Tarski, A.,A Decision Method for Elementary Algebra and Geometry, University of California Press, Berkeley, USA, 1951.

    MATH  Google Scholar 

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Joxan Jaffar, Ph. D.: He received his Ph. D. from Monash University, was a lecturer there from 1982 to 1986, and since 1986 has been with the IBM T. J. Watson Research Center. He is currently a project leader at IBM, and the Area Editor for Theory, Journal of Logic Programming.

Michael Maher, Ph. D.: He received his Ph. D. in computer science from the University of Melbourne. He is currently a research staff member of the IBM T. J. Watson Research Center. His research interests involve constraint systems, logic programming and databases.

Peter J. Stuckey, Ph. D.: He has been a lecturer in Computer Science at the University of Melbourne since 1990. His research interests include logic programming, deductive databases and constraint programming. He is one of the authors of the constraint logic programming languages CLP(R). Peter holds a B. Sc(Hons) and Ph. D. in computer science from Monash University. He is a member of the Association of Logic Programming.

Roland H. C. Yap, Ph. D.: He is a researcher at the University of Melbourne. He is currently finishing a Ph. D. at Monash University. His research interests include constraints, logic programming, programming languages, compilers and computational molecular biology.

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Jaffar, J., Maher, M.J., Stuckey, P.J. et al. Projecting CLPR constraints. New Gener Comput 11, 449–469 (1993). https://doi.org/10.1007/BF03037187

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  • DOI: https://doi.org/10.1007/BF03037187

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