A new method for solving linear constraints on the natural numbers

  • Ana Paula Tomás
  • Miguel Filgueiras
Constraints
Part of the Lecture Notes in Computer Science book series (LNCS, volume 541)

Abstract

In the recent past much attention has been given to the handling of constraints. The focus of this paper is solving linear constraints on the natural numbers, a problem that is also of great importance in AC-unification. We describe a new algorithm that is faster than the methods we compared it with, and that may well contradict the view that this kind of algorithms is too expensive to be of practical use, for instance in the implementation of Constraint Logic Programming languages.

Keywords

Linear Constraint Minimal Solution Diophantine Equation Finite Domain Linear Diophantine Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Abdulrab and Pécuchet 1989]
    Habib Abdulrab and J.-P. Pécuchet, Solving systems of linear Diophantine equations and word equations. In N. Dershowitz (ed.) Proceedings of the 3rd International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science, 355, Springer-Verlag, 530–532, 1986.Google Scholar
  2. [Boudet et al. 1990]
    Alexandre Boudet, E. Contejean and H. Devie, A new AC Unification algorithm with an algorithm for solving systems of Diophantine equations. In Proceedings of the 5th Conference on Logic and Computer Science, IEEE, 1990.Google Scholar
  3. [Chou and Collins 1982]
    Tsu-Wu J. Chou and G. E. Collins, Algorithms for the solution of systems of linear Diophantine equations. SIAM J. Comput., 11(4), 687–708, 1982.Google Scholar
  4. [Cohen 1990]
    Jacques Cohen, Constraint Logic Programming Languages. Comm. ACM, 33(7), 1990.Google Scholar
  5. [Colmerauer 1987]
    Alain Colmerauer, Opening the Prolog III Universe. Byte, 12(9), 1987.Google Scholar
  6. [Dincbas et al. 1988]
    M. Dincbas, P. van Hentenryck, H. Simonis, A. Aggoun, T. Graf, F. Berthier, The constraint Logic Programming language CHIP. In Proceedings of the International Conference on Fifth Generation Computer Systems, ICOT, 1988.Google Scholar
  7. [Filgueiras 1990]
    Miguel Filgueiras, Systems of Linear Diophantine Equations and Logic Grammars. Centro de Informática da Universidade do Porto, 1990.Google Scholar
  8. [Filgueiras and Tomás 1990]
    Miguel Filgueiras and A. P. Tomás, Relating Grammar Derivations and Systems of Linear Diophantine Equations. Centro de Informática da Universidade do Porto, 1990.Google Scholar
  9. [Filgueiras and Tomás 1991]
    Miguel Filgueiras and A. P. Tomás, Solving Linear Constraints on Finite Domains through Parsing. This volume.Google Scholar
  10. [Guckenbiehl and Herold 1985]
    Thomas Guckenbiehl and A. Herold, Solving Linear Diophantine Equations. Memo SEKI-85-IV-KL, Universität Kaiserslautern, 1985.Google Scholar
  11. [Huet 1978a]
    Gérard Huet, An algorithm to generate the basis of solutions to homogeneous linear Diophantine equations. Information Processing Letters, 7(3), 1978.Google Scholar
  12. [Huet 1978b]
    Gérard Huet, An Algorithm to Generate The Basis of Solutions to Homogeneous Linear Diophantine Equations. Rapport de Recherche no. 274, I.R.I.A., 1978.Google Scholar
  13. [Jaffar et al. 1986]
    Joxan Jaffar, J.-L. Lassez and M. Maher, Logic Programming language scheme. In D. DeGroot and G. Lindstrom (eds.), Logic Programming: Functions, Relations, and Equations, Prentice-Hall, 1986.Google Scholar
  14. [Jaffar and Lassez 1987]
    Joxan Jaffar and J.-L. Lassez, Constraint Logic Programming. In Proceedings of the 14th POPL Conference, 1987.Google Scholar
  15. [Lassez and McAloon 1989]
    Jean-Louis Lassez and K. McAloon, A Canonical Form for Generalized Linear Constraints. IBM Research Report, Yorktown Heights, 1989.Google Scholar
  16. [Pottier 1990]
    Loïc Pottier, Solutions Minimales des Systèmes Diophantiens Linéaires: Bornes et Algorithmes. Rapport de Recherche no. 1292, I.N.R.I.A., 1990.Google Scholar
  17. [Steele and Sussman 1982]
    G. Steele and G. Sussman, CONSTRAINTS — A constraint based programming language. Artificial Intelligence, 1982.Google Scholar
  18. [Stickel 1981]
    M. E. Stickel, A unification algorithm for associative-commutative functions. JACM, 28(3), 1981.Google Scholar
  19. [Tarjan 1980]
    Robert E. Tarjan, Recent Developments in The Complexity of Combinatorial Algorithms. Report No. STAN-CS-80-794, Stanford University, 1980.Google Scholar
  20. [Tomás and Filgueiras 1991]
    A. P. Tomás and M. Filgueiras, A Congruence-based Method for Finding the Basis of Solutions to Linear Diophantine Equations. Centro de Informática da Universidade do Porto, 1991.Google Scholar
  21. [van Hentenryck 1989]
    P. van Hentenryck, Constraint Satisfaction in Logic Programming, MIT Press, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Ana Paula Tomás
    • 1
  • Miguel Filgueiras
    • 1
  1. 1.Centro de InformáticaUniversidade do PortoPortoPortugal

Personalised recommendations