Skip to main content
SpringerLink
Log in

Solving linear constraints on finite domains through parsing

  • Constraints
  • Conference paper
  • First Online:
EPIA 91 (EPIA 1991)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 541))

Included in the following conference series:

  • 121 Accesses

Abstract

In this paper we present results from ongoing research which allows the use of parsing methods to solve a particular kind of constraints, namely linear constraints on finite domains. Solving this kind of constraints is equivalent to solving systems of linear Diophantine equations on a finite subset of the naturals. We associate, to such a system, a definite-clause grammar that can be used to enumerate its solutions, and define a class of grammars, the connected grammars, for which the set of successful derivations covers the set of non-negative solutions of the associated system. This definition is based on a study of cycles in context-free grammars using compiler construction concepts and techniques.

The research described in this paper was partially supported by Instituto Nacional de Investigação Científica.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alfred V. Aho, R. Sethi and J. D. Ullman, Compilers — Principles, Techniques and Tools. Addison-Wesley, 1986.

    Google Scholar 

  2. 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. Gordon Bradley, Algorithm and Bound for the Greatest Common Divisor of n Integers, Comm. ACM, 13(7), 1970.

    Google Scholar 

  4. 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 

  5. Jacques Cohen, Constraint Logic Programming Languages. Comm. ACM, 33(7), 1990.

    Google Scholar 

  6. Alain Colmerauer, Opening the Prolog III Universe. Byte, 12(9), 1987.

    Google Scholar 

  7. 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 

  8. Miguel Filgueiras, Systems of Linear Diophantine Equations and Logic Grammars, Centro de Informática da Universidade do Porto, 1990.

    Google Scholar 

  9. Miguel Filgueiras, Ana Paula Tomás, Relating Grammar Derivations and Systems of Linear Diophantine Equations. Centro de Informática da Universidade do Porto, 1990.

    Google Scholar 

  10. H. Greenberg, Integer Programming, Academic Press, 1971.

    Google Scholar 

  11. Thomas Guckenbiehl and A. Herold, Solving Linear Diophantine Equations. Memo SEKI-85-IV-KL, Universität Kaiserslautern, 1985.

    Google Scholar 

  12. Andrew Haas, A parsing algorithm for Unification Grammar. Computational Linguistics, 15(4), 1989.

    Google Scholar 

  13. John E. Hopcroft and J. D. Ullman, Formal Languages and Their Relation to Automata. Addison-Wesley, 1969.

    Google Scholar 

  14. Gérard Huet, An algorithm to generate the basis of solutions to homogeneous linear Diophantine equations. Information Processing Letters, 7(3), 1978.

    Google Scholar 

  15. 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 

  16. Joxan Jaffar and J.-L. Lassez, Constraint Logic Programming. In Proceedings of the 14th POPL Conference, 1987.

    Google Scholar 

  17. G. Mitra, D. B. C. Richards and K. Wolfenden, An improved algorithm for the solution of integer programs by the solution of associated Diophantine equations. R.I.R.O., 1970.

    Google Scholar 

  18. F. Pereira and D. H. D. Warren, Definite Clause Grammars for language analysis — a survey of the formalism and a comparison with Augmented Transition Networks. Artificial Intelligence, 13, 1980.

    Google Scholar 

  19. Loïc Pottier, Solutions Minimales des Systèmes Diophantiens Linéaires: Bornes et Algorithmes. Rapport de Recherche no. 1292, I.N.R.I.A., 1990.

    Google Scholar 

  20. A. P. Tomás and M. Filgueiras, A New Method for Solving Linear Constraints on the Natural Numbers. This volume.

    Google Scholar 

  21. 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 

  22. P. van Hentenryck, Constraint Satisfaction in Logic Programming, MIT Press, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro de Informática, Universidade do Porto, R. do Campo Alegre 823, 4100, Porto, Portugal

    Miguel Filgueiras & Ana Paula Tomás

Authors
  1. Miguel Filgueiras
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ana Paula Tomás
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Pedro Barahona Luís Moniz Pereira António Porto

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Filgueiras, M., Tomás, A.P. (1991). Solving linear constraints on finite domains through parsing. In: Barahona, P., Moniz Pereira, L., Porto, A. (eds) EPIA 91. EPIA 1991. Lecture Notes in Computer Science, vol 541. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54535-2_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-54535-2_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54535-4

  • Online ISBN: 978-3-540-38459-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation