Weakly Regular Relations and Applications

  • Sébastien Limet
  • Pierre Réty
  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2051)

Abstract

A new class of tree-tuple languages is introduced: the weakly regular relations. It is an extension of the regular case (regular relations) and a restriction of tree-tuple synchronized languages, that has all usual nice properties, except closure under complement. Two applications are presented: to unification modulo a rewrite system, and to one-step rewriting.

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References

  1. 1.
    A.C. Caron, F. Seynhaeve, S. Tison, and M. Tommasi. Deciding the Satisfiability of Quantifier Free Formulae on One-Step Rewriting. In Proceedings of 10th Conference RTA, Trento (Italy), volume 1631 of LNCS. Springer-Verlag, 1999.Google Scholar
  2. 2.
    H. Comon, M. Dauchet, R. Gilleron, D. Lugiez, S. Tison, and M. Tommasi. Tree Automata Techniques and Applications (TATA). http://l3ux02.univ-lille3.fr/tata.
  3. 3.
    L. Fribourg. SLOG: A Logic Programming Language Interpreter Based on Clausal Superposition and Rewriting. In proceedings IEEE Symposium on Logic Programming, pages 172–185, Boston, 1985.Google Scholar
  4. 4.
    V. Gouranton, P. Réty, and H. Seidl. Synchronized Tree Languages Revisited and New Applications. In Proceedings of FoSSaCs, volume to appear of LNCS. Springer-Verlag, 2001.Google Scholar
  5. 5.
    M. Hermann and R. Galbavý. Unification of Infinite Sets of Terms Schematized by Primal Grammars. Theoretical Computer Science, 176, 1997.Google Scholar
  6. 6.
    F. Jacquemard. Automates d’Arbres et Réécriture de Termes. Thèse de Doctorat d’Université, Université de Paris-sud, 1996. In French.Google Scholar
  7. 7.
    S. Limet and P. Réty. E-Unification by Means of Tree Tuple Synchronized Grammars. In Proceedings of 6th Colloquium on Trees in Algebra and Programming, volume 1214 of LNCS, pages 429–440. Springer-Verlag, 1997. Full version in DMTCS (http://dmtcs.loria.fr/), volume 1, pages 69–98, 1997.Google Scholar
  8. 8.
    S. Limet and P. Réty. A New Result about the Decidability of the Existential One-step Rewriting Theory. In Proceedings of 10th Conference on Rewriting Techniques and Applications, Trento (Italy), volume 1631 of LNCS. Springer-Verlag, 1999.Google Scholar
  9. 9.
    S. Limet, P. Réty, and H. Seidl. Weakly Regular Relations and Applications. Research Report RR-LIFO-00-17, LIFO, 2000. http://www.univ-orleans.fr/SCIENCES/LIFO/Members/rety/publications.html.
  10. 10.
    S. Limet and F. Saubion. On partial validation of logic programs. In M. Johnson, editor, proc of the 6th Conf. on Algebraic Methodology and Software Technology, Sydney (Australia), volume 1349 of LNCS, pages 365–379. Springer Verlag, 1997.CrossRefGoogle Scholar
  11. 11.
    S. Limet and F. Saubion. A general framework for R-unification. In C. Palamidessi, H. Glaser, and K. Meinke, editors, proc of PLILP-ALP’98, volume 1490 of LNCS, pages 266–281. Springer Verlag, 1998.Google Scholar
  12. 12.
    J. Marcinkowski. Undecidability of the First-order Theory of One-step Right Ground Rewriting. In Proceedings 8th Conference RTA, Sitges (Spain), volume 1232 of LNCS, pages 241–253. Springer-Verlag, 1997.Google Scholar
  13. 13.
    J. Niehren, M. Pinkal, and P. Ruhrberg. On Equality up-to Constraints over Finite Trees, Context Unification and One-step Rewriting. In W. Mc Cune, editor, Proc. of CADE’97, Townsville (Australia), volume 1249 of LNCS, pages 34–48, 1997.Google Scholar
  14. 14.
    P. Réty. Regular Sets of Descendants for Constructor-based Rewrite Systems. In Proceedings of the 6th international conference on Logic for Programming and Automated Reasoning (LPAR), Tbilisi (Republic of Georgia), Lecture Notes in Artificial Intelligence. Springer-Verlag, 1999.Google Scholar
  15. 15.
    F. Seynhaeve, M. Tommasi, and R. Treinen. Grid Structures and Undecidable Constraint Theories. In Proceedings of 6th Colloquium on Trees in Algebra and Programming, volume 1214 of LNCS, pages 357–368. Springer-Verlag, 1997.Google Scholar
  16. 16.
    R. Treinen. The First-order Theory of One-step Rewriting is Undecidable. Theoretical Computer Science, 208:179–190, 1998.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    S. Vorobyov. The First-order Theory of One-step Rewriting in Linear Noetherian Systems is Undecidable. In Proceedings 8th Conference RTA, Sitges (Spain), volume 1232 of LNCS, pages 241–253. Springer-Verlag, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Sébastien Limet
    • 1
  • Pierre Réty
    • 1
  • Helmut Seidl
    • 2
  1. 1.LIFOUniversité d’OrléansFrance
  2. 2.Dept. of Computer ScienceUniversity of TrierGermany

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