Advertisement

Homomorphisms and concurrent term rewriting

  • Franck Seynhaeve
  • Sophie Tison
  • Marc Tommasi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)

Abstract

In this paper we study applications of relations based on rewrite systems to regular tree languages. For instance, we want to deal with decidability problems of the form “R el(L 1) ⊆ L 2” where L 1, L 2 are regular tree languages and R el can be either IO, OI, parallel, or one step rewriting for a given rewrite system. Our method somehow standardizes previous ones because it reveals conditions R el must fulfill to preserve recognizability for the language R el(L 1). Thanks to classes of recognizable languages wider than the regular one, we get some new results. We pursue this method to tackle the problem of computing the set of descendants of a regular tree language by a rewrite system.

Keywords

Normal Form Regular Language Inclusion Problem Ground Term Tree Automaton 
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. [AD82]
    A. Arnold and M. Dauchet. Morphismes et bimorphismes d’arbres. Theorical Computer Science, 20:33–93, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [BST99]
    B. Bogaert, F. Seynhaeve, and S. Tison. The recognizability problem for tree automata with comparisons between brothers. In W. Thomas, editor, Proceedings, Foundations of Software Science and Computation Structures, number 1578 in Lecture Notes in Computer Science, Amsterdam, 1999. Springer Verlag.CrossRefGoogle Scholar
  3. [CDG+97]_H. Comon, M. Dauchet, R. Gilleron,, F. Jacquemard, D. Lugiez, S. Tison, and M. Tommasi. Tree automata techniques and applications. Available on: http://www.grappa.univ-lille3.fr/tata, 1997.
  4. [CDGV94]
    J.L. Coquidè, M. Dauchet, R. Gilleron, and S. Vágvolgyi. Bottom-up tree push-down automata: Classification and connection with rewrite systems. Theorical Computer Science, 127:69–98, 1994.zbMATHCrossRefGoogle Scholar
  5. [DCC95]
    M. Dauchet, A.-C. Caron, and J.-L. Coquidè. Reduction properties and auto-mata with constraints. Journal of Symbolic Computation, 20:215–233, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [DT90]
    M. Dauchet and S. Tison. The theory of ground rewrite systems is decidable. In Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, pages 242–248. IEEE Computer Society Press, 1990.Google Scholar
  7. [Eng75]
    J. Engelfriet. Bottom-up and top-down tree transformations. a comparision. Mathematical System Theory, 9:198–231, 1975.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [Eng78]
    J. Engelfriet. A hierarchy of tree transducers. In Proceedings of the third Les Arbres en Algèbre et en Programmation, pages 103–106, Lille, 1978.Google Scholar
  9. [ES77]
    J. Engelfriet and E.M. Schmidt. IO and OI I. Journal of Comput. and Syst. Sci., 15:328–353, 1977.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [ES78]
    J. Engelfriet and E.M. Schmidt. IO and OI II. Journal of Comput. and Syst. Sci., 16:67–99, 1978.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [FJSV98]
    A. Fülöp, E. Jurvanen, M. Steinby, and S. Vágvölgy. On one-pass term rewriting. In L. Brim, J. Gruska, and J. Zlatusaksv, editors, Proceedings of Mathematical Foundations of Computer Science, volume 1450 of Lecture Notes in Computer Science, pages 248–256. Springer Verlag, 1998.CrossRefGoogle Scholar
  12. [Gen98]
    T. Genet. Decidable approximations of sets of descendants and sets of normal forms. In Nipkow [Nip98], pages 151–165.CrossRefGoogle Scholar
  13. [GS84]
    F. Gècseg and M. Steinby. Tree Automata. Akademiai Kiado, 1984.Google Scholar
  14. [Jac96a]
    F. Jacquemard. Automates d'arbres et rèècriture de termes. PhD thesis, Universitè de Paris XI, 1996.Google Scholar
  15. [Jac96b]
    F. Jacquemard. Decidable approximations of term rewriting systems. In H. Ganzinger, editor, Proceedings. Seventh International Conference on Rewriting Techniques and Applications, volume 1103 of Lecture Notes in Computer Science, 1996.Google Scholar
  16. [Nip98]
    T. Nipkow, editor. Proceedings. Ninth International Conference on Rewriting Techniques and Applications, volume 1379 of Lecture Notes in Computer Science, Tsukuba, 1998.Google Scholar
  17. [Sal88]
    K. Salomaa. Deterministic tree pushdown automata and monadic tree rewrit-ing systems. Journal of Comput. and Syst. Sci., 37:367–394, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [Wal98]
    J. Waldmann. Normalization of s-terms is decidable. In Nipkow [Nip98], pages 138–150.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Franck Seynhaeve
    • 1
  • Sophie Tison
    • 1
  • Marc Tommasi
    • 1
  1. 1.LIFLVilleneuve d’Ascq cedexFrance

Personalised recommendations