Skip to main content
SpringerLink
Log in

Homomorphisms and concurrent term rewriting

  • Conference paper
  • First Online:
Book cover Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

Included in the following conference series:

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.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Arnold and M. Dauchet. Morphismes et bimorphismes d’arbres. Theorical Computer Science, 20:33–93, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  2. 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.

    Chapter  Google 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. 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.

    Article  MATH  Google Scholar 

  5. M. Dauchet, A.-C. Caron, and J.-L. Coquidè. Reduction properties and auto-mata with constraints. Journal of Symbolic Computation, 20:215–233, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  6. 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. J. Engelfriet. Bottom-up and top-down tree transformations. a comparision. Mathematical System Theory, 9:198–231, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  8. 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. J. Engelfriet and E.M. Schmidt. IO and OI I. Journal of Comput. and Syst. Sci., 15:328–353, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Engelfriet and E.M. Schmidt. IO and OI II. Journal of Comput. and Syst. Sci., 16:67–99, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  11. 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.

    Chapter  Google Scholar 

  12. T. Genet. Decidable approximations of sets of descendants and sets of normal forms. In Nipkow [Nip98], pages 151–165.

    Chapter  Google Scholar 

  13. F. Gècseg and M. Steinby. Tree Automata. Akademiai Kiado, 1984.

    Google Scholar 

  14. F. Jacquemard. Automates d'arbres et rèècriture de termes. PhD thesis, Universitè de Paris XI, 1996.

    Google Scholar 

  15. 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. 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. K. Salomaa. Deterministic tree pushdown automata and monadic tree rewrit-ing systems. Journal of Comput. and Syst. Sci., 37:367–394, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. Waldmann. Normalization of s-terms is decidable. In Nipkow [Nip98], pages 138–150.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIFL, Bât M3, Universitè Lille 1, F59655, Villeneuve d’Ascq cedex, France

    Franck Seynhaeve, Sophie Tison & Marc Tommasi

Authors
  1. Franck Seynhaeve
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sophie Tison
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marc Tommasi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Seynhaeve, F., Tison, S., Tommasi, M. (1999). Homomorphisms and concurrent term rewriting. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_40

Download citation

  • DOI: https://doi.org/10.1007/3-540-48321-7_40

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation