Skip to main content
SpringerLink
Log in

Tree Automata and Term Rewrite Systems

(Extended Abstract)

  • Conference paper
Rewriting Techniques and Applications (RTA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1833))

Included in the following conference series:

Abstract

This tutorial is devoted to tree automata. We will present some of the most fruitful applications of tree automata in rewriting theory and we will give an outline of the current state of research on tree automata. We give here just a sketch of the presentation. The reader can also refer to the on-line book “Tree Automata and Their Applications” [CDG + 97].

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Brainerd, W.S.: Semi-thue systems and representations of trees. In: Proc. 10th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 240–244 (1969)

    Google Scholar 

  2. Brainerd, W.S.: Tree generating regular systems. Information and Control 14(2), 217–231 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  3. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (1997), Available on: http://l3ux02.univ-lille3.fr/tata

  4. Coquide, J.L., Dauchet, M., Gilleron, R., Vagvolgyi, S.: Bottom-up tree pushdown automata: Classification and connection with rewrite systems. Theorical Computer Science 127, 69–98 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Comon, H., Jacquemard, F.: Ground reducibility and automata with disequality constraints. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 151–162. Springer, Heidelberg (1994)

    Google Scholar 

  6. Comon, H., Jacquemard, F.: Ground reducibility is EXPTIMEcomplete. In: Proceedings, 12th Annual IEEE Symposium on Logic in Computer Science, pp. 26–34. IEEE Computer Society Press, Los Alamitos (1997)

    Google Scholar 

  7. Comon, H.: Sequentiality, second-order monadic logic and tree automata. In: Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science, pp. 26–29. IEEE Computer Society Press, Los Alamitos (1995)

    Google Scholar 

  8. Caron, A.-C., Seynhaeve, F., Tison, S., Tommasi, M.: Deciding the satisfiability of quantifier free formulae on one-step rewriting. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, p. 103. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  9. Dauchet, M.: Rewriting and tree automata. In: Comon, H., Jouannaud, J.-P. (eds.) Proc. Spring School on Theoretical Computer Science: Rewriting, Odeillo, France. LNCS. Springer, Heidelberg (1994)

    Google Scholar 

  10. Dauchet, M., Caron, A.-C., Coquidé, J.-L.: Reduction properties and automata with constraints. Journal of Symbolic Computation 20, 215–233 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dauchet, M., Tison, S.: The theory of ground rewrite systems is decidable. In: Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, pp. 242–248. IEEE Computer Society Press, Los Alamitos (1990)

    Chapter  Google Scholar 

  12. Flp, A., Jurvanen, E., Steinby, M., Vagvlgy, S.: On one-pass term rewriting. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 248–256. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  13. Genet, T.: Decidable approximations of sets of descendants and sets of normal forms. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 151–165. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Genet, T., Klay, F.: Rewriting for cryptographic protocol verification. Technical Report, INRIA, 2000, to appear in CADE2000 (2000)

    Google Scholar 

  15. Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 1–68. Springer, Heidelberg (1996)

    Google Scholar 

  16. Gilleron, R., Tison, S.: Regular tree languages and rewrite systems. Fundamenta Informaticae 24, 157–176 (1995)

    MATH  MathSciNet  Google Scholar 

  17. Jacquemard, F.: Decidable approximations of term rewriting systems. In: Ganzinger, H. (ed.) RTA 1996. LNCS, vol. 1103. Springer, Heidelberg (1996)

    Google Scholar 

  18. Kounalis, E.: Testing for the ground (co)-reducibility in term rewriting systems. Theorical Computer Science 106(1), 87–117 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  19. Limet, S., Réty, P.: Solving Disequations modulo some Class of Rewrite System. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 121–135. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  20. Limet, S., Réty, P.: A new result about the decidability of the existential one-step rewriting theory. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, p. 118. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  21. Nagaya, T., Toyama, Y.: Decidability for left-linear growing term rewriting systems. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, p. 256. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  22. Otto, F.: On the connections between rewriting and formal languauge theory. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 332–355. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  23. Plaisted, D.A.: Semantic confluence tests and completion method. Information and Control 65, 182–215 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  24. Salomaa, K.: Deterministic tree pushdown automata and monadic tree rewriting systems. Journal of Comput. and Syst. Sci. 37, 367–394 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  25. Seynhaeve, F., Tison, S., Tommasi, M.: Homomorphisms and concurrent term rewriting. In: Ciobanu, G., Păun, G. (eds.) FCT 1999. LNCS, vol. 1684, pp. 475–487. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  26. Vágvölgyi, S., Gilleron, R.: For a rewrite system it is decidable whether the set of irreducible ground terms is recognizable. Bulletin of the European Association of Theoretical Computer Science 48, 197–209 (1992)

    MATH  Google Scholar 

  27. Waldmann, J.: Normalization of s-terms is decidable. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 138–150. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Sophie Tison

Authors
  1. Sophie Tison
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Stony Brook University, Stony Brook, P.O. Box, New York

    Leo Bachmair

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tison, S. (2000). Tree Automata and Term Rewrite Systems. In: Bachmair, L. (eds) Rewriting Techniques and Applications. RTA 2000. Lecture Notes in Computer Science, vol 1833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721975_2

Download citation

  • DOI: https://doi.org/10.1007/10721975_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67778-9

  • Online ISBN: 978-3-540-44980-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation