Skip to main content
SpringerLink
Log in

On the Parallel Complexity of Tree Automata

  • Conference paper
  • First Online:
Rewriting Techniques and Applications (RTA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2051))

Included in the following conference series:

Abstract

We determine the parallel complexity of several (uniform) membership problems for recognizable tree languages. Furthermore we show that the word problem for a fixed finitely presented algebra is in DLOGTIME-uniform NC1.

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. D. A. M. Barrington and J. Corbet. On the relative complexity of some languages in NC1. Information Processing Letters, 32:251–256, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. A. M. Barrington, N. Immerman, and H. Straubing. On uniformity within NC1. Journal of Computer and System Sciences, 41:274–306, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Beaudry and P. McKenzie. Circuits, matrices, and nonassociative computation. Journal of Computer and System Sciences, 50(3):441–455, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Berman, A. Drisko, F. Lemieux, C. Moore, and D. Thérien. Circuits and expressions with non-associative gates. In Proceedings of the 12th Annual IEEE Conference on Computational Complexity, Ulm (Germany), pages 193–203. IEEE Computer Society Press, 1997.

    Google Scholar 

  5. S. R. Buss. The Boolean formula value problem is in ALOGTIME. In Proceedings of the 19th Annual Symposium on Theory of Computing (STOC 87), pages 123–131. ACM Press, 1987.

    Google Scholar 

  6. S. R. Buss. Alogtime algorithms for tree isomorphism, comparison, and canonization. In Kurt Gödel Colloquium 97, pages 18–33, 1997.

    Google Scholar 

  7. 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.

  8. S. A. Cook and P. McKenzie. Problems complete for deterministic logarithmic space. Journal of Algorithms, 8:385–394, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Dauchet and S. Tison. The theory of ground rewrite systems is decidable. In Proceedings of the 5th Annual IEEE Symposium on Logic in Computer Science (LICS’ 90), pages 242–256. IEEE Computer Society Press, 1990.

    Google Scholar 

  10. N. Dershowitz and J.-P. Jouannaud. Rewriting systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 243–320. Elsevier Publishers, Amsterdam, 1990.

    Google Scholar 

  11. J. E. Doner. Decidability of the weak second-order theory of two successors. Notices Amer. Math. Soc., 12:365–468, 1965.

    Google Scholar 

  12. J. E. Doner. Tree acceptors and some of their applications. Journal of Computer and System Sciences, 4:406–451, 1970.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. Engelfriet and H. J. Hoogeboom. Tree-walking pebble automata. In J. Karhumäki, H. Maurer, G. Paun, and G. Rozenberg, editors, Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa, pages 72–83. Springer, 1999.

    Google Scholar 

  14. F. Gécseg and M. Steinby. Tree automata. Akadémiai Kiadó, 1984.

    Google Scholar 

  15. G. Gottlob, N. Leone, and F. Scarcello. The complexity of acyclic conjunctive queries. In Proceedings of the 39th Annual Symposium on Foundations of Computer Science (FOCS 98, Palo Alto, California, USA), pages 706–715. IEEE Computer Society Press, 1998.

    Google Scholar 

  16. S. Greibach. The hardest context-free language. SIAM Journal on Computing, 2(4):304–310, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  17. M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, 1978.

    Google Scholar 

  18. M. Holzer and K.-J. Lange. On the complexities of linear LL(1) and LR(1) grammars. In Z. Ésik, editor, Proceedings of the 9th International Symposium on Fundamentals of Computation Theory (FCT’93, Szeged, Hungary), number 710 in Lecture Notes in Computer Science, pages 299–308. Springer, 1993.

    Google Scholar 

  19. B. Jenner, P. McKenzie, and J. Torán. A note on the hardness of tree isomorphism. In Proceedings of the 13th Annual IEEE Conference on Computational Complexity, pages 101–105. IEEE Computer Society Press, 1998.

    Google Scholar 

  20. N. D. Jones. Space-bounded reducibility among combinatorial problems. Journal of Computer and System Sciences, 11(1):68–85, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  21. D. C. Kozen. Complexity of finitely presented algebras. In 9th Annual Symposium on Theory of Computing (STOC 77), pages 164–177. ACM Press, 1977.

    Google Scholar 

  22. R. McNaughton. Parenthesis grammars. Journal of the Association for Computing Machinery, 14(3):490–500, 1967.

    MATH  MathSciNet  Google Scholar 

  23. C. H. Papadimitriou. Computational Complexity. Addison Wesley, 1994.

    Google Scholar 

  24. W. L. Ruzzo. Tree-size bounded alternation. Journal of Computer and System Sciences, 21:218–235, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  25. W. L. Ruzzo. On uniform circuit complexity. Journal of Computer and System Sciences, 22:365–383, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  26. I. H. Sudborough. On the tape complexity of deterministic context-free languages. Journal of the Association for Computing Machinery, 25(3):405–414, 1978.

    MATH  MathSciNet  Google Scholar 

  27. J. W. Thatcher and J. B. Wright. Generalized finite automata with an application to a decision problem of second order logic. Mathematical Systems Theory, 2:57–82, 1968.

    Article  MathSciNet  Google Scholar 

  28. M. Veanes. On computational complexity of basic decision problems of finite tree automata. Technical Report 133, Uppsala Computing Science Department, 1997.

    Google Scholar 

  29. H. Venkateswaran. Properties that characterize LOGCFL. Journal of Computer and System Sciences, 43:380–404, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  30. H. Vollmer. Introduction to Circuit Complexity. Springer, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Stuttgart, Breitwiesenstr. 20-22, 70565, Stuttgart, Germany

    Markus Lohrey

Authors
  1. Markus Lohrey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, 305-8573, Japan

    Aart Middeldorp

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lohrey, M. (2001). On the Parallel Complexity of Tree Automata. In: Middeldorp, A. (eds) Rewriting Techniques and Applications. RTA 2001. Lecture Notes in Computer Science, vol 2051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45127-7_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-45127-7_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42117-7

  • Online ISBN: 978-3-540-45127-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation